THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING MEASUREMENT OF DYNAMIC SURFACE TENSION CHANGES IN FROTH-FORMING AQUEOUS SOLUTIONS Robert J. Van Duyne A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1961 October, 1961 IP- 537

ACKNOWLEDGMENTS The author wishes to express his appreciation to the members of his doctoral committee for their advice and cooperation. Special thanks are due to Professor Kenneth F. Gordon, chairman of the committee, for his unselfish contribution of time, counsel and encouragement throughout the course of the study, and to Professor G. Brymer Williams for his interest and advice. Grateful acknowledgement is also made to the following individuals and organizations: Messrs. Cleatis Bolen and William Hines, for their help in constructing the equipment. Mr. Frank Drogosz, who gave invaluable advice and assistance in designing and building the oscillating jet apparatus. Professor L. V. Colwell and the Industrial Engineering Department, for the use of the LVDT and "Dyna-Myke" measuring equipment, Mrs. Madelaine Ingerson, for her cheerful assistance with clerical details, as well as her personal friendship. The University of Michigan Computing Center, for making available many hours of IBM 704 computer time, and for the helpful advice and assistance offered by its staff members. The General Motors Research Staff, Data Processing Group, who provided much of the early computing time, ii

The American Institute of Chemical Engineers, whose Plate Efficiency Research Program provided financial assistance for several semesters, as well as supplying the inspiration for this study. The Monsanto Chemical Company, for the financial assistance afforded by their fellowship awarded for two semesters. My wife Shirley, for her remarkable patience, uncomplaining sacrifices, and her invaluable assistance in preparing the manuscript. iii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS. e.. o o..... o, e,,........... o............. ii LIST OF TABLES..................................................... oiv LIST OF FIGUREE S.............................................. ii LIST OF APPENDICES................. o o.. o.. o. o.. 40 o...xiii ABSTRACT........... o...................... 0 O....... xiv I. DEVELOPMENT OF RESULTSo o o o... o o........ o o......... 1 A. INTRODUCTION................................... 2 B. IMPORTANCE OF PREVIOUS FROTH STUDIES..,....,,..... 5 C. PLAN OF INVESTIGTIION........o......,......... 8 D. RESULTS OF FROTHING STUDIES,..........,.....o 13 Effect of Dispersing Geometryo.......o,....,, 16 Effect of Clear Liquid Depth,...,.....,,... 21 Effect of Liquid Properties,,...o,.......o.....o 25 E. RESULTS OF DYNAMIC SURFACE TENSION STUDIES,......,,., 34 Calibrationo oo....O...ooo...oo...o 34 Surface Tensions of Solutions..e...,...........ooo 36 Comparison with Froth Propertieso,........ooo,.. 55 F. CONCLUSIONS,....O o o................. o... 74 II. THEORY AND EQUIPMENT.. o o.......... o............... 77 A. FROTHING STUDIES o........... o o......, o o o o78 1o Previous Work and Theory,...........oo.ooo 78 Previous Froth Studieso......,........,,. 78 Mechanical Model for Froth Formation,...... 97 Theories of Foam Formation............o., 98 2. Experimentalo o O.O.,................. 115 Description of Frothing Column., o........1. 115 Operation of Frothing Column,.,o...,,.,o... 122 iv

TABLE OF CONTENTS CONT'D Page B. OSCILLATING JET STUDIES.............. o*....o...eo 125 1. Previous Work and Theories................ 125 Theory of the Oscillating Jet...*........... 125 Effect of Orifice on the Oscillating Jet.... 128 Formation of Fresh Surface with the Oscillating Jet............................... 152 Electrokinetic Effects with the Oscillating Jet................................. 133 2. Experimental..................................0. 136 The Oscillating Jet for High Frequency Measurements........... o.......... 136 Description of the Micro-Orifice Apparatus.. 141 Operation of the Micro-Orifice.............. 154 Calibration of the Micro-Orifice............ 157 NOMENCLATURE................. o 168 BIBLIOGRAPHY..............o * o...... 0............. 170 APPENDICES...... 0 0..................................... 0 a 0 * a 0 a * 0.... 179 v

LIST OF TABLES Table Page I PERFORATED PLATE DETAILS............................ 118 II A.I.Ch.E. BUBBLE CAP DIMENSIONS..................... 118 III DIMENSIONS OF ORIFICES USED IN LIQUID-GAS INTERFACIAL STUDIES..e............................ 138 vi

LIST OF FIGURES Figure Page 1 Oscillations in a Liquid Jet from an Elliptical Orifice....................................... 11 2 Typical Froth Curves for Large and Small Diameter Columns............................................ 14 3 Relative Froth Densities of Distilled Water and Air.. 15 4 Relative Froth Densities of Distilled Water and Air.. 17 5 Relative Froth Densities of Distilled Water and Air.. 18 6 Relative Froth Densities of Distilled Water and Air.. 20 7 Relative Froth Densities of Distilled Water and Air.. 22 8 Relative Froth Densities of Distilled Water and Air.. 23 9 Relative Froth Densities of Distilled Water and Air.. 24 10 Relative Froth Densities of Acetone and Air.......... 26 11 Relative Froth Densities of Carbon Tetrachloride and Air...................................... 26 12 Relative Froth Densities of Cyclohexanol and Air..... 27 13 Relative Froth Densities of Several Organic Liquids and Air......................................... 27 14 Relative Froth Densities of Aqueous Acetic Acid Solutions and Air.............................. 29 15 Relative Froth Densities of Potassium Carbonate Solutions and Air....................o...... 30 16 Relative Froth Densities of Aqueous Glycerol Solutions and Air............................... 31 17 Relative Froth Densities of Aqueous Benzene Solutions and Air.... I**a...,................................ 32 18 Surface Tensions Calculated from Triple-Distilled Water Data.................................. 355 vii

LIST OF FIGURES CONT'D Figure Page 19 Calculated Dynamic Surface Tensions for 0.01 Vol. Percent Acetic Acid Solution............... 37 20 Calculated Dynamic Surface Tensions for 0.10 Vol. Percent Acetic Acid Solution......o................. 37 21 Calculated Dynamic Surface Tensions for 1.0 Vol. Percent Acetic Acid Solution........................ 38 22 Calculated Dynamic Surface Tensions for 5.0 Vol. Percent Acetic Acid Solution......................... 58 23 Calculated Dynamic Surface Tensions for 10.0 Vol. Percent Acetic Acid Solution........................ 39 24 Calculated Dynamic Surface Tensions for 10.0 Vol. Percent Acetic Acid Solution........................ 39 25 Calculated Dynamic Surface Tensions for 14.0 Vol. Percent Acetic Acid Solution................... 40 26 Calculated Dynamic Surface Tensions for 18.0 Vol. Percent Acetic Acid Solution.....> o..o..oo..o.....o 41 27 Calculated Dynamic Surface Tensions for 25.0 Vol. Percent Acetic Acid Solution......... o41 28 Calculated Dynamic Surface Tensions for 0.003 Molar Potassium Carbonate Solutiono...................o. 42 29 Calculated Dynamic Surface Tensions for 0.010 Molar Potassium Carbonate Solutiono..,.,............ 42 50 Calculated Dynamic Surface Tensions for 0.030 Molar Potassium Carbonate Solution.........o...... 43 31 Calculated Dynamic Surface Tensions for 0.10 Molar Potassium Carbonate Solution....................... 43 32 Calculated Dynamic Surface Tensions for 0024 Molar Potassium Carbonate Solution...... o... o.o......... o 44 33 Calculated Dynamic Surface Tensions for 0.30 Molar Potassium Carbonate Solution.o................. 44 viii

LIST OF FIGURES CONTID Figure Page 34 Calculated Dynamic Surface Tensions for 1.0 Vol. Percent Glycerol Solution........................... 4 35 Calculated Dynamic Surface Tensions for 10.0 Vol. Percent Glycerol Solution....4....................... 45 36 Calculated Dynamic Surface Tensions for 18.0 Vol. Percent Glycerol Solution......4.................... 46 57 Calculated Dynamic Surface Tensions for 20.0 Vol. Percent Glycerol Solution............................ 46 38 Calculated Dynamic Surface Tensions of 0.001 Vol. Percent Benzene Solution......................... 47 39 Calculated Dynamic Surface Tensions of 0.01 Vol. Percent Benzene Solution........o................. 47 40 Calculated Dynamic Surface Tensions of 0.045 Vol. Percent Benzene Solution......................... 48 41 Effect of Expanding Surface on Dynamic Surface Tension on Oscillating Jet.......................... 52 42 Shape of Jet Leaving Orifice......................... 5 43 Comparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tension; Acetic Acid Solutions............................................ 57 44 Comparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tension; Benzene Solutions............................................ 59 45 Comparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tension; Glycerol Solutions......o....................... 60 46 Comparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tension; Potassium Carbonate Solutions.......................... 61 47 Calculated Dynamic Surface Tensions for 0.005 Molar Ferric Chloride in 10 Vol. Percent Acetic Acid Solution............................. 6 48 Calculated Dynamic Surface Tensions for 0.020 Molar Ferric Chloride in 10 Vol. Percent Acetic Acid Solution......................................... 6 ix

LIST OF FIGURES CONT D Figure Page 49 Calculated Surface Tensions as a Function of Surface Age; 0.01 Vol. Percent Acetic Acid......o.... 66 50 First Node Surface Tensions as a Function of Surface Age; 0.01 Volo Percent Acetic Acid....,...... 67 51 First Node Surface Tensions as a Function of Surface Agej 1.0 Volo Percent Acetic Acid. o.**,.... 67 52 First Node Surface Tensions as a Function of Surface Age; 10 Volo Percent Acetic Acido......oo..,a 67 553 First Node Surface Tensions as a Function of Surface Age; 14 Vol. Percent Acetic Acid............ 68 54 First Node Surface Tensions as a Function of Surface Age; 18 Vol. Percent Acetic Acido..oo........ 68 55 First Node Surface Tensions as a Function of Surface Age; 25 Vol. Percent Acetic Acido...so. o o.. 68 56 First Node Surface Tensions as a Function of Surface Age; 0~003 Molar Potassium Carbonate........ 69 57 First Node Surface Tensions as a Function of Surface Age; 0o010 Molar Potassium Carbonateo...oo... 69 58 First Node Surface Tensions as a Function of Surface Age; 0o03 Molar Potassium Carbonate........ 69 59 First Node Surface Tensions as a Function of Surface Age; 0o10 Molar Potassium Carbonate.......... 69 60 First Node Surface Tensions as a Function of Surface Age; 0.24 Molar Potassium Carbonate.....o oo a. 70 61 First Node Surface Tensions as a Function of Surface Age; 1 Vol. Percent Glycerolo....0...o..o..... 70 62 First Node Surface Tensions as a Function of Slrface Age; 10 Vol. Percent Glycerolo............... 70 63 First Node Surface Tensions as a Function of Surface Ageg 20 Vol. Percent Glycerol..,.o. oo. o.... 70 x

LIST OF FIGURES CONTID Figure Page 64 Comparison of Frothiness with Indicated Rate of Decrease in Dynamic Surface Tensionsj Acetic Acid Solutions. **. o o o a * o o o o o o o o * o o O * *. o... 71 65 First Node Surface Tensions as a Function of Surface Age; 10 Vol. Percent Acetic Acid with Ferric Chloride Additions o o o, o.. o.......,. 72 66 Relative Froth Densities of Air-Water Froths in Large-Diameter Columns........................... 82 67 Relative Froth Densities of Air-Water Froths in Small-Diameter Columns o..ooo.....e..o o........o.. 85 68 Relative Froth Densities of Two Hydrocarbons in Small-Diameter Columns.........o.......,......... 84 69 Relative Froth Densities in Various Columns.......... 87 70 Relative Froth Densities of Water-Air System......... 89 71 Relative Froth Densities of Aqueous Ammonia-Air System............................... 89 72 Relative Froth Densities of Air-Water Froths in a 6-inch Diameter Column......................... 90 73 Relative Froth Densities of Several Liquids with Air in a 12-inch Diameter Column.................... 90 74 Relative Froth Densities of Several Liquids with Air in a 55-mm Diameter Column....................... 92 75 Relative Froth Densities of Several Liquids with Air in a 3.14-inch Diameter Column.................. 93 76 Relative Froth Densities of Water in Several Gases, Plotted as Function of Superficial Gas Velocity...... 96 77 Relative Froth Densities of Water in Several Gases, Plotted as Function of the "F-Factor"................ 96 78 Thin-Film Dome Formation by Rising Vapor Bubble...... 99 79 Change of Surface-Active Solute Concentration with Time at a Newly-Formed Surface..............o......... 108 xi

LIST OF FIGURES CONTVD Figure Page 80 Change of Surface Tension at a Newly-Formed Surface.. 108 81 Frothing Column............................... 116 82 Perforated Plate Layout............................ 117 83 Flow Diagram of Froth Measuring Apparatus............ 121 84 Photomicrograph of Exit Face of Micro-Orifice, 500 X. 143 85 Flow Diagram for Oscillating Jet Apparatus........... 144 86 Detailed Construction of Reservoir Flask............. 146 87 Diagram of Oscillating Jet Barrel Assembly, Exploded View................................... 147 88 Optical Arrangement of Cathetometer Microscope........ 149 89 Microscope Mounting with LVDT Sensing Element........ 151 90 LVDT Sensing Element for Measuring Vertical Movement of Microscope................. o............. 152 91 Change in Radius Along Length of Jet................ 160 92 Relation of Correction Factor, K, to Jet Radius..... 161 93 Relation of Intercept I to Jet Velocity.............. 162 94 Plot of Equation (16a) for Several Water Calibration Runs......... D. * o* *.......................... 164 95 Approximate Correlation for Empirical Constant A in Equation (15)..........o...**....o...............1. 166 xii

LIST OF APPENDICES Appendix Page A OUTLINE OF RAYLEIGH'S DERIVATION FOR THE OSCILLATING JET, o......,.. o...... o..,.. 179 B OUTLINE OF BOHR S MODIFICATION OF RAYLEIGH'S EQUATIONo..oo...o000.....* o. o....0..... o 189 C FURTHER REARRANGEMENT OF THE OSCILLATING JET EQUATION o............................*. 202 D DEVELOPMENTAL PROBLEMS WITH THE MICRO-ORIFICE....... 207 E DEVELOPMENT OF COMPUTING EQUATION FOR THE "MICROORIFICE"...... o.......................... 210 F IBM "FORTRAN" COMPUTER PROGRAM.,.................. 220 G CALIBRATION OF EQUIPMENT............................ 224 H FROTHING DATA............................... 231 I OSCILLATING JET DATA............................... 242 J EXPERIMENTAL ERRORS.............................. 252 xiii

MEASUREMENT OF DYNAMIC SRWFACE TENSION CHANGES IN FROTH-FORMING AQUEOUS SOLUTIONS Robert Jo Van Duyne ABSTRACT Froth densities are given for distilled water and aqueous solutions of acetic acid, potassium carbonate, benzene, and glycerol aerated in a four-inch glass column with a perforated steel dispersing plate. Problems associated with using the oscillating jet technique for measuring the rapid dynamic surface tension changes in these aqueous solutions were studied, Measurements of surface tensions made at 30microsecond intervals with a minute oscillating jet show apparent increases in surface tension along the free surface of the jet. Possible explanations for this are offered, and the significance of these results in interpreting the mechanism of froth formation are discussed. Accepting agitation of the jet surface as the cause for these increasing surface tensions permits one to conclude that in positively adsorbed solutions good frothability might occur when agitation of the froth surface causes rapid increases in surface tension, Conversely it appears that small increases in surface tension due to agitation should enhance frothing in solutions of negatively adsorbed solutes, Slight additions of ferric chloride reduce the severity of the surface tension increase due to agitation in acetic acid solutions, thereby decreasing frothiness, xiv

A modification of Rayleigh's oscillating jet equation, in c. g s units, P z 2ir 2 /r 2 1 ( r2 rr2 1 r 2 1 rr 2(r2dr PC 2 I2 (kr)1 +( ) +- ()-) -2 y+ ) + l(r) + (7) r 00^ k I4(kr) 2 r / 2T /+ r 2 1 6r 2 1 r 2 ar2 1 r 2 f r 1 + + (3) + t z) ( — ) d - 2:rz 0 0. was developed for use with oscillating jet from the "micro-orifice" (0o00179inch mean diameter), integration being performed numerically with a digital computer. A semi-empirical correction factor, with c in fto/sec. K 6ocalc = {2.63 - 00082c 834irg} * - [17.9 -41200 (Lor0 O0004 3 cyknown - y715pL) o6 e C J compensates for velocity distribution and orifice effects imparted by the small, smooth-edged orifice, In these equations, r radius at point on jet surface, cm, rg geometric mean radius of jet, inches. ro = mean jet radius, extrapolated to orifice exit, inches. z = distance from orifice, cmq,. c bulk linear velocity of liquid, cm/sec or ft/sec, L volumetric liquid flow rate, cm3o per min. k wavenumber, 2i/X) XV

a = major axis of nodal ellipse, b = minor axis of nodal ellipse, and _z = dimensionless group. pL xvi

PART I DEVELOPMENT OF RESULTS -1

A. INTRODUCTION The purpose of this study is two-fold. First, to study the role of dynamic surface tension in the froth behavior of aerated, nonfoaming liquids to gain insight into factors believed to be important in froth information. Second, to investigate the possibility of following extremely rapid changes in dynamic surface tension in some dilute frothforming solutions, It was necessary to attempt a refinement of the classical "oscillating jet" method of dynamic surface tension measurement. The development of this refinement, the "micro-orifice", constituted a major part of the investigation. Dynamic surface tension changes determined in this manner for dilute aqueous solutions were compared with the frothing characteristics of the solutions when aerated in a four-inch diameter glass column with a perforated steel plate. The term "aeration" in this report refers to the act of passing any dispersed gas through a bed of liquid. Although the terms froth and foam are frequently used interchangeably, exact usage requires that the following distinction be made between the two: a froth is unstable, has a very short lifetime, and requires continuous regeneration by bubbling, agitation, etc,, while a foam, being more stable, has a longer lifetime, lasting for a period of seconds to days without regeneration. There is no clear "dividing line" between froths and foams. For the case of gas-in-liquid dispersions -2

having intermediate lifetimes, say, several seconds, the classification as either foam or froth is purely arbitrary. Frothing is of interest to the engineer because of its frequent appearance in industrial operations. Frothing and foaming of lubricating oils in gasoline and diesel engines is of concern to the refiner as well as the automotive engineer. Unwanted frothing and foaming is also encountered in many hydraulic systems. Frothing in steam boilers has received attention because of its adverse effect on boiler performance. In evaporator operation both efficiency and quality of product suffer as a result of excessive frothing and foaming. Gas-liquid contacting devices constitute an important part of chemical engineering operations. Predominant among them are absorption and distillation columns employing bubble-cap or sieve-type trays in which formation of aerated froth is essential for mass transfer. Recent work has indicated that the mass transfer efficiency on a bubble-tray can be correlated as a function of the height of froth on the tray. The depth of froth on the tray also determines the minimum allowable tray spacing and the optimum downcomer design. In the design of bubble-tray columns, stable foaming is not often encountered, and constitutes a special problem. On the other hand, most ordinary liquids treated in such columns do yield some quantity of unstable froth. Although mass-transfer mechanisms and liquid hydraulics on bubble-trays are fairly well understood very little is known regarding the froth on the tray. At present there are no reliable methods for predicting the height of froth expected

in a new column, and designers must rely upon past experience with similar liquid systems or upon "rules of thumb." The problem of dynamic froth formation has, for the most part been ignored. The regime of unstable frothing lies midway between those of stable foaming and two-phase fluid flow. Nevertheless, relatively little concerning froth behavior of non-foaming liquids has been reported despite the large volume of literature about foams and two-phase fluid flow. Previous attempts at explaining the difference in froth magnitudes encountered between different liquids in typical commercial equipment, such as bubble-tray columns, etc., have relied primarily on fluiddynamics concepts. The present study was undertaken in the belief that froth behavior might be studied more successfully by considering unstable froths to be essentially short-lived foams complicated by turbulence, In this light, then, aerated frothing is largely a problem of surface chemistry, and those theories which have been offered to explain foam behavior in terms of surface phenomena should also apply, to some extent, to aerated froths. The behavior of non-rigid, stable foams is most convincingly explained by consideration of the effects of surface activity and dynamic surface tension lowering,

B. IMPORTANCE OF PREVIOUS FROTH SITUDIES Early attention to frothing and foaming in distillation and absorption columns appears to have been limited to those instances in which frothing caused excessive entrainment(39'87'88'135'156'149'153'157, 162,165,166,17), or flooding(79 More recently, attention to aerated froth on bubble trays, etc., stems from attempts at developing mathematical models to explain observed mass-transfer efficiencies, The Two-Film Theory of Whitman(l79) and the Penetration Theory of Higbie(85) have been employed with froth models ranging from spherical bubbles(69164177) to a series of oblong vertical channels (13) A recent general correlation of bubble-tray efficiency employs average gas contact time in the aerated liquid, as determined from the froth height and the vapor rate. (7,63,70) In these calculations it is necessary to estimate the time of contact between the gas bubbles and the liquid, relying on scant froth height data available for a specific liquid and apparatus, Froth data are most commonly reported as froth heights or relative froth densities. The froth height is the total height above the disperser tray attained by the frothing mixture, while the relative froth density is the weight of the aerated mixture relative to that of an equal volume of the unaerated liquid, The role of each of the many variables effecting frothing is poorly understood. As evidenced by Figures 66 through 69, froth behavior is very sensitive to vessel geometry, including column diameter and gas disperser configuration. However, examples of froths which are independent -5

of column size(2) and dispersing configuration(1211) have been reported, Froth density is known to depend on the depth of liquid in the column as well as the motion of the liquid. Many contradictions regarding the apparent relationships between the physical properties of liquids and their frothing behavior exist. Although several investigators have demonstrated an apparent independence between froth performance and physical properties, many observe marked differences in froth behavior for different liquids. There is no general agreement regarding the relative importance of surface tension, viscosity, or density. Similarly there is lack of agreement about the effects of gas density, temperature, and the presence of solid particles on frothingo Unstable frothing and stable foaming are related in that both involve the formation and rupture of thin liquid filmso The importance of surface chemistry in foam behavior is well established, and several theories relating surface activity and foaming have received support, Prominent among them is the explanation of film elasticity offered by the Marangoni Effect,(107'108) which attributes the "healing" of ruptures or weak spots on the liquid film to differences in surface tension, Recent postulates suggest that for the Marangoni Effect to be most effective an optimum. rate of surface tension lowering with aging of the surface must occur. The lowering of dynamic surface tension with surface age, and its effect on Marangoni elasticity are discussed more fully in Section II-A.

Because of the similarity between frothing and foaming, it might be suggested that the froth behavior of aerated liquids should also be influenced by the rate of dynamic surface tension changes of the liquid. It is therefore not surprising that consideration of dispersing variables, bulk liquid physical properties, and gas properties alone lead to apparently contradictory results,

C, PLAN OF INVESTIGATION To study the relation between frothing tendencies and dynamic surface tension changes the relative frothing behavior of four series of aqueous solutions was determined by frothing them in a small glass column. It was then attempted to measure the rate of dynamic surface tension lowering for each of the solutions for comparison with froth behavior. The frothing column was of four-inch I. D glass pipe, and froth studies were performed using three different gas-dispersing plates, as described in Section II-A, Dry air was blown at various rates through non-circulating beds of liquid with clear liquid depths from one to 24 inches above the dispersing plate, and the resulting froth heights were observed. The measurement of dynamic surface tension change rates involves creating a "new" (i.e., zero age) liquid surface and then determining its surface tension as it ages. The method employed for this task depends on the rate at which the surface tension decreases during the aging of the surface. In some instances, the dynamic surface tension change is slow enough to permit its detection by a series of measurements with a (52) standard du-Nouy ring tensiometer52 Modifications in the drop-weight method(29) as well as in the pendent drop method(96) for measuring surface tensions have permitted their use in measuring somewhat more rapid changes in dynamic surface tension. The minimum surface age capable of being investigated by the fastest of these methods, the drop-weight modification, is probably of the order of magnitude of one-half second. -8

-9 Detection of surface tension changes occurring at surface ages less than this may be accomplished by observations with jets of the liquid. At least three different techniques have been reported employing liquid jets for the measurement of rapidly changing dynamic surface tension. The earliest of these is the classical "oscillating jet" method, in which a series of standing waves is induced on the jet and the wavelength of each node is measured.(3' ) In the usual operation, the standing waves are induced by passing the liquid through an elliptically-shaped orifice. In the "contracting jet" method, reported by Addison and Eliot(5), the curvature of the jet contraction as it leaves the nozzle is measured. These authors state that very short surface ages can be studied accurately with this method. A fourth method, used by Posner and Alexander(23) consists of measuring the electrical potential along the surface of the liquid jet. A small, ionizing prove is moved along the length of the jet to determine the EMF at each point, which is then compared against a calibration curve of EMF vs. static surface tension. The "oscillating jet" method was chosen for measuring surface tensions in this study because of the uncertainties involved in attempting to use the "contracting jet" technique with liquids covering a wide range of physical properties,(5 3) and because of the possible disturbing effects of electrokinetic phenomena on the measurement of surface EMeFs. The oscillating jet technique utilizes the principle that a jet of liquid issuing from a non-circular orifice will attempt to adjust its crosssectional shape to achieve a minimum surface energy. Thus, when a liquid is passed through an elliptically-shaped orifice into still air, the

unbalance of lateral surface tension forces about the perimeter of the initially-formed elliptical cross-section of the jet causes the jet to rearrange its cross-sectional shape to that of a circle at some short distance from the orifice. Because of the inertia of the liquid in the rapidly changing jet, the liquid overshoots this optimum circular shape and forms an ellipse with its major axis parallel to the minor axis of the orifice ellipse. This again results in an unbalance of surface tension forces which tends to restore the jet to its circular shape, and the jet is seen to oscillate between circular and elliptical cross-sections. Hence a series of standing waves is produced along the surface of the jet, as in Figure 1. Consideration of surface energy and momentum forces permits calculation of the surface tension at each node if the wavelength is measured, Since the age of the liquid on the surface of an ideal jet should increase with the distance from the orifice, any time-dependent change in surface tension should be detected by changes in wavelength along the length of the jet. It follows from the surface energy-momentum balance that the period of oscillation decreases with decreasing jet radius. Since the aqueous electrolytes in this study were expected to have extremely rapid rates of surface tension decrease, it was necessary to employ as small an orifice as could be made in the laboratory. An orifice with a mean diameter of 0.00179 inch in a disc of 0.001 inch thick stainless steel foil was used for this study. This is referred to as the "microorifice. "

FLOW AMPLITUDE, a -. WAVE LENGTH, X Dmax -> -1 Dmin I - ^ K7j ORIFICE CROSS- SECTIONS THROUGH JET Figure 1. Oscillations in a Liquid Jet from an Elliptical Orifice

-12The "micro-orifice" was first calibrated with triple-distilled water, then measurements were made with the aqueous electrolytes to determine rates of change in dynamic surface tension.

D, RESULTS OF FROTHING STUDIES The nature of the froth density vs. gas velocity curve depends largely on the geometry of the frothing column. The typical curve for small diameter columns may be considered to consist of three regimes, as shown in Figure 2. In the frothy, or "true frothing" zone, occurring at low gas rates, the froth is very light and fluffy, and appears to be a piling up of small stable bubbles separated by thin liquid films. At higher gas rates slugs of gas begin to appear and the froth becomes quite agitated. This will be termed the transition region, in which the froth density decreases with increasing gas rate. Finally, in the turbulent or "churning" region, the mixture appears to consist of sheets of liquid agitated violently by the rapidly rising channels of air. There is little or no "pile-up" of discrete bubbles. In larger diameter columns "true frothing" seldom occurs and only turbulent and possibly some amount of transition frothing is observed. As in Figure 2, froth density results of this study will be plotted vs. logrithmic air rate in order to expand the true frothing zone, since it is in this region that differences in frothing tendencies of liquids are most observable. Some froth densities measured during this study in the fourinch diameter glass column using the perforated steel plate are plotted in Figure 3. This typical curve exhibits the three distinct frothing regimes. During most frothing runs with the sieve plates some slow -13

LARGE DIAM. COLUMN Iz w o SMALL DIAM. COLUMN IL FROTHY | TRANSITION I TURBULENT REGION I REGION | REGION LOG SUPERFICIAL AIR VELOCITY Figure 2. Typical Froth Curves for Large and Small Diameter Columns.

1.0 0.8 0o^ * I 4" DIAM. COLUMN 0 A-4 >-OS.~~~~~ ~ ~~~A A-6 ---- 1 o A-7 u) W 0 A-I0 o 0.6 LL i I I I ~ h E > 0. 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 SUPERFICIAL AIR VELOCITY. FT. PER SEC. I-Figure Relative Froth Densities of Distilled Water and Air 0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 SUPERFICIAL AIR VELOCITY, FT.PER SEC. Figure 3, Relative Froth Densities ofi Distilled Water and Air I I

pulsing of the froth at intermediate air rates was observed. This consists of a gradual rise and fall of the froth, indicated in Figure 3 by solid vertical lines connecting the maximum and minimum observed froth densities. Froth heights and densities for all the froth runs are tabulated in Appendix H, with the froth curves in this discussion presented without data points for clarity. Effect of Dispersing Geometry The shape of the froth density curves for the experimental column was dependent on the dispersing plate used. For example, Figure 4 shows the difference in froth density when a 2-inch depth of water is aerated in the 4-inch diameter column using: (a) a single A.I.Ch.E. bubble cap, (b) a wire gauze sieve tray, and (c) a stainless steel sieve tray. Figure 5 shows the froth densities for a 6-inch depth of water, using these three dispersers. The bubble cap, by virtue of its jetting action and poorer gas dispersion, yields the most dense froths. The sieve plates, because of their finer, more uniform gas dispersion, produce less dense froths, Contrary to expectation the fine-mesh gauze disperser did not disperse the gas as uniformly as did the perforated plate, and consequently did not exhibit as much froth as the perforated plate. Three explanations for this have been considered:

1.0 0.8 - - 0.6 in) z w I o I0 nr L 0.4 - w -J w LU. 0.2 0 - 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2.0 SUPERFICIAL VELOCITY, FT. PER SEC..0 I I.2. I I I.08.1.2.3.4.5.6 3.0 4.0 5.0 6.0 8.0 10.0 I I I I I.03.04.05.06.07 I I I I.8 1.0 2.0 2.0 F - FACTOR Figure 4. Relative Froth Densities of Distilled Water and Air.

1.0 09 - 0.8 k- 0.7 - Z x 06 - 0.5 I.0 0.4 0.3 02 - 0.1 0 0.1 I co (~ 1 Q3 Q4 0.5 0.6 0.8 1.0 2 SUPERFICIAL AIR VELOCITY, FT/SEC Figure 5. Relative Froth Densities of Distilled Water and Air. 10

(a) Although care was taken to maintain the wire gauze as taut and level as possible, it quite likely bulged or "rippled" slightly during operation, so that the gas flow channeled preferentially through portions of the gauze, leaving areas of inactive holes through which liquid weeped. (b) Liquid capillary forces may have made it difficult to force air through the small holes, so that air passed through a small number of "dry" holes, leaving many inactive, "'wet" holes, (c) Even if all the holes were active, the closeness of the holes caused a large degree of coalescence during bubble formation, so that the bubble size and bubble distribution in the froth was less uniform than in the froth above the perforated plate, with which much less coalescence occurred because of its wider hole spacing. It may be noted from Figures 4 and 5 that while the froths above the two sieve plates show the usual minimum in the froth density curve, the bubble-cap plate produces no minimum, probably because of the turbulence induced by the jetting action of the cap. The flow pattern of the gas below the dispersing plate can also effect the froth behavior, as shown by Figure 6, in which froth densities of a 4-inch depth of liquid above the bubble cap plate and the perforated plate are compared. As in Figures 4 and 5, the perforated plate yields lower froth densities than does the bubble capo Also shown, however, is the effect of placing a fine mesh wire gauze across the air-space below the perforated plate. This gauze, of finemesh monel, was installed about 4 inches below the plate in order to

0.9 0.8 0.7 Iz o 0 IL Q I -J a: 0.6 0.5 0.4 0.3 - 0.2 - 0. 0.2 0.3 0.4 0.5 0.6 1.0 2.0 3.0 4.0 5.0 6.0 SUPERFICIAL AIR VELOCITY, FT/SEC Figure 6. Relative Froth Densities of Distilled Water and Air. 8.0

-21 promote more uniform distribution of air to the perforated plate. However, because of liquid weepage through the perforated plate, the wire gauze became covered with liquid during operationo As expressed above, it was feared that the presence of the wet gauze might actually cause more uneven gas distribution below the plate, and therefore it was removed after the first several runs. If the higher froth density with the gauze is attributed to uneven gas distribution, Figure 6 indicates that the gas distribution to the plate at low rates is probably more uniform without the gauze. It appears further that at higher gas rates the presence of the gauze enhances uniform gas distribution. It is interesting to note that the minimum froth density of the two curves are almost identical and also that, within the limits of experimental accuracy, the curves appear to coincide in the turbulent, or churning region. Effect of Clear Liquid Depth Another factor which must be considered in studying frothing is the effect of clear liquid depth, Figures 7, 8, and 9 show froth density curves obtained in the 4-inch diameter column with various clear liquid depths, employing the three dispersing plates. Figure 7 illustrates the difference in froth densities with changes in clear liquid depth when the perforated. plate is usedo With increasing liquid depth the froth density increases, and the frothy and transition regions become less and. less distinct, until at sixteen or more inches of clear liquid depth the entire curve appears to be of the turbulent character, The curves are more closely grouped in the turbulent region than in the other two regions.

1.0 09 0.8 >- 0.7 U5 z w o Q6 U 0.5' 04 -i w.I 0.3 0.2 0.1 I 1>D r ) 0.3 0.4 Q5 Q6 0.8 1.0 2 SUPERFICIAL AIR VELOCITY, FT/SEC Figure 7. Relative Froth Densities of Distilled Water and Air. 10

1.0 0.9 0.8 uz w IJ 0 Ii. I4 -J w cr 0.7 0.6 0.5 0.4 0.3 | - _ = 5 —< —=- - ------ l 2 I DISTILLED WATER 4-IN. DIAMETER COLUMN l~ ~'"' ^J|'^ — ^ ^SINGLE BUBBLE CAP 4" P.'..AMiETERS ARE CLEAR LIQUID DEPTHS 1 l, 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5.6 0.8 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 SUPERFICIAL AIR VELOCITY, FT. /SEC. Figure 8. Relative Froth Densities of Distilled Water and Air.

1.0 0.9 0.8 - DISTILLED WATER - 4-IN. DIAMETER COLUMN WIRE GAUZE SIEVE PLATE e0> z I W LL w -J 0.7 0.6 6" _ 2 I I I I~1j r 05 0.4 0.3 PARAMETERS ARE CLEAR LIQUID DEPTHS._______________~~~~~~ X T_________ _______________ __________ _______________ __________~~~~~~ ~~~~~~~~~~~~~ i- C- -,_ - i i I' l 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 SUPERFICIAL AIR VELOCITY, FT/SEC Figure 9. Relative Froth Densities of Distilled Water and Air.

-25 Figure 8, on the other hand, shows that when the bubble cap is employed, the effect of clear liquid depth is not nearly so noticeable. The curves for 6 and 8 inches of clear liquid are almost identical, and that for 4 inches of depth is only slightly lower, showing just a hint of frothiness or transition. The curve for 2-inch clear liquid is out of line, falling higher than the others, This is apparently due to poor gas dispersion from the bubble cap resulting from such a small head of liquid above the cap. However, at the highest gas velocities the froth density of the 2-inch curve rapidly falls below the others, suggesting that in the turbulent region the dispersion of the gas is of less importance than gas momentum. As discussed above, the froth densities above the wire gauze dispersing plate are intermediate between those above the bubble-cap and the perforated plate. The effect of clear liquid depth is not very noticeable, Because of the non-uniform gas dispersion with the wire gauze it is difficult to interpret the resulting froth curves, Figure 9. Effect of Liquid Properties Froth curves for acetone, carbon tetrachloride, and cyclohexanol are shown in Figures 10, 11, and 12. Only the acetone exhibits froth behavior similar to that of water, i.e., the effect of clear liquid depth is marked, and the frothy and transition regions are well defined at small clear liquid depths. The frothy and transition zones are barely observable for the cyclohexanol, but neither cyclohexanol nor carbon tetrachloride show as much effect of clear liquid depth as water or acetone. It appears therefore that only in the true frothing regime is clear liquid depth of

-26 Q9 SUPERFICIAL AIR VELOCITY, FT/SEC Figure 10. Relative Froth Densities of Acetone and Air. as 0.7 Q6 Oa CARBON TETRACHLORIDE 44-IN. DIAM. COLUMN -------- ---- -- _ PERFORATED SIEVE PLATE <" S P C 1ARAMETERS:CLEAR UQUID DEPTH I2 % 91 | N 1 1 1 1 1 1 1 I I TY ISSII~~~~~~~~,.. Q3 02 0.1 0.1.2.3 A.5.6.8 ID 2 3 4 5 6 SUPERFICIAL AIR VELOCITY, FT/SEC Figure 11. Relative Froth Densities of Carbon Tetrachloride and Air.

0.9 0.8 I — U) z 0 0 LJ w w w 0.7 0.6 Q50.40.30.2 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 SUPERFICIAL AIR VELOCITY, FT/SEC Figure 12. Relative Froth Densities of Cyclohexanol and Air. 0.9 0.8 u) z w ILL. w i.. Li 13: 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2.0 3.0 40 5.0 60 80 10.0 SUPERFICIAL AIR VELOCITY,FT/SEC Figure 13. Relative Froth Densities of Several Organic Liquids and Air.

much importance, and for those liquids in which true frothing does not occur the froth behavior over the entire range of gas velocities may be considered essentially a churning or turbulent phenomenon. This is shown more clearly by Figure 13, in which the froth curves of four organic liquids, as well as that for water, are compared. Significantly, in the turbulent region of the curves, the froth density is observed to decrease with decreasing values of kinematic viscosity: L-quid Approx. Kinematic Viscosity, Centistokes cyclohexanol 69.0 water 0.9 dibromoethane. 8 carbon tetrachloride 0.6 acetone 0.4 In the frothy region of the curves, however, this relationship does not hold, indicating that a study of momentum and turbulence relationships is insufficient in attempting to explain froth behavior when true frothing -occurs. This is brought out even more clearly by observation of the froth behavior of some aqueous solutions. Figures 14 through 17 show froth density curves for various concentrations of aqueous solutions of acetic acid, potassium carbonate, glycerol and benzene. The curves for the acetic acid solutions indicate that relatively small changes in solute concentration can promote very marked changes in froth behavior even though the physical properties of the liquid are apparently not changed appreciably. In Figure 15 it is seen that the presence of very

0.7 0.6 - - -_........... 4 -IN. DIAMETER COLUMN:/\\^ \ \ 4-IN. CLEAR LIQUID DEPTH PERFORATED PLATE > 0.4 Z \\\\\ \\ I z \ \/ I t I 0.3 0 U. SUPERCIAL AIR VELOCITY, FT/SEC. 0 I 0.1 0.2 0.3 a4 0.5 0. 0.8 i.0 2 3 4 5 6 8 10 SUPERCIAL AIR VELOCITY, FT/SEC. Figure 14, Relative Froth Densities of Aqueous Acetic Acid Solutions and Air. I \) I

0.7 06 0.5 Iz w 0.4 0.2 0.1 w >: Q3 0.2 0.1 0 I 0 SUPERFICIAL AIR VELOCITY, FT/SEC. Figure 15. Relative Froth Densities of Aqueous Potassium Carbonate Solutions and Air.

0 IV,,. 0. 0. Iz I-0 I> 0. -J a:o.7.6 -_____ J~\c^~~ E I I I I I IGLYCEROL SOLUTIONS \\, ~4 -IN. DIAMETER COLUMN ^^^JS.o}~~~~~~~~~~. 4 -IN. CLEAR LIQUID DEPTH 5 PERFORATED PLATE 3 PARAMETERS: GLYCEROL CONC, VOL.% j I 0. 0. I 0 L 0.1 0.2 0.3 04 0.5 0.6 0.8 1.0 2 3 4 5 6 8 10 SUPERFICIAL AIR VELOCITY, FT/SEC. Figure 16. Relative Froth Densities of Aqueous Glycerol Solutions and Air.

07 | _____6__ oak~\>& ___ ___ _ BENZENE SOLUTIONS 0.6 \"^ —- -- - --- ---- 4-IN. DIAM. COLUMN -__ --- ~~~~~~\ \ I\~~~~~~~~ I 4-IN. CLEAR LIQUID DEPTH PERFORATED PLATE PARAMETERS: BENZENE CONC., VOL.% 05 \.1.2.3.4.5 6.8 1.0 2 3 4 5 6 8 10 w.001 02..2.3 4.5.6.8 1.0 2 3 4 5 6 8 10 SUPERFICIAL AIR VELOCITY, FT/SEC. Figure 17. Relative Froth Densities of Aqueous Benzene Solutions and Air. 4

minute quantities of K2CO0 can drastically increase the frothiness of water. Further, increasing the K2CO3 concentration from 0.015 M to 1.5 M causes only a very slight change in froth density even though the viscosity increases from 1. 0 to 1. 5 cpSo As seen in Figure 16 relatively large amounts of glycerol added. to water cause only moderate increases in forthiness, even though the viscosity is varied markedly. Also, in Figure 17 it is shown that minute amounts of benzene have only slight effect on the froth behavior of water, even though these amounts of benzene are sufficient to lower the surface tension of the liquid appreciably. Of further significance is the fact that all of the froth systems of Figures 14 through 17 appear to have some intermediate concentration for which the froth densities are minimum.

E. RESULTS OF DYNAMIC SURFACE TENSION STUDIES The behavior of oscillating liquid jets from the "microorifice" was studied with three aims in minds 1L To develop an empirical calibration relationship to correct the theoretical surface energy-momentum balance, Equation (23-E), for nonideal jet behavior imparted by the large wave amplitudes and non-uniform velocity distributions encountered in such small diameter jets. 2. To utilize this calibration for calculating surface tensions along the length of jets of aqueous electrolyte solutions, thus determining the time rate of change of dynamic surface tension for these liquids. 3. To compare these rates of surface tension change with the relative frothiness of each liquid to determine what relation, if any, might exist between dynamic surface tension changes and frothability. Calibration A semi-empirical correction-factor relationship K L 2 6 - 0. 0082c - 834r. {1 -17. 9 4120- Lro- - 00004) e... 1 [ I r 7 () e. 1 ('. 6 (19) which accounts for the effects of jet radius, initial wave-amplitude, and velocity distribution along the jet was developed by calibration with triple-distilled water. Details of its development are given in Section II-B. Figure 18, in which are plotted surface tensions for tripledistilled water calculated from Equation (25-E) using correction factors

-35 ie rV E _,, RUN 4104 a )o c ( I t 0 0 703 0 40 80 120 160 200 24 AGE,L SEC 76 E | RUN 405 7 74 0 0' 72 - b' 70 40 80 120 160 200 24 AGE, $ SEC. O 40 80 120 160 200 24 AGE, L SEC. 76 -- E RUN 406,74 72 b 0 40 80 120 160 200 24 AGE,, SEC 72 RUN 413 70 _G_ _ _-_ 70 68 0 40 80 120 160 200 24 AGE, /LSEC 74 - RUN 416,70 68 0 40 80 120 160 200 24( AGE, uSEC 74 I —I RUN 419 79 E l i i i RUN 407 C I -- -- -- __r — -- 70 - - - 10 0 40 80 120 160 200 24 AGE,. SEC. 4 } 4 8 10 1020RUN 408 7 b'72 -------- 10 0 40 80 120 160 200 24 E I I I IRUN 409 74 co 0 z 0 72 AGE,,u SEC. 72 O 0 40 80 120 160 200 24( RUN 414 70 ------------- 068 -- - - --- 66 0 0 40 80 120 160 200 24( AGE,. SEC 7614 RUN 417 7 --- - - - - - S2 _ _ b 0 0 0 40 80 120 160 200 24C AGE, /pSEC 74 --- I 7I JlL_ 6S~~~ o RUN 410 u,76 -- ~ f ~ 40 0 40 80 120 160 200 240 AGE,$ SEC. 76 --- -TE RUN 411 40 l._74'a ~70 0 + 0 40 00 120 260 240 AGE, L SEC. 76 - -- _E _RUN 412 0 0 0 40 80 120 160 200 240 AGE, IL SEC. 74 -- a, RUN 415 72 z I e I ~ -T0 41 a w. b 11 c. L b 68 3 0 40 80 120 160 200 240 AGE, /LSEC a ~s 2, 70 - a68 b 66, 0 RUN 418'-.-G =-.- --- P- -- 40 80 120 160 2 AGE, ASEC O) 2 0 u 0 u) z b70n b 0`C w c L f a L> U I) 2 z in RUN 502 0 G 0 " IL: L b o 0 I 0 40 80 120 160 200 241 AGE, / SEC 0 0 40 80 120 160 200 24 AGE, $SEC 0 70 - - 0 40 80 120 160 200 24C AGE, F/SEC b 76 74 7270. -1 - - r — 78-, —— 7 1 - 74- - - - - - - 0 RUN 503 RUN 504 RUN 505 -76 72 40 80 120 160 00 240. 0 0 20 200 240 40 80 120 160 200 20 AGE, / SEC. AGE, $SEC. AGE, /SEC. Figure 18. Surface Tensions Calculated From Triple-Distilled Water Data Using Equations (23-E) and (19).

from Equation (19), gives an indication of the accuracy obtained using the micro-orifice for determining surface tensions. It will be noted that although the accuracy of the calibration is such that the absolute value of the calculated surface tension may differ by as much as fourdynes per cm, from the accepted value (about 72 dynes per cm. for water) the surface tension at any node does not usually deviate more than + Oo8 dynes per cm. (+ 1.1 percent) from the mean value. Such errors are within the limits of accuracy of the jet measurements. They are acceptable, for the jet is used to determine the changes in surface tension rather than absolute values. Surface Tension of Solutions Using Equations (23-E) and (19) surface tensions were calculated for aqueous solutions of acetic acid, potassium carbonate, glycerol and benzene. The results, plotted versus the "apparent" age of the liquid in the jet, appear in Figures 19 through 40o Observation of these curves immediately raises a question about the validity of the calculated surface tensions. In employing the oscillating jet, the intention is to measure the surface tension of the aging liquid surface as it moves along the length of the jet. Consideration of the excess energy at the liquid surface dictates that if any spontaneous change in surface tension is to occur on aging, it must be a decrease. In apparent disregard of thermodynamics, however, most of the calculated surface tensions in Figures 19 through 40 are found to increase with age, Four possible explanations for this discrepancy can be offered: a) First, it can be argued that the calibration obtained for triple-distilled water is not suitable for these aqueous solutions, This

Q E o z U) z II uL 0 n, r: (0) z IL U) 72 0.01 VOL/o ACETIC ACID 70 68 l _. 66 64 0 RUN 513 62 A'- --- A RUN 514. 2 RUN 515 60.....-.0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 19. Calculated Dynamic Surface Tensions for 0.01 vol. Percent Acetic Acid Solution. 74-..1 0.10 VOL% ACETIC ACID 72. 70 1... 70O0 68 66 o 64 o RUN 516 1 A RUN 517 62 I, A~~~~~~~~~Mk AMlk......... u 40 80 120 160 200 240 APPARENI AGE,MICROSECONDS Figure 20. Calculated Dynamic Surface Tensions for 0.10 vol. Percent Acetic Acid Solution.

-38 E U) w z U) z w w LL U) 70 -- - 1.0 VOL % ACETIC ACID 68 A 66 A 64.. - -''I O 62 gQ60 ___ __ __ __ ____ 0 RUN 518 A RUN 519 RA __^^. ______ ____ ___ _____.^_______ ^____^__ — --- - -- - -—.^-^^.^^-, 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 21. Calculated Dynamic Surface Tensions Percent Acetic Acid Solution. for 1.0 vol. 0 62 cn >- 60 z 58 0 u) zI 54 IL u) 52 0 40 80 120 140 200 240 APPARENT AGE, MICROSECONDS Figure 22. Calculated Dynamic Surface Tensions Percent Acetic Acid Solution. for 5 vol.

-39 E I. 58 8 -— I i 10 VOL % ACETIC ACID 56 54 --- o RUN 476 RUN 492 A RUN 477 RUN 493 46 El__~ __ _____ _ ___ RUN 478 * RUN 486 A RUN 487 44 - -- — lflola k Ark'0 40 80 120 160 200 Z40 APFARENT AGE, MICROSECONDS Figure 23. Calculated Dynamic Surface Tensions for 10 voL Percent Acetic Acid Solution, a I4 Iu U^ Wj a I0 VOL% ACETIC ACID -A 50 46 _ 44, ) — /13 0 RUN 520 42, -- A RUN 521. El RUN 522 As 40 80 120 140 200 240 APPARENT AGE, MICROSECONDS Figure 24. Calculated Dynamic Surface Tensions for 10 vol4 Percent Acetic Acid Solution.

52 03 14 VOL. % ACETIC ACID, 50 z 48 46 La 44 Figure 25. Calculated Dynamic Surface Tensions for 14 vol. Percent Acetic Acid Solution.

E 50 0 z44 ZI a 40 0) z 44 0I42 40 cI)4 18 IVOL % ACETIC ACID............., RUN. 452 ~ RUN 453........ _I I. ~ A A ) 40 80 IZO 160 200 240 APPARENT AGE, MICROSECONDS Figure 26. Calculated Dynamic Surface Tensions for 18-vol. Percent Acetic Acid Solution. E48 0 m 46 w z C. 44 z 0 z42 w I-. w 0 40 38 cn 38 25 VOL % ACETIC ACID _______ ________ A __a_____. 0 RUN 474 A RUN 475 * RUN 481 ________ ________ RUN 482 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 27. Calculated Dynamic Surface Tensions for 25-vol, Percent Acetic Acid Solution.

78 76 X 74 U /) w z 72 z 70 - 68 w U e: 66:) 64 62 I I I I r I I I I I 0.003 M K C03 I I 0 0 0 RUN 443... —-- A RUN 442 El RUN 538 0 RUN 539 0 40 80 120 160 200 APPARENT AGE, FL SEC Figure 28. Calculated Dynamic Surface Tensions for 0.003 M K2CO3 Solutions. 240 74 72 2 u,, 70 1 z C 68 z 0 en z 66 u w u 64 L0: c" 62 60 0 40 80 120 160 200 APPARENT AGE, / SEC Figure 29. Calculated Dynamic Surface Tensions for 0.010 M KCCO3 Solution. 240

-43 E () z LJ 0 0 IU tD 0.030 M K2CO3 72 70 68 $~^ O l0 RUN 436 ___________________ __A RUN437 66 ---- ---- ---- ---- -------- 0 RUN542 A RUN543 C ___ — — _4- -____ _ 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 30. Calculated Dynamic Surface Tensions of 0.030 M K2CO3 Solution. E IT z z 0 C-:) 7 0 f _ _ _ I I - - 0.10 M K2CO0 72 A 68 66 64 ------ - 0 RUN 438 62 ---- --- --- --- ___ _________ A RUN 439 El RUN 544 O RUN 545 60.I —-—. - 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 31. Calculated Dynamic Surface Tensions of 0410 M K2C03 Solution.

E 76 0 () w 74 z Z 72 0 IIt I O 68 Uto 66 0.24 M K2CO03 0 ________0 RUN 440 RUN 44 _ 0 40 80 120 160 APPARENT AGE, MICROSECONDS 200 240 Figure 32. Calculated Dynamic Surface Tensions of 0.24 M K2C03 Solution. 74 E 0 C) z Z C z 0 () z Id IId 3 U) 72 70 68 66 64 62 60 0 60 80 120 160 200 APPARENT AGE, MICROSECONDS Calculated Dynamic Surface Tensions of 0.30 M K2C03 Solution, 240 Figure 33.

E U) z LJ (0 76!',.. -, -, -I 0 RUN 548 I VOL /o GLYCEROL A RUN 549 ___ ___ 7 O RUN 458' 0 RUN 459 72 70 68, 66 __ _ 64 62 __-. — 0 40 80 120 160 APPARENT AGE, MICROSECONDS Calculated Dynamic Surface Tensions for Glycerol Solution. 200 240 Figure 34. 1 vol. Percent z I rr (0 76 -------- 0 RUN 550 10 VOL% GLYCEROL A RUN 551 74 0 RUN 460 0 RUN 461 72 _ 70 68 66__ _ 4 E 4- 3 6~_6.._.. —--- -------- -, -_ -- z~ J........... "0 40 80 120 160 200 APPARENT AGE, MICROSECONDS Figure 35. Calculated Dynamic Surface Tensions for 10 vol. Percent Glycerol Solution. 240

-46 E 72 0 z. 68 z 0 z 66 LU I. u 64 n 62 I 18 VOL % GLYCEROL --- -I..-... —- -. 0 RUN 462 A RUN 463 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 36. Calculated Dynamic Surface Tensions for 18 vol. Percent Glycerol Solution. E 72 0 w 70 z 0 z 68 o 0 w 66 Iw < 64 LL n 62 b ~\i3~~ | ]20 VOL % GLYCEROL A \ _- - _ ____. f _- 4.-___. I 1__ ___ _______'b I 1i1 l' Ai s__ \ Al -___._____________ _ 0 RUN 552 RUN 553 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 37. Calculated Dynamic Surface Tensions for Glycerol Solution. 20 vol. Perce

2 70 U) w, 68 0 66 w 64 IJ S 62 U) 60 i I I I 0.001 VOL % BENZENE AA_ 0 RUN 556 a RUN 557 0 40 80 120 160 200 240 Figure 38. APPARENT AGE, fLSEC Calculated Dynamic Surface Tensions of 0.001 vol. Percent Benzene Solution. 72 I70 r) 0 68 z 0 ) 66 Z I o 64 n u 62 60 I I I 0.01 VOL % BENZENE A _____A_____ ___ ___ ___ ___ _______________~Q- - 0 RUN 554 A RUN 555, —I.. - 0 40 80 120 160 200 240 APPARENT AGE, {/SEC Figure 39. Calculated Dynamic Surface Tensions of 0.01 vol Percent Benzene Solution.

72 70 E C) w z 0 cn z w C() 68 66 64 62 60 0.045 VOL /% BENZENE a.... ( RUN 558 RUN 559 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Calculated Dynamic Surface Tensions for 0.045 vol. Percent Benzene Solution. Figure 40.

is no doubt a valid criticism for the more concentrated solutions of glycerol and potassium carbonate because of their increased viscosities, On the other hand, the physical properties of the very dilute solutions are almost identical with those of the triple-distilled water with which the calibration was obtained., thus there is no reason to question its validity for these solutions. Unquestionable increases in calculated surface tension are observed even with very dilute solutions. More basically, it was assumed in calibrating the orifice that the dynamic surface tension of the triple-distilled water must undergo no change as it proceeds along the jet. As noted in Section II-B the uncorrected surface tensions calculated from the water measurements consistently decrease with increasing distance from the orifice. To compensate for this the empirical calibration applies successively larger corrections to each node along the jet. If by virtue of contaminating solutes, molecular rearrangement, or other poorly understood effects, the actual dynamic surface tension of the water jet were to decrease with increasing distance from the orifice, then the calibration would be in error, and the calculated surface tensions would be overcorrectedl For liquids whose rates of dynamic surface tension lowering were less rapid than that for water, use of the empirical correction factors would result in apparent increases in surface tension along the length of the jet. b) Secondly, one may accept that the dynamic surface tension of the aging jet surface truly increases as the liquid moves away from the influence of the orifice. As discussed in Section II-B one such influence

might consist of abnormal solute distribution due to contact with the orifice wall. Redistribution of solute when the jet leaves the orifice could conceivably result in an increase in surface energy. Potential fields from electrokinetic effects at the orifice (Section II-B) could also lead to increasing surface tension along the jet. Unfortunately these phenomena are not well enough understood to permit discussion of their feasibility. c) Thirdly, another likely explanation for the observed increases in surface tension in. these two component systems is the inability to maintain an undisturbed "skin" of aging liquid moving along the surface of the jet over its entire length. As evidenced by the several runs exhibiting orthodox decreases in surface tension, it is apparently sometites possible to obtain the desired aging "skin" over the measured portion of the jet. However, a number of other runs yield decreasing surface tensions for several nodes, followed by a series of nodes for which the surface tension increases. It is probable that on these jets the aging skin exists over the first several nodes, while further out on the jet it becomes unstable, permitting fresh liquid from the jet to contaminate it. A third type of surface tension curve displays increasing surface tension from the first node onward. One must conclude for these runs that instability of the surface skin occurred at least before the second node. Surface instability with its attendent increase in surface tension (Marangoni effect) might arise from, radial velocity components in the jet liquid, turbulent liquid motion, or expansion of the surface

-51 area due to axial deceleration of the jet. Rayleights model for the geometry of the oscillating jet in his original derivation of the surface tension equation (Appendix A) implies an expansion and contraction of the jet surface as the liquid passes through each nodeo If this geometrical model for the jet is accurate (which one assumes when using any of the equations based on Rayleigh's analysis) then one cannot hope to measure dynamic surface tensions corresponding to an aging undisturbed surface, In the absence of other disturbing influences, one might expect to obtain surface tension values corresponding to Figure 41, Partial renewal of the expanding surface at each node results in a series of upsurges in the surface tension curve, with a cyclic equilibrium being reached at some intermediate surface tension. The severity of the upsurge should decrease with decreasing wave amplitude, so that only by employing extremely small wave amplitudes would it be theoretically possible to closely approximate the true dynamic surface tension curve, Although any tendency of the jet towards turbulence or surface instability most likely originates from entrance effects at the orifice, it has not been possible to correlate the non-ideal jet behavior to liquid rate, This'undoubtedly results from the rounded shape of the orifice section, The two sets of jet outlines in Figure 42 depict the range of jet shapes observed leaving the orifice. It is apparent that the shape of the jet separation from the orifice determines to a large extent the nature of the orifice effects, Unfortunately, the factors influencing separation of such free liquid surfaces are poorly understood(24 103) so that it is impossible to predict the surface stability from knowledge of liquid rate, etc.,

i z z \ w I-L w Q: La.I O <) UNDI! Figure 41. I ro I TIME s Effect of Expanding Surface on Dynamic Surface Tension on Oscillating Jet.

.55^ Flow Figure 42, Shape of Jet Leaving Orifice. While the orderly expansion and contraction of the jet perimeter does interfere with the aging of the surface, it does not explain the observed increases in surface tension, It is not difficult to imagine that such periodic migration of liquid to and from the changing surface at early nodes could eventually develop into turbulence which circulates more and more fresh liquid to the surface at later nodes, Nevertheless, it is difficult to explain the steepness of the surface tension curve for one percent glycerol solution, Figure 345 The static surface tension for this solution is only one-tenth dyne per cm. lower than that for water, so that no measurable change in surface tension should be expected, regardless of the behavior of the liquid surface. Evidently factors other than disturbance of the liquid skin on the jet are involvedo

d) A fourth possible cause for the increase in dynamic surface tensions observed with the oscillating jet may be desorption of dissolved gas from the jet. Due to the operation of the constant head reservoir the liquid in the system probably becomes saturated with air at several psig. pressure shortly after the flow has been started (see Section II-B). Upon issuing from the orifice the liquid suffers a drop in pressure, which probably results in rapid desorption of air from the liquid at the surface. Lowering of the gas solute concentration will normally be accompanied by an increasing surface tension. In this respect it is significant that in every instance where a decreasing surface tension curve is encountered, it corresponds to the initial run following start-up of the jet, whereas later runs from the same reservoir of solution invariably show increasing surface tension curves. This would occur if the measurements for the first run were obtained before the gas content of the solution became excessive. It is also interesting to note that such curves with decreasing surface tension are found only in the series of runs numbered from 500 higher. In this "500" series, measurements for the first run were often begun almost immediately after starting the liquid flow. In the'400" series, on the other hand, the flow was allowed to "stabilize" for at least one half hour after each start-up before taking any measurements, No curves with decreasing surface tension are found in the''400o" series of runs. Although the effect of dissolved gases on surface tension values of aqueous solutions is not well known(23) it is not unreasonable to expect the supersaturated liquid near the orifice to have quite

-55 a low surface tension. In effect then, those curves in Figures 19 through 40 may actually represent the rates of dissolution of air from solution, and its effect on the surface tension, If the presence of dissolved air in liquid were responsible for surface tension changes of the magnitude observed in Figures 19 through 40, then the assumption of non-changing surface tension for the distilled water calibration runs would be quite inaccurate. It would then be necessary to know the rate of surface tension increase due to air desorption from water before calibration of the orifice could be achieved. Comparison with Froth Properties Because of the above difficulty in interpreting the dynamic surface tension curves from the micro-orifice, it is impossible to make any valid comparison of surface tension rates with frothing properties for the four series of solutions investigated. The significance which one attaches to any particular confrontation of the froth data against the oscillating jet results depends wholly upon which of the above explanations one is inclined to favor. Obviously, if one accepts the premise that the apparent surface tension increases are not real, resulting only from the use of an incorrect calibration, then a comparison of the data becomes meaningless. If on the other hand one is willing to assume that the calibration is sound, so that the observed increases in surface tension do in fact occur on the jet surface, then some interesting observations can be made.

In Figure 43 the average slope of the surface tension vs time curves for each acetic acid solution is plotted versus acetic acid concentration, If surface agitation is occurring in the jets, then the rate of surface tension increase, as determined by this slope, may offer an index to the relative magnitude of the Marangoni Effect expected for each liquid. Use of these surface tension rates involves the somewhat naive assumption that the severity and nature of the surface disturbances along the jet are similar for each run, regardless of differing liquid properties or liquid velocity, and that these disturbances are comparable to those experienced on the surface of a liquid froth film. No conclusions concerning the spontaneous surface tension decrease during aging can be deduced from these slopes. In Figure 43 the apparent rate of surface tension increase for acetic acid solutions passes through two maxima, one near ten percent concentration and another in the vicinity of 0.01 percent. Because of the rapid rate of surface tension rise at these concentrations, if the surface of each froth film, is in constant agitation, as suggested by Burcik(33) (Section II-A), then these films should have large effective surface tensions due to partial replacement by interior liquid, thereby decreasing the efficiency of the Marangoni Effect, When the maximum froth expansions for acetic acid solutions are plotted versus concentration, it is observed that the froth expansion also passes through a maximum near ten percent acid concentration, Maximum froth expansion is determined by taking the reciprocal of the minimum froth density for each liquid in Figure 14. Because it is suspected that frothiness is enhanced by a strong Marangoni Effect, the coincidence of

-57 32,000 -- 16 28,000 14 U c) I co - \ U0 Z / \ N > 20,000 ---------- 10. //2 4 2,, ^ ^ oS,,W I 16,000 -- 8 0 / \ 0 j 12,000 6 —-- 6 lU 4 4000 2 0 0 0 4 8 12 16 20 24 28 PERCENT ACETIC ACID BY VOLUME Figure 43. Comparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tension; Acetic Acid Solutions.

-58 these peaks suggests that the surfaces of the acetic acid froth films may not be in continuous agitation but are instead static, A similar relationship possibly exists between rate of surface rise and froth expansion for aqueous solutions of benzene, Figure 44, Although only minor differences of questionable significance are encountered in the froth expansion values for the benzene solutions studied, a possible maximum in the froth expansion curve is indicated at the same concentration where the maximum in surface tension rate occurs, It is difficult to make any such comparison for the glycerol solutions because of the limited data, The dashed curves in Figure 45 have been drawn through the data in such a way as to give surface tension rate and froth expansion curves having the same general shape as those of Figures 43 and 44. It is not difficult to visualize curves having their maxima at the same low concentration, Since acetic acid, benzene, and glycerol cause lowering of the surface energy they are all positively adsorbed at the liquid surface, although to widely differing extents. Potassium carbonate, on the other hand, is negatively adsorbed at the surface because of its role in increasing the surface energy. For this reason it is interesting, when comparing the rate of surface tension rise and froth expansion curves for potassium carbonate solutions Figure 46, to observe that maximum frothiness occurs when the rate of surface tension rise is minimal. Why the difference in adsorption might lead to this difference in froth response is not understood. Because of the low rate of surface tension increase at the concentration of maximum

-59-. 20000 (0 w 16000 -------------------------------- 2 z 8 12000 U..i 4000 0 W % 4000 0 0.006 0.016 0.024 0.032 0.040 0.048 PERCENT BENZENE BY VOLUME Figure 44. Ccparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tension; Benzene Solutions.

-60 56000 0C w E.) Z c,) w v: C3 0o z Lw n, w LJ Ir 0 z z 0 U) z U. < U. 0 I-. 41 48000 40000 32000 24000 P'"~^N -1 ____/ "X _ -RATE OF INCREASE_ I I I \. \ \~[ -# - ft 11. l I / I I %... —.\,o i.I... %ft.4 "!, I... Ift — ft FRO I — 11., THIJVEss,IN-. I I / / / I I, 8000 0 % % % 0 4 8 12 16 20 PERCENT GLYCEROL BY VOLUME Figure 45. Comparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tensionj Glycerol Solutions.

28,000 14 U i 24,000 cn u) IJ a z c 20,000 w coC U Z 16,000 z U t-,, 12,000 Co nIL 0 8000 4L 4000 12 10 N N 8 0 u, x w 6 0 I]E X 2 4 4 2 0 I I P,,. I..I I I I I I I I I I 1 0 0 0 005 0.10 0.15 0.20 0.25 0.30 0.35 0.40 MOLES PER LITER OF K2CO0 Figure 46. Comparison of Frothiness with Indicated Rate of Increase in Dynamic Surface Tensionj K2CO3 Solutions.

-62 frothiness the K2C03 solution should suffer only a slight increase in surface tension when agitated continuously, so that the Marangoni Effect would lose little of its effectiveness. Thus unlike the results for the positively adsorbed solutes, the K2CO3 froths give no indication that the surface of the froth films cannot be in constant agitation. Curves of surface tension versus time for ten percent acetic acid solution to which small amounts of ferric chloride had been added are plotted in Figures 47 and 48. The slope of the curves for the solutions with the ferric salt additions appears significantly lower than that for ten percent acetic acid without salts (dashed curve, Figure 47), From Figures 47 and 48 then, one should expect a decrease in frothiness if small amounts of ferric chloride are added to ten percent acetic acid solution. Although the effect of adding controlled amounts of ferric chloride to liquids in the frothing column was not studied, it was consistently observed that contamination of the frothing liquid in the column by entrainment caused marked decreases in frothing. Severely contaminated liquids exhibited an orange color indicative of dilute ferric salts. As pointed out earlier, it is also possible that the apparent rate of surface tension increase observed with the oscillating jet may in reality be a measure of the rate of desportion of air from the jet surface. If outward diffusion of the air through the liquid to replace that which has desorbed from the surface is considered to be the ratecontrolling process, then a rapid decrease in air concentration at the surface (i.e., a rapid increase in surface tension) suggests a slow

-65 E 54 UC) w 52 z C)' 50 z 0 (n z 48 LJ IC 46 IL m 44 10 VOL% ACETIC ACID +0.005 M FeCIs I _RUN 48 A RUN 489 --— CURVE FROM FIG. 23 _ _ _ _...... _ _ _ _...... I I.. 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Figure 47. Calculated Dynamic Surface Tensions for 0.005 Molar FeCl3 in 10 vol. Percent Acetic Acid Solution. E m 52 z C. 50 z 0 c) z 48 Iz I-. IAJ o 46 4.< C),a CO Ad 10 VOL % ACETIC ACID + 0.020 M FeCI3 0. ]~^^ ~ A _________________A^"^__________________________l___l_ I I ( RUN 490 RUN 491 4 0 40 80 120 160 200 240 APPARENT AGE, MICROSECONDS Calculated Dynamic Surface Tensions for 0. 020 Molar FeC13 in 10 vol. Percent Acetic Acid Solution Figure 48.

-64 diffusion rate in the liquid. Conversely, high rates of diffusion in the liquid jet should result in more gradual declines in the surface concentration, hence should yield lower rates of increase in surface tension along the jet. In this view then, Figure 43, 44, and 45 indicate that in positively adsorbed solutions frothing is enhanced by low rates of gas diffusion through the liquid, while Figure 46 suggests that frothing in negatively adsorbed K2C03 solutions is more pronounced when the gas diffusion is rapid. While gas permeability of the liquid film is important to the stability of foam films, it is uncertain whether such permeability is significant in unstable frothing. In Figures 19 through 40 the dynamic surface tensions are plotted versus the "apparent" age of the jet. Calculation of the apparent age assumes plug flow in the jet, so that the age at any distance, z, from the orifice is tapp = Z/c More accurately, because of the non-uniform velocity profile, the age of the jet surface at z should be z t a f td (1) ts - (g 0 Bohrls(27) equation for the velocity distribution through a free liquid jet permits the surface velocity to be expressed as -7. 15(e ) (2 cs = c - Ae p 2)

In Section II-B calibration of the orifice with triple-distilled water provides an empirical approximation of the constant A for each run. Integration of Equation (1), utilizing Equation (2) leads to 2 -7r 715 ( ts tpp + 2p in c-Ae 3 (3) 7. 15 ln c-A Using the surface ages estimated from Equation (3) as the abscissa, the surface tension curves for 0.01 percent acetic acid are replotted in Figure 49. It can be seen that although tapp of the first node is almost identical for each of the three runs, ts for the first node increases with decreasing liquid rate for each run. As indicated in Figure 49 then, if it can be assumed that no appreciable increase in surface tension due to turbulence occurs before the first node for each run, then it should be possible to approximately determine the rate of spontaneous decrease in dynamic surface tension for the undisturbed aging surface of the 0.01 percent acetic acid solution. Indication of the rate of surface tension for several of the other solutions were obtained from similar plots of first node values versus surface age, Figures 50 through 65, In some instances it was possible to use values from the first two nodes of the jet. Obviously, considering the small number of runs for each solution, and the inherent inaccuracy at the first node, as well as the necessity of assuming no surface disturbances on the jet prior to the first node, the dashed curves indicating the change in surface tension with age must be recognized as grossly approximate. Even so, the data for acetic acid suggest that unless the liquid rate is quite

-66 72 I-II. L~~~~, - 0.01 VOLI ACETIC ACID 0.01 VOL% ACETIC ACID 70 I --- n- J — - - 0 E 0 V) w z If) z ILJ () \rn \11,1 3 — I A & I - __ ___ I - -.- i S - I z< ---------— \ —- -— t- I — I ll |\ l | |0 RUN 513 L=0.68 60 -lV _ _ i \ _ I| \ A RUN 514 L=0.76 _ 3 RUN 515 L = 0.82 cI I I, I — I- -I "V0 40 80 120 160 200 240 SURFACE AGE, MICROSECONDS Figure 49. Calculated Surface Tensions as a Function of Surface Agej 0.01 vol. Percent Acetic Acid.

74 u UJ w z z 0 u) z Iw U Ca u) 72 70 68 66 64 I I I | \ |O.1 VOL% ACETIC ACID \ 0 RUN 516 \ L'0.70 A RUN 517 La 0.80 --.. I - 68 u w z I 66 0 64 * 62 w U W: 60 70 1.0 IVOL% ACETIC ACID \ %X SX _ RUN 518 L__LO.72 A RUN 519 L 0.80 I, I I I 62 58 0 40 80 120 0 40 80 120 SURFACE AGE, /LSEC SURFACE AGE,,SEC Figure 50. First Node Surface Tensions as a Function of Surface Age; 0.1 vol. Percent Acetic Acid. Figure 51. First Node Surface Tensions as a Function of Surface Age; 1. vol. Percent Acetic Acid. 52 U) w 0 Q z 0 U) z w w U U) 50 48 46 44 42 _ _ -\ m ||)I0 VOL % ACETIC ACID \^ \ A 0 RUN 492 La0.71 * RUN 493 L=0.81 \ 0 RUN 520 L=0.62 A RUN 521 L=0.71 - 3 RUN 522 L=0.59 \ ( RUN 476 L 0.66 ___ A RUN 477 L=0.79 \ Il RUN 478 L0.86,,. RUN 486 La0.70 - A RUN 487 L=0.78 i l I... 40 38 0 40 80 120 160 200 240 Figure 52. SURFACE AGE,,LSEC First Node Surface Tensions as a Function of Surface Age; 10 vol. Percent Acetic Acid.

-68 52 E u w z n, z w Icr n C4i LL. E P-) U) w z 0 w fU) 18 VOL/o ACETIC ACID 50 48 - 46 I 44 _- - 0 RUN 452 L=0.76 42 RUN 453 L=0.84 401 0 40 80 120 SURFACE AGE, MICROSECONDS SURFACE AGE,MICROSECONDS Figure 53. First Node Surface Tensions as a Function of Surface Age; 14 vol. Percent Acetic Acid. Figure 54. First Node Surface Tensions as a Function of Surface Age; 18 vol. Percent Acetic Acid. E U V) z a (n z Z U),. (n 25 VOL/o ACETIC ACID 46 44 42 -..^ 0 RUN 474 L=0.73 A RUN 475 L-0.79 * RUN 481 L-0.66 A RUN 482 L=Q72 38 I I 0 40 80 120 160 SURFACE AGE, MICROSECONDS Figure 55. First Node Surface Tensions as a Function of Surface Age; 25 vol. Percent Acetic Acid.

U (0 70 - 68 - 66-0 RUN 443A RUN 442 \ E] RUN 538 64 0 RUN 53962 --- I -_- I.J. E To..El ODI M 68 \ \ I 66 - \ * 64 62 0 RUN 433 A RUN 434 l RUN 435 60- * RUN 541. * RUN 540 \ 58., -0) 40 80 120 ftl 40 80 120 SURFACE AGE, MICROSECONDS SURFACE AGE, MICROSECONDS Figure 56. First Node Surface Tensions as a Function of Surface Agej 0. 003 M K2C03o Figure 57. First Node Surface Tensions as a Function of Surface Agej 0.010 M K2CO:3 E U)!i 74 14............ —-. I 0C3 M K2CO0 72 N \ 0 RUN 436 A RUN 437 64 RUN 542 \ A RUN 543 62_ __ E. I 74 - 0.10 M KCO, 72 70 -- -, — - - A \0 68 - -- \ 0 66 - 0 RUN 438 \ A RUN 439 \El _El RUN 544 __ 64\ 0 RUN 545 \ 62 ---- — 0 40 80 120 — 0o 40 80 120 SURFACE AGE, MICROSECONDS Figure 58. First Node Surface Tensions as a Function of Surface Age; 0 03 M K2C03. SURFACE AGE, MICROSECONDS Figure 59. First Node Surface Tensions as a Function of Surface Agej 0.10 M K2CO3

-70 76 x 74 o 0 (n' 72 0 z " 68 I 66 64 64 I I 0.24 M KzCO3 \I \ 0 RUN 440 \ A RUN 441 I I 74 U I 0 z z iJ, w u U n) 72 70 68 66 64 I VOL % GLYCEROL I \ o RUN 548 \ A RUN 549 0 RUN 458 \ E RUN 459 I I I I I 0 40 62 80 120 0 40 80 120 SURFACE AGE, p.SEC Figure 60. First Node Surface Tensions as a Function of Surface Age; 0.24 M K2CO3. SURFACE AGE, /LSEC Figure 61. First Node Surface Tensions as a Function of Surface Age; 1 vol. Percent Glycerol. 2 C-) w z O Z 0 w w n IL 72 IOVOL%GLYCEROL 70 68 66 64 \ 0 (A 0 RUN 550 A RUN 551 l RUN 460' 0 RUN 461 I I 74 2 un 72 w z 0. 70 z 0 0 Z 68 w w u 66 64 \ \ \ _0 RUN 552 _-\ A RUN 553 5 IJ I I \ I 20 VOL % GLYCEROL 62 0 40 80 120 0 40 80 120 SURFACE AGE,,L SEC Figure 62. First Node Surface Tensions as a Function of Surface Age; 10 vol. Percent Glycerol. SURFACE AGE, /SEC Figure 63. First Node Surface Tensions as a Function of Surface Agej 20 vol. Percent Glycerol.

UJ w 0 V) 0 cc z )e Q. U) z 4 U) 0 O Iw (0 z r) z t 0 I. O I N N 8 2 O 0 X IL 6 0 Ix 4 2 PERCENT ACETIC ACID BY VOLUME Figure 64, Ccmparison of Frothiness with Indicated Rate of Decrease in Dynamic Surface Tension; Acetic Acid Solutions.

-72 52 a U) 50 Zw z 0 2 48 0 w 46 I1U 44 L: 42 10 VOL % ACETIC ACID+ FeCI l O.005M FeCI, 0.020M FeCI \ 0 RUN 488 L0.71 - * RUN 490 L0O.78 \ A RUN 489 L*0.78 A RUN 491 L~0.72 " 0 40 80 120 160 200 SURFACE AGE, A SEC Figure 65. First Node Surface Tensions as a Function of Surface Agej 10 vol. Percent Acetic Acid with Ferric Chloride Additions.

high, the values at the first nodes give a good estimate of the dynamic surface tension. In Figure 64 the rates of dynamic surface tension lowering in Figures 49 through 63 are compared with the frothiness of acetic acid solutions. The indicated rate of dynamic surface tension lowering appears to be maximum near 0.1 percent concentration. Maximum frothiness occurs in acetic acid solutions at approximately ten percent. There are insufficient data for the K2C03, glycerol, or benzene solutions to permit comparison of their rates of surface tension lowering with frothiness. It is interesting to note that the rate of surface tension lowering in the ten percent acetic acid solution does not, within the accuracy of the measurements, appear to be changed appreciably by small additions of ferric chloride, First node surface tensions for the acetic acid-ferric chloride mixtures are plotted in Figure 65. The dashed curve in Figure 65 is the same curve as in Figure 52.

F. CONCLUSIONS An oscillating jet technique for measuring dynamic surface tensions was developed using a 0.00179-inch diameter orifice, one-eighth the size of any orifice reported previously. This allowed measurements of dynamic surface tensions at 30-microsecond intervals, compared to about 1000 microseconds for the shortest intervals found in the literature. Although calibration for water was obtained it was not possible to develop one valid for organic liquids covering a range of physical properties. This is believed due to the poorly understood flow pattern at the orifice exit, which makes an accurate mathematical analysis difficult. For use with the minute orifice, the Rayleigh Equation for the oscillating jet was modified to z 2 Xr - - 2 r r(z)I2(kr) / r 2 1,r 2 Or21,r 2 1 Or 2 Or 2 2 k I (kr) vl+() +7() l+ + ) ( t 2 )r 2 1 2 (r)r)2 2 rz wz r2 on az 6a which was integrated on an IBM 704 digital computer. The oscillating jet was still inadequate for accurately measuring the desired small rapid decreases in dynamic silrface tensions. The oscillating jet apparently introduces a turbulence which forces fresh liquid to the surface from the jet interior, giving a surface which does not age in the same manner as would a quiescent, normally aging surface. Using the calibration from distilled water measurements, the apparent surface tensions for aqueous solutions were foumnd to increase

along the length of most jets, with only a few runs showing the normally expected spontaneous decrease in dynamic surface tension, It is thought that these increases result from turbulent renewal of the liquid surface. The assumption that surface tension-turbulence relationships on the jet are indicative of the surface tension behavior on agitated froth films leads to the conclusion that solutions of positively adsorbed solutes whose surface tensions increase rapidly, due to introduction of bulk liquid to the surface by agitation, show good froth ability. Conversely, negatively adsorbed solutions appear to froth more readily when the surface tension is changed only slightly by surface agitation. If the observed increases in dynamic surface tension are due to desorption of air from the jet surface it can be concluded that low rates of gas diffusion in the liquid are beneficial to froth formation in positively adsorbed solutions, while rapid diffusion rates appear to enhance frothing in negatively adsorbed solutions. The actual rate of spontaneous dynamic surface tension lowering for aqueous solutions can be approximated from the measurements at the first node on each jet using surface ages estimated from the velocity distribution along the jet. Data for acetic acid indicate that maximum frothiness occurs at an intermediate rate of dynamic surface tension lowering. The data for the potassium carbonate, benzene and glycerol solutions do not permit an accurate estimate of the rate of surface tension lowering. Slight additions of ferric chloride cause apparent decreases in the rate of dynamic surface tension lowering in acetic acid, solutions,

-76The rate of surface tension rise due to turbulence on the jet also decreases with ferric chloride additions, as does the frothiness of the solutions.

PART II THEORY AND EQUIPMENT -77

A, FROTHING STUDIES 1. PREVIOUS WORK AND THEORIES PREVIOUS FROTH STUDIES Most investigations on the formation of bubbles concern either single orifices or comparatively low gas rates, therefore are of little value in estimating conditions in an aerated froth. Axelrod and Dilman(1O) have derived an equation relating froth density above a sieve plate with perforation size, gas rate, and liquid density and surface tension. Since the derivation assumes spherical bubbles having uniform equilibrium bubble size and free-rising velocity, it too is valid only for low gas velocities. Several investigators have shown that the bubble-size distribution at high gas rates in experimental columns using single orifices(l~5) and porous plates(90), conform reasonably to a normal probability distribution. Bubble size distribution from vertical slots under water were studied by Spells and Bakowski(16). The problem is complicated by the strong influence on bubble formation exerted by the geometry of the system. (43,91,173 ) Frothing observations in aerated liquids are usually reported in one of the following manners: Froth Height - the total height above the tray, or disperser, attained by the frothing mixture. This was the most common method of reporting frothing in the early studies of distillation and absorption columns. Since the depth of the clear liquid (the depth of the same

quantity of liquid if it were not aerated) was not usually reported, these froth heights gave little information about the nature of the froth. Relative Froth Density - the weight of the aerated mixture relative to that of an equal volume of the unaerated liquid. The ratio indicates the fraction of the mixture consisting of liquid. If Zc is the clear liquid depth, and zf is the total froth height, when pg < pL L 9g L the relative froth density is I -= zc/zfo At very low gas rates, the froth may exist as a "raft", or second phase, floating on top of the almost undisturbed clear liquid(9 7) Crozier(4) has shown that even at high gas velocities the froth above a bubble-tray may be "stratified", exhibiting a region of constant density at the top, an intermediate zone of increasing density with a dense bottom layer consisting of liquid pierced by gas jets. The results of many froth investigations are reported as relative froth densities. The reciprocal value, zf/Zc, called the froth "expansion'l is sometimes used. Gas Content -- that fraction of the aerated mixture which is gas, expressed as (zf-zc)/zf = 1 -. The reciprocal of the gas content, the volume of foam per volume of gas, has been termed the "degree of continuity" by one investigator. (3, 31) Gas-Liquid Ratio -- the volume ratio of gas to liquid in the froth, expressed as (zf-zc)/z 0 1/0 - 1L Data on frothl properties available in the literature are of a limited nature. Souders, et al(5) presented froth height data for water, kerosene and a light lubricating oil, obtained in a 12-inch I.D. experimental column in which air was bubbled through the liquid on a

single-cap bubble tray. The data cover a temperature range from 65~ - 200~F with air rates up to 43, ft, per sec.. Froth data for kerosene and air or natural gas in a 2-inch diameter column with a single bubble cap are given by Ashrof, et al.(9) Houghland and Schreiner(89) have reported froth heights obtained by passing air through static beds of water in a 6-inch I.D. glass column. Clear liquid depths of 10, 20, and 30 inches were employed with air rates from 0.1 to 2.0 ft. per sec. Ragatz and Baxter(127), in studying the cause of increased absorber efficiencies with increased vapor loading, frothed light absorption oils in a 1 1/2-inch diameter plastic column. Absorber discharge gas at 50, 100, and 200 psig was bubbled into the oils through perforated plates with varying orifice sizes. Their data indicate that froth behavior is influenced more by the superficial gas velocity in the column than by the "jet" velocity of the gas leaving the orifices. Warzel(178), Ashby(8), and Begley(16) have reported froth heights on a 13 x 7.5-inch rectangular absorber tray containing nine small bubble-caps. In Warzel's studies, air was passed through tap water, in Ashby's work the liquids were water, isobutyl alcohol and methyl isobutyl ketone, while the gases were air, helium, nitrogen, and Freon 12, Begley investigated the passage of nitrogen gas through cyclohexanol and ethylene dichloride at various temperatures. Miller(lll) has reported froth data for air and aqueous ammonia solutions in the same absorber column using a "valve-tray" and a sieve plate with very large perforations.

-81 Gerster, et aL(70'71) have indicated the need for knowing froth heights in order to predict mass transfer efficiencies in bubbletray devices. They present a small amount of froth data for aerated water on a 13-foot tray section and a 13-inch diameter tray, both employing bubble caps, as well as some data by Bagnoli(ll) for aerated water on two different 13-inch diameter sieve trays. More air-water froth heights are reported for a long, narrow perforated tray by Foss and Gerster(63). Hutchinson and Baddour(93) give air-water froth data for a 27-inch diameter column with several'ripple trays"o Bailey, et al 12) aerated water, methanol and glycerine in columns ranging from 2 inches to 24 inches in diameter with and without a canvas dispersing plate. Verschoor(174) studied the froth densities of aerated beds of water, methanol and 42% aqueous glycerine in 55-mm. and 87.5-mm glass tubes using a sintered glass dispersero In a recent work by Houghton, et al.(90) six pure liquids, as well as sea water and several aqueous glycerine and acetic acid solutions were frothed with N2, 02 and C02 in a 3-inch glass tube using various porous discs as gas dispersers. Robinson and Gilliland(l39), as a result of observations by Klein(100) state as a rule-of-thumb that typical absorption and distillation bubble-tray columns will generate froths having relative densities of about one-third or higher. The froth data presented in Figures 66 through 7 indicate th a at this minimum density may be somewhat lower than 0.33.

z o C 0 L.U > 4 -~.J I..8.7.6 A.5 2 0o 1 2 3 4 5 6 0I SUPERFICIAL GAS VELOCITY, FT/SEC Figure 66. Relative Froth Densities of Air-Water Froths in Large-Diameter Columns. A: 13x7.5-inch rectangular, bubble caps; Warzel(178) B: Long, narrow tray, bubble capsJ Gerster(70) CS Long, narrow tray, perforated; Foss(63) Di 13-inch diam., perforated, wide centers; Bagnoli(ll) E: 13-inch diam., perforated, narrow centersj Bagnoli(ll) Fx 24-inch diam., no disperser; Bailey 12) G: 27-inch diam., single bubble cap; Souders(157)

-85 1.0 ------- 0.9 A J - 0.8 oz w X 0.7 0 U. C ol /-C w 0.6 w D —0.5 0.4 ---- 0 2 3 SUPERFICIAL, VELOCITY, FT/SEC. Figure 67. Relative Froth Densities of Air-Water Froths in SmallDiameter Columns. A: 2 1/2-inch Diameter, sintered disc dispersers Verscho r(174) B: 3-inch Diameter, sintered disc disperser; Houg hton 9 C: 6-inch Diameter, gas jet dispersersJ Houghland~00) D: 2-inch Diamter, canvas disperser; Bailey 12)

-84 Iz 0 I.LL Q0 U. 4 -J Icd 1.0.9.8.7.6.5 _____XKEROSENE -AIR, 2-IN. COLUMN (9).4 LIGHT ABSORBER OIL - GAS, 1.5-IN. COLUMN (127).3 l.3 -- -I ----------------------- * 0 I 2 3 SUPERFICIAL GAS VELOCITY, FT./SEC. Figure 68. Relative Froth Densities of Two Hydrocarbons in Small-Diameter Columns.

Effect of Vessel Geometry The importance of the geometry of the apparatus in which aeration occurs is indicated by Figures 66 and 67, in which froth densities of aerated water in a number of different devices are plotted as a function of the air rate. There is seen to be only occasional agreement between the results of the various investigatorso Of particular interest is a comparison between the froth heights in large-diameter columns, plotted in Figure 66, and those in small-diameter columns, plotted in Figures 67 and 68. In largediameter columns, with increasing air rate, the froth density consistently decreases, eventually approaching some minimum level. In smaller columns, however, the froth density curve is generally observed to fall off rapidly at low air rates until a minimum or plateau is achieved, Further increase in gas rate beyond this point is accompanied by the formation of "plugs" of gas which break up the froth as they riseo This causes the froth level in the column to rise and fall periodically, yielding either a constant average froth density at higher air rates, or a slight increase in density until some maximum or constant density is attained. According to Houghton, et al, (90) the formation of gas "plugs" results when the rate of bubble formation is greater than the rate at which gas can be carried away by the rising bubbles. The velocity of bubble rise in aerated froths has received some study (9o 98 y 7 5 ) As the gas velocity is increased further, the plug flow gives way to a region of turbulent or churning frotho Verschoor(174) attempted unsuccessfully to correlate bubble characteristics in this turbulent region using

the dimensionless relation suggested by Kaiszling(98): 4 2 Zivb ^ (Zf Zc g&t D2gp Ya Kzf p53 a where ti = liquid viscosity a surface tension Vb = bubble velocity and D = column diameter. Kaiszling's relation is based on the Reynolds Number, Froude Number and (91) Weber Number, Hughes, et al.(91) also report lack of success in applying dimensional analysis to the turbulent frothing regime, with attention again placed on Reynolds, Froude and Weber Number. The significance of these groups is detailed by Klinkenberg and Mooy (101) Dimensional analysis has also been attempted in the study of stable foam formation. (5 62) In view of the wide differences in froth density observed in Figures 66 and 67, it is interesting to note that Bailey, et al (12) found no difference in the froth behavior in tubes with and without a canvas gas dispersing plate at the bottom. They further observed no effect of column diameter on the froth density when diameters larger than six inches were tested. They observed lower froth densities in a two-inch diameter column. Miller also observed negligible differences in froth density between operation with a valve-tray: and a sieve-tray with large perforations. The curves of Miller and of Bailey, et al, are shown in Figure 69. These observations suggest that some of the differences in froth densities observed by the various authors may be attributed to differences in liquid cross.flow on the

-87 1.0 0.9 0.8 > 0.7 z Ia0.6 0, Iw -J0.5 0.3 0.2 0.2 6,12, AND 24 - INCH DIAMETER COLUMN, WATER - AIR, WITH AND WITHOUT CANVAS DISPERSER; BAILEY, ET AL (12). 13 7.5 - INCH RECTANGULAR COLUMN, AQUEOUS NH, -AIR, VALVE TRAY AND PERFORATED PLATE MILLER (11) 13 x 7.S - INCH REC~~~~~TANUA COLUMN, AQUEOUS N8,,-A~~ ~ ~~iR\ 0 I 2 3 4 SUPERFICIAL GAS VELOCITY, FT/SEC Figure 694 Relative Froth Densities in Various Columns,

plates. Certainly, the liquid rate across bubble trays in distillation and absorption columns influences the liquid hold-up and the froth density(8,16,111,158,178) In a detailed analysis of bubble-tray hydraulics, Hutchinson, et al. (94) have indicated that the placement of inlet and outlet baffles on the tray can strongly influence the buildup of froth on the tray, Evidence of this is shown by Begley(l6) who compares froth densities from his bubble-cap tray with and without splash baffles. The presence of the splash baffles causes higher froth densities, which Begley attributes to increased liquid depth on the tray as a result of increased resistance to liquid flow. Effect of Liquid Depth The effect of weir height on froth formation is apparent from Figures 70 to 72. Although the bubble size at orifices is not considered to be influenced appreciably by the liquid depth(91), the subsequent coalescence and/or break-up into smaller bubbles is probably appreciably affected. The work of Crozier(40) Spells and Bakowski (161) and Chu, et al(38) indicate the importance of liquid depth on bubble formation from bubble caps. Liquid turbulence, as influenced by the liquid depth, has an effect on bubble formation from orifice plates(l9'80o10:I159160'l6l1l73) Effect of Liquid Properties The role of liquid physical properties in the froth behavior of aerated liquids is not well understood, the literature offering contraditions and questionable conclusions concerning these properties.

-89 IV) z 2 Jr I bJ I.8.7 45 ______ ^ ^ 3-2-IN. WEIR 2-IN. WEIR.3.2 - I I — -- - -I I — I 2 SUPERFICIAL GAS VELOCITY, FT/SEC. 3 4 Figure 70. Relative Froth Densities of Water-Air System, for 13x7.5-inch A.I.Ch.E. Column. Data by Warzel(178) IC) z lI LU. Id IM LU, F:.7.6.5.3 _ _ _ _ _ _ _ _ 0 I 2 3 4 SUPERFICIAL GAS VELOCITY, FT/SEC. I Figure 71L Relatiye Froth Densities of Aqueous NH^-Air System, Data by Miller(111) for 13x7. 5-inch A.I.Ch.E. Column.

-90-.0) u. w LJ 1.0.9 - PARAMETERS: CLEAR LIQUID DEPTS.8.7.64 -..-.....- -. —5.4 _ 0 I 2 3 SUPERFICIAL GAS VELOCITY, FT/SEC. Figure 72. Relative Froth Densities of Air-Water Froths in a 6-inch Diam. Column. Data of Houghland and Schreiner09). iz o5 I u. w _J w 1.0 _6 — _ __ _ -.5 LIGHT UWBEOIL.3.2 -------- ^ KEROSENE.1~~~~~~~~~~~~~~~~~~~~.0 0 I 2 3 SUPERFICIAL GAS VELOCITY, FT/SEC. Figure 73. Relative Froth Densities of Several Liquids with Air in a 12-inch Diameter Column. Data of Souders, et al. 15 ).

At least three investigators appear to demonstrate that the gas hold-up in aerated liquids is independent of liquid physical properties. Quigley (124125) studied the effects of viscosity, surface tension, and density on the air hold-up from single orifices in a small mass-transfer column, employing water, carbon tetrachloride, and aqueous glycerine, concluding that the air velocity was the only important factor, Because of the low air rates and low gas contents studied, it is doubtful that his mixtures could be considered "froths". However, Bailey, et alo (12) observed no apparent effect of liquid properties in frothing water, methanol and glycerine over a wide range of air rates with and without a gas dispersing plate. Begley(16) also concluded that the physical properties of the liquid exert little influence on the froth height or froth density in a typical bubble-tray column. Comparing his froth data (nitrogen-cyclohexanol and nitrogen-ethylene dibromide) in a 13 x 7.5-inch rectangular bubble-cap column with data by Warzel(l78) (air-water), and Ashby(8) (air-water, helium-water, Freon 12-water, helium-isobutanol, nitrogen-isobutanol, and helium-methyl isobutyl ketone) in the same column, Begley showed that the froth height and froth density were primarily functions of gas rate and liquid depth. On the other hand, many investigators have observed appreciable differences in behavior of different liquids, although the reason for these differences is not always clear. Figures 73 through 75 show some typical results obtained by frothing different liquids in the same column. Seeliger(152) found that addition of small amounts of methanol to water caused a marked increase in frothiness, He attributed this to

-92 1.0 -.- - - 0.9 1 - \ \ - METHANOL z w 0 A 0.7 __ 42 % AQUEOUS GLYCEROL 0 0.1 0.2 0.3 0.4 0.5 0.6 SUPERFICIAL GAS VELOCITY, FT/SEC Figure. 74. Relative Froth Densities of Several Liquids with Air in a 55-mm. Diameter Column. Data of Verschoor(174)

-93 1.0 0.9 0.8 0.7 z w I I0 IL. It. w 0.6 0.5 0.4 0.3 0.2 0.1 100 % GLYCEROL WATER ETHYL ACETATE 100% ACETIC ACID / 37 WT % GLYCEROL ~ _______..0.1 WT % ACETIC ACID i i,, ~ Jl ~~~~IiJi 0 0.1 0.2 0.3 0.4 0.5 SUPERFICIAL GAS VELOCITY, FT/SEC Figure 75. Relative Froth Densities of Several Liquids with Air in a 3.14-inch Diam. Column. Data of Houghton, et al. (90)

the formation of smaller bubbles by virtue of the lower surface tension of the methanol solutions, Surface tension is known to influence the equilibrium size of bubbles formed in liquids (17,31 75) Verschoor(174) challenged the conclusion that surface tension is important in determining froth formation in aerated liquids, demonstrating that pure water and pure ethanol, although having widely different surface tensions, exhibit quite similar froth behavior. Verschoor concluded that kinematic viscosity is the important variable in frothing. This conclusion is also supported by some bubble observations. (146147) However, Eversole and Myers(59) obtained bubbles at low gas rates in ethanol and aqueous ethanol solutions whose size was independent of both surface tension and viscosity. Quigley(24 125) also observed no appreciable effect of surface tension or viscosity on bubble size. Effect of Gas Properties Some discrepancies also are reported concerning the influence of the physical properties of the gas phase upon froth formation. Recent studies by Houghton, et aL(90) indicate no difference in froth densities when 02, N2, and CO2 were bubbled through each of several different liquids. Schmidt, et al.(145) studied froth formation by steam bubbles in water in a 57-mm diameter pipe. The density of the steam was varied by changing the pressure through a range from 4 atm. to 40 atm., yet only a very slight decrease in the froth density vs. steam velocity curve was observed at the higher pressures. Ragatz and Baxter(l27) frothed absorber oils in a 1.5-inch column at pressures of 50, 100, and

-95 200 atm,, and observed no appreciable change in froth behavior with respect to superficial gas velocity, In contrast, Ashby(8) found a marked effect due to gas density when frothing water and isobutanol with air, Freon 12, helium and nitrogen in the rectangular bubble-cap column. Freon, the heavest gas, produced the lowest froth density, while helium, the lightest gas, produced the highest froth density. Begley(16) showed that Ashby's froth data, as well as his own density measurements for C02-cyclohexanol and N2-cyclohexanol froths, could be correlated with some degree of success by use of the Ffactor. The F-factor, commonly used to characterize the gas flow through distillation and absorption columns, is expressed as F vs fPg where vs = superficial gas velocity, ft./sec. and p = gas density, lbs./ft.5 Ashby's froth densities for water are plotted in Figures 76 and 77 versus the superficial gas velocity and the F-factor respectively. Although Ashby and Begley found that at a given vs dense gases promote froth formation, it has been noted that frothing and foaming during distillation is enhanced by vacuum. (134 Foaming in air-craft lube oils has also been found to be more pronounced at reduced pressures(86,17) although this may be partly due to the evolution of gases which were dissolved in the oils at higher pressure, Other Effects In studying the effects of viscosity, Begley(16) varied liquid and gas temperatures from 57T to 100~ F, and observed no effects on froth

-96 0.5 () z I L.. LUJ _> 0.4 0.3 0.2 0 I 2 3 4 5 6 SUPERFICIAL VELOCITY, FT/SEC. Figure 76. Relative Froth Densities of Water in Several Gases, Plotted as Function of Superficial Gas Velocity. Data of Ashby(8). 0.5 CZ z w I LU w w LJ Qr 0.4 0.3 O AIR, p= 0.068 LB./FT - -----—....... —_.- 10 FREON- 12, p=0.27 LB./FT3 1O HELIUM, p= 0.10 LB./FT3 I T —---— L ___ ___ __ _ _ ___ __ ___ __ ^ ^ ___ ___iii i 0.2 0.2 0.4 0.6 0.8 1.0 1.2 1.4 F- FACTOR, vs,/ Figure 77. Relative Froth Densities of Water with Several Gases, Plotted as Function of the "F-Factor". Data of Ashby80).

density other than those attributable to the slight change in gas density. Souders, et al, (158) varied the temperature of aerated kerosene finding no change in froth density. However, upon increasing the temperature of a light lube oil in the same column a marked decrease in froth density was observed. Joseph and Hancock(97) observed that the presence of solid particles had little effect on the froth layer in high pressure steam boilers. Eberle(55) found that solid particles enhanced the froth formation markedly in boilers. Villar(176) states that the presence of CaC03 precipitate in water noticeably favors froth formation. Foulk(65) concluded that wettable solids do not influence froth, but non-wettable solids stabilize them. Conversely. Shkodin( 154) claims that unwettable solids can destroy foams. THE MECHANICAL MODEL FOR FROTH FORMATION Gas entering the liquid through a disperser is broken up into discrete bubbles which, because of their buoyancy, rise immediately toward the surface of the liquid. On reaching the surface each bubble is arrested momentarily before bursting, Its place at the surface is quickly taken by another rising bubble and the process is repeated. If each "layer" of bubbles bursts before the next bubble layer reaches the surface, no froth will form. If, however, the pause at the surface is of sufficient duration for the next rising layer of bubbles to impact against the surface layer of bubbles, a piling up of bubbles occurs, resulting in the formation of froth. The problem of exploring the criteria for frothing in aerated liquids may then be regarded as essentially that of

-98 trying to determine those factors which influence the length of the bubblers pause at the liquid surface, Of course, in an actively aerated froth, termed "dynamic" froth by Foulk and Miller(68), the piling up of bubbles is hindered to a large extent by the destructive effects of turbulence. Ross and Miles(142) state that such dynamic froth formation is actually more of a measure of the film stability than of the liquid's frothability or foamability. Foamability, or foam tendency, refers to the ability of a liquid to form foam films. Foam stability, on the other hand, refers to the resistance to rupture exhibited by the foam film after its formation. As pointed out by Bartsch(l4), the two phenomena are not necessarily related, for a liquid may show high foamability and low foam stability, or vice-versa, Froth formation and foam formation are therefore basically identical processes, with the major difference between them being the length of the bubbleXs pause at the surface. Some of the concepts and theories generally considered useful in explaining stable foam phenomena are reviewed in the next section, THlEORIES OF FOAM FORMATION An excellent critical review of the foam literature up to 19553 has been made by Bikerman, (22) Although the exact nature of the phenomenon is not understood, enough is known about foaming to permit some general conclusions regarding the effects of various physical properties. The conditions occurring as a bubble approaches the surface were analyzed by Foulk(614'68) In Figure 78A, a single bubble is shown as it

VAPOR I <0 A B C Figure 78. Thin-Film Dome Formation by Rising Vapor Bubble.

rises through the liquid near the surface. As the bouyant force pushes the bubble closer and closer to the surface, the approach of the two gas-liquid interfaces ftrms a thin liquid film, from which the liquid must be squeezed, Figure 78B. As the bubble moves even closer to the surface, a thin liquid dome is formed, as shown in Figure 78C. This dome is subjected to mechanical stress by the buoyant force of the bubble, surface tension forces, and differential pressure forces. (The gas pressure inside a bubble is greater than that of the surrounding atmosphere by AP = acr( + -), where a is R1 R2 the surface tension and R1 and R2 are the major radii of curvature of the bubble film. This is Laplace s well-known equation of capillarity. ) In addition, the liquid tends to "drain" out of this dome film due to gravity. It is the ability of the liquid film to resist these disrupting forces that determines the lifetime of the bubble at the surface hence the foamability and foam stability. For relatively non-foaming liquids such as pure water, the surface residence time for a bubble may be as low as 0.01 second(ll5), while for foaming liquids bubbles may persist for hours, or even days. The lifetimes of bubbles on the surface of liquids has frequently been used as a measure of their foaming tendency.(22,150,169) The manner in which the film breaks up has been studied by Stumpner(168), Stuhlman(167), Davis(44), and Dombrowski and Fraser(50), as well as by Newitt, et al (115), who have observed by high-speed photography that the liquid drains from the dome until some point near the top of the dome is so weakened that it can no longer withstand the internal pressure in the dome, and a "blow out" occurs at that point, a mechanism proposed in 1929 by Foulk. (64)

The conditions influencing the resistance to rupture in the dome film apply equally well to the thin films formed by two or more bubbles pressing against one another. Density Since buoyancy is one of the forces tending to force the two gas-liquid interfaces together, causing the dome film to become thinner, high gas density is theoretically beneficial to foamability and foam stability, although the magnitude of its importance is less than that of the liquid density, Because of the effect of buoyant forces on the film thickness, foam film formation and stability are enhanced by low liquid densities, Further, the decreased weight of liquid supported in the dome film decreases the mechanical stresses and the rate of drainage from the dome, thereby adding to the stability of the film, Liquid Viscosity The rate at which the two gas-liquid interfaces approach one another depends on the ease with which the liquid may be "squeezed" out of the film. For this reason, a high viscosity theoretically is desirable for film stability. The role of viscosity on foamability is uncertain, with one viewpoint being that the retarding effect on the approaching interfaces is desirable for initially producing a film having sufficient thickness to support mechanical stresses exerted on it. The other point of view, stressing the importance of having a thin film form in the first place, concludes that low viscosities promote film formation

102 by allowing the two interfaces to rapidly approach one another closely enough to allow other stabilizing influences to occur( ), as discussed later. Surface Tension Foaming is enhanced by low surface tension. The raising of a dome at the surface layer involves an increase in interfacial area, and hence in surface energy. Less work must be performed to create the dome film in a liquid having a low surface tension than in a liquid having a high surface tension, thus the former will have a greater foaming tendency. The film will be more stable because the surface tension stresses and the internal gas pressure will be lower hence the tendency to rupture will be less if the surface tension is small Vapor Pressure Film stability may suffer if the liquid has a tendency to evaporate rapidly from the thin film. For this reason low vapor pressure and near saturation of the gas are theoretically desirable for increasing foam stability. Unfortunately, most of the literature concerning foaming points out the ineffectiveness of attempting to explain foam behavior in terms of these usual physical properties. Bikerman(22) shows that gravitational forces involved in foaming are insignificant compared to surface energy forces, so that foam properties should be independent of gas density. Kaulfmann and Kirsch(99) found that vegetable oil foams show decreasing stability when foamed with N2, H2, and Co2, respectively; but it is more likely that these variations were due to differences in permeability of

-103 the gases through the liquid film(32) rather than to differences in density. Berkman and Egloff(18) point out that in most pure liquids those having the lowest surface tensions also have the highest vapor pressures further complicating attempts at explaining foaming in terms of physical properties alone, Surface Viscosity Numerous investigations have shown that the foaming properties of liquids cannot be satisfactorily explained by consideration of density, viscosity, and surface tension (22) Because liquid viscosities are too low to explain the very low rates of liquid drainage from most foam films, Plateau(l20l121) postulated that the viscosity of the thin liquid layer at the surface is higher than that of the bulk liquid, This effect, named surface viscosity has been confirmed for a large number of liquids by many investigators. (2223) Shorter(l55) divided forming liquids into two classes: those exhibiting very high surface viscosity (rigid foams), and those with no appreciable surface viscosity (mobile foams). The rigidity shown by foams of the first group (saponins, proteins, etc. ) has been attributed to non-Newtonian viscous effects in the thin liquid films. (172,180) The existence of such non-Newtonian effects in foam films was predicted by Gibbs. (72) "Balanced Layer" Theory When non-Newtonian rigidity is not present in the film, as in Shorter's second class of foams, the foam stability cannot be completely explained by the effect of surface viscosity on the foam drainage, (110)

Foulk(64'68) attempted to explain the formation of thin liquid films in such solutions by a "balanced layer" theory, which is based on the fact that the solute concentration at the surface of a solution is usually different from the concentration in the bulk liquid. Because of this concentration gradient at each interface, the very close approach to two interfaces must result in a disturbance of the solute distribution across the contained liquid film. The "balanced layer" theory proposed that the approach of the two gas-liquid interfaces forming the liquid film is arrested when the film thickness becomes so small that the mechanical forces pushing the interfaces together are exactly counterbalanced by the thermodynamic forces required to disturb the concentration gradients in the very thin liquid film. The thermodynamic force, as used by Foulk, is not clearly defined. According to his theory, pure liquids should be unable to form stable foams, as has been verified. (67'76,114) A quite similar, but more thermodynamically elegant, theory has been recently proposed by Nakagaki. (112,113) The importance of surface concentration was studied experimentally by Foulk(68); however, the interpretation of his results was disputed by Hazelhurst and Neville(66'83) who suggested that film (73, 74,122,170) formation and stability are the result of surface structure' and "cybotaxis"(8l182) The idea of "cybotaxis", or "crystalline orderliness" of the liquid molecules, especially at the surface interface, has received much support. ( 95 )

-105 Other Theories Other theories have been offered for explaining the stability of thin liquid films. The stabilizing effects of "wedge pressure"(48) and "disjoining pressure" (4546 47) have been suggested by Derjaguin. The escape of gas from the foam by permeability(32), as well as by fissures in the liquid film(172) has been suggested. The existence of electrical charges at gas-liquid interfaces is treated in most texts on surface chemistry. The arrest of the two approaching interfaces in foam films is considered at least partially due to the repulsion of the charges having like sign on each interface. (60) In support of this theory, it has been shown that reduction of the charge by addition of electrolytes can cause the liquid film to become thinner(55'36182), It has also been found that foam films can be collapsed by strong electric fields(28'119148), and by ionizing radioactive radiation(6'37). Further support has been given by Reinold and Rucker(15), who apparently observed electro-osmotic movement of the liquid surface of soap films. Film Resiliency Thin mobile liquid films of stable foaming liquids display remarkable resilience, or "self-healing", even to the extent of allowing such solid objects as lead shot to pass through the film without rupturing it(2l' 9'53'137) The above theories are completely inadequate in attempting to explain such resilience and at the present time the most accepted explanation of film stability and resilience is based on surface activity and dynamic surface tension.

Surface Activity In liquids containing two or more components, the composition of'the liquid in the interfacial region will usually be different from that of the bulk liquid'The surface concentration of solutes is given by the Gibbs adsorption equation(72) r = -a c (4) in which r excess concentration of solute at the surface, moles/cm2 a = activity of solute a surface tension, dynes/cm, Equation (4) states that (a) if a solute causes a decrease in surface tension, it will be accumulated at the liquid surface ("positive" adsorption), and (b) if the solute causes an increase in surface tension, it will be repelled from the liquid surface ("negative" adsorption). Those solutes which are positively adsorbed are called surface active agents. Similarly, those which are negatively adsorbed are frequently referred to as surface inactive, Dynamic Surface Tension Changes The surface activity (or inactivity) of solutes gives rise to dynamic surface tension changes. Consider, as an example, an aqueous alcohol solution at rest. Because of the positive surface activity of alcohol in water, the alcohol concentration, xs, at the gas-liquid interface of the liquid is appreciably higher than that in the bulk liquid, x<. Consider next that it is possible to suddenly create a new gas liquid surface within the bulk of the liquid,

-107 At the instant that the new gas-liquid interface is created, the liquid composition at the surface will be that of the bulk liquid, xo. Because of the non-minimal surface energy, water molecules are repelled from the surface while alcohol molecules migrate to the surface until the equilibrium alcohol concentration, xs, is established at the interface. This rearrangement takes place over a finite length of time, with Figure 79 depicting the shape of a typical concentration versus age curve for the surface. Of course, the rearrangement is accompanied by a decrease in surface energy, or surface tension, Figure 80 showing a typical surface tension versus age plot for such a surface. The final surface tension, as, corresponds to the "static", or "equilibrium" surface tension measured by the usual methods. In the above analysis the alcohol solution was considered surface active. It may just as validly be considered to be a surfaceinactive solution of water dissolved in alcohol, from which it becomes apparent that regardless of whether the solute is positively or negatively adsorbed, the surface tension at a freshly-formed surface of a solution will decrease with age. Thus the dynamic surface tension of a solution interface will always be higher than the static surface tension, which it approaches with increasing age, Perfectly pure liquids theoretically should exhibit no dynamic surface tension changes. The Role of Surface Activity in Foaming The relationship between dynamic surface tension and film resiliency was first proposed by Marangoni (07,108) in 1871o Although the principles of surface activity were not fully understood at the time,

-108 z 0 cr z w L) z 0 u IJ J en Xs X0 0 Figure 79. INCREASING TIME -- Change of Surface-Active Solute Concentration with Time at a Newly-Formed Surface. (ro z 0) z IU),L u) 0 SURFACE AGE Figure 8o. Change of Surface Tension at a Newly-Formed Surface.

-109l by watching the movement of talc on disturbed liquid surfaces, Marangoni observed that the surface tension of a freshly formed surface appeared higher than that of an aged surface. He noticed that whenever a portion of the talc-covered surface was scraped clean, the talc from the surrounding areas quickly invaded the cleaned area. This led Marangoni to suggest that the surface tension of any liquid is decreased by aging, probably due to contamination, so that whenever the surface of a liquid is disturbed in such a manner as to expose fresh liquid, the higher surface tension in the freshly exposed area pulls the surrounding, aged liquid into the area, thereby "healing" the disturbed area. This healing has been called the "Marangoni Effect." Rayleigh(131) and Gibbs(72) explained the Marangoni effect in the light of surface activity of the solute pointing out its special significance in affecting foam-film resilience, They concluded that stretching of the liquid films at thin spots caused by uneven drainage would also be opposed by the Marangoni effect, since any increase in surface area at that spot causes a momentary decrease in surface concentration of the surface active component. This results in increased surface tension in the stretched area, which opposes further stretching of the film, as well as tending to elastically restore it, thus pramoting film resilience. Gibbs(72) defined the elasticity, E, of the film due to this mechanism as E 2A, aA where A is the area of the stretched portion.

The absence of the Marangoni effect in pure liquids explains t.he observation that pure liquids d.o not foam. Since the foaminess versus concentration curve is bounded on each end by a pure liquid, there must be some intermediate solute concentration having a maximum foaminess. Several investigators have attempted to define the surface concentration relationships necessary to explain this optimum foaming concentration. Quincke(126) suggested that the maximum foam stability results when the difference between the surface tension of the fresh surface and that o ththe aged sulrface is a maximumL Since the maximum foaminess usually occurs at very low concentration of surface active agent, the surface tension of the fresh surface is almost that of the pure liquid, so that the fulfillment of Quickels condition would co:rrespond to a minimum in the surface tension versus concentration curve. The absence of such a minimum in surface tension is notable, even in solutions showing marked peaks in foaming. Bartsch(l5) proposed.that the maximum foaminess occurs when the molecules of the surface active solute and the surface inactive solvent are present at tlhe surface in equal numbers, The'bulk concentration corresponding to tiis condition can be calculated frm Gibbs equation, Equation 4), if e surfae tension versus concentration curve is known. No confirmation of this theory has been found. It has tbeen s ggested that that concen' —ation at which the excess surfaze cornenration equal to -c frm Equation (4) at low concentrations) is a max.imumr, will yield the most etable foam. (22) Although -c - does pass through a maximum in the low con; 6c centration region for most surface acti.'v'e solutions, correlation with the concentration of maximum foaminess has not been generally observed,

Sasaki 3) concluded that the value of a is important in determining He (112, 113) foaminess, as did Nakagaki. Donnan(51) pointed out the importance of the rate at which the dynamic surface tension decreases with respect to time. Since the healing and restoration of thin spots depends upon an appreciable difference in surface tension between the old and the new surfaces, he suggested that a slow rate of dynamic surface tension lowering should be beneficial to foam stability. That is, the surface tension of the liquid surface in the distorted area must remain appreciably higher than the equilibrium surface tension in the surface surrounding for a long enough time to permit the affected area to completely close. Ross and Haak(l41) have recently indicated that the decrease in dynamic surface tension in the disturbed area is accomplished by two mechanisms: (a) diffusion of the surface active agent from the bulk liquid, and (b) diffusion of surface active agent from the aged surface (high concentration) into the disturbed surface (low concentration). The second mechanism "drags" surface liquid into the distorted area, restoring the film thickness. (60) They suggest that it is the comparative rates of the two processes that determine the film stability, with mechanism (a) being relatively slow in stable foams. Since the fundamentals of the above theories were postulated as early as 1890 and the probable importance of the rate of dynamic surface tension in foaming is almost universally recognized, it is surprising that very few attempts to verify the theories have been reported. Burcik(33) attributes this primarily to the lack of a suitable means of measuring dynamic surface tension rates. Burcik appears

-112 to be the first investigator to have employed the oscillating jet method of dynamic surface tension rate measurement for studying foaming properties of solutions, Foulk and Miller(68) had previously used the oscillating jet to indicate the difference between the initial surface tension, at the freshly formed surface, and the static surface tension of frothfoarming salt solutions, but their results were in. error. (668 Ross and Haak(141), using the oscillating jet technique, showed that the addition of several foam inhibitors to sodium oleate solutions markedly increased the rate of dynamic surface tension lowering in every case, thus supporting the concept that low surface tension rates are beneficial to foaming. Burcik(33), studying several long-chain detergents, found the rate of surface tension lowering increased as the bulk detergent concentration increased,. He observed t.he foaminess of these solutions to pass through a maximum at some intermediate concentration, so that the foaminess was not necessarily enhanced by a low rate of surface tension lowering. Burcik offered two possible explanations, First, he pointed out that the role of the Marangoni effect in the formation of liquid films must be considered also. Since the -evolution of foam films involves expansion of interfacial area, mostly'by stretching, film formation is opposed. by the Marangoni effecto For this reason it would be desirable for the freshly formed portions of -the liquid surface to have as low a surface tension as possible. This th;en suggests that foamability should be enhanced by (a) a high rate of

dynamic surface tension lowering, or (b) a low rate of film formation. Since foam stability, as already discussed, should be enhanced by a low rate of surface tension lowering, Burcik suggested that foaminess, being the net result of foamability and stability, should be a maximum at some intermediate rate of surface tension lowering. Secondly, Burcik suggests that the surface liquid, instead of being stagnant, is constantly being recycled with bulk liquid from within the film. He therefore assigns to the surface liquid some average age, hence some average dynamic surface tension, higher than the equilibrium tension. If the surface tension of the average surface is to be appreciably lower than any fresh surface exposed by disturbances of the film, the rate of dynamic surface tension lowering must be rapidAs before, the rate of lowering must be slow enough to permit the disturbed area to heal itself before the surface tension in the effected area becomes too low. From this reasoning also, Burcik proposes that film stability may require some optimum rate of surface tension lowering, above and below which the film will be unstable. This view is supported by the observation that the rate of surface tension lowering in sodium laurate solutions is decreased by increasing the pH,(116) where it has been shown(34'109) that sodium laurate solutions exhibit less foam stability at high pH valueso Burcik(34) showed that the addition o electrolytes to the aitio of tose high pH laurate solutions increases the rate of surface tension lowering even further, thereby increasing the foam stability. Camp and Durham(35) also demonstrated that a large number of electrolytes cause marked increase in the foam stability of sodium laurate solutions at high pH

-values. They cite the observation by Posner and Alexander(123) that lithium ions increase the rate of surface tension lowering in detergents to a far greater extent than do rubidium ions, thus possibly explaining, in view of Burcikgs concept, why lithium, ions show less stabilizing effect on detergent foams than cesium ions. For the Marangoni effect to be operative, the liquid film mfust be thick enough to contain a layer of "bulk" liquid. However, very stable liquid films are frequently observed whose film thicknesses are as small as two molecular lengths. (22, chap.8) Early explanations of the stability of these thin films assumed very low surface tensions by virtue of the reduction in the number of neighboring molecules exerting attractive forces, but no evidence of this decreased surface tension has been shown. (22) The stability of such thin films is now generally attributed to surface rigidity or plasticity. Ross and Haak(141) suggest that stable foaming is therefore a two-step mechanism. They propose that the film., as initially formed, is thick enough to exhibit resiliency due to the Marangoni effect. Regardless of this resiliency, the liquid gradually drains out of the film until it reaches the point at which the Maranlgoni effect is no longer operative, so that any further stability of the film is the result of surface plasticity. Since the development of surface plasticity requires times of the order of about sixty seconds14 0), the film must exhibit Marangoni resiliency for at leasst this long in order for the film to survive. Thus it appears that film stability requires the proper combination of dynamic surface tension lowering rate, drainage rate, and rate of plasticity growtho It is therefore not surprising that consideration of any one of these properties alone leads to discrepancies.

2. EXPERDimENTAL DESCRIPTION OF THE FROTHING COLUMN The relative frothing behavior of several liquids was studied by aerating them in a small glass laboratory column, Figure 81 The column is of standard 4-inch I.D. Pyrex pipe, flanged at the bottom to accommodate interchangeable gas-dispersing plates. Three plates were used in this study as follows~ Perforated Plate Most of the liquids were frothed using a 1/8-inch thick stainless steel (inconel) perforated plate having 198 holes, 3/64-inch in diameter, on 0.20-inch square centers, Figure 82 and Table Io The center hole and one of the peripheral holes contain 1/2-inch lengths of 1/8-inch O.D. stainless steel tubing, pressed in and silver soldered so that polyethylene tubing leading to the liquid feed line and the clear liquid manometer could be attached at the bottom side of the plate, The edges of the perforations were polished free of burrs while the top surface of the plate was polished smooth. A copper-constantan thermocouple, in a sheath of 1/8-inch O.D, stainless steel tubing, extended from the bottom of the column, through an enlarged peripheral hole in the plate, into the liquid zone above the plate. Bubble Cap Plate A second dispersing plate, of 1/8-inch stainless steel (inconel), contains a single stainless steel bubble cap at its center. The bubble cap (Table II) is identical to that used in the A.I.Ch.Eo tray efficiency -115

-116 EXIT GAS THERMOCOUPLE T( W n^t[F —-. —_ - 0 VENT Ii _ I Ir A EXIIT GAS PRSSUKRE TAP I I I —,, Iy i i r II ENTRAINED LIQUID BAFFLE 4-INCH I.D. PYREX PIPE FLANGED JOINT PERFORATED PLATE el _1 5' I _ P L lr — -1 t =9. 6" I 4-INCH I. LIQUID A? PRESSL INLE D. PYREX PIPE - ) FEED 4D -- - JRE TAP:T GAS WEEPAGE DRAIN IiI1 i LIQUID TEMPERATURE THERMOCOUPLE INLET GAS PRESSURE TAP Figure 81. Frothing Column.

-117 THERMOCOUPLE HOLE MANOMETER TAP WUID FILL HOLE Figure 82, Perforated Plate Layout.

TABLE I PERFORATED PLATE DETAILS Plate Thickness Column Area (4" Dian Number of Active Ho] Hole Diameter Area per Hole Total Active Hole Az Percent Active Area A. I. CH. E. 0.125 inch 0.1872 ft. 2 (12.566 in.2) 197 3/64-inch 0.001724 in 2 0.340 in.2 2. 7 percent TABLE II BUBBLE CAP DIMENSIONS Bubble Cap: Diameter (O.D,) Height Metal Thickness 1.5 inch 1. 5 inch 1/16 inch Slots: Height Width Number per Cap Area, per Cap 0.75 inch 0 125 inch 18 0.0117 inch Riser: Diameter (O. D. ) Diameter (I.D. ) Height Above Plate 1.125 inch 1. 0 inch 10L inch

studies(8'16,178). The skirt of the cap is flush with the floor of the plate with the slots extending to the floor. A 1/16-inch diameter hole in the floor, with a 1/2-inch length of 1/8-inch OoDo stainless steel tubing silver soldered to the bottom of the plate, served as a liquid inlet as well as a pressure tap for the clear liquid manometer. Wire Gauze Disperser Several water froth studies were made employing a fine copperwire gauze as a seive tray. The gauze, of. 0l18-inch copper wire, 31.5 wires per inch, has 41 4 percent open area. A short length of 1/8-inch O.D. copper tubing, soldered to the bottom of the gauze near its periphery, served as a pressure tap and liquid inlet connection. Clear Liquid Manometer The pressure tap at the floor of eachr dispersing plate was attached, by polyethylene tubing, to the bottom of a 1/4-inch IDo vertical glass tube, which indicated the depth of clear liquid on the plate during frothing. The top of the glass tube was connected by rubber tubing to the top of the colnun. A small constriction in the polyethylene connecting line reduced manometer pulsations. It was observed that the clear liquid manometer gave an accurate indication of the clear liquid. depth when the bubble-cap plate was employed, regardless of the air rate. However, when the perforated plate or the wire gauze was used the reading of the clear liquid manometer was meaningless, with the indicated liquid level falling markedly below the level of the clear liquid in the colsun, even at low gas rates, For this reason, when these dispersers were

used for frothing, it was necessary to determine the clear liquid depth by occasionally stopping the flow of air and observing the actual unaerated liquid depth. Liquid Feed Liquid was fed into the frothing column by gravity from a one-gallon glass reservoir through a 1/8-inch IoDo polyethylene tubing to the inlet hole in the dispersing plate. Flow was regulated by adjusting a pinch-cock. Liquid was removed from the plate through the inlet hole and polyethylene tubing. Flow Diagram Air from the laboratory supply line was filtered and pressureregulated, then passed through a 2-inch diameter by 2-foot deep bed of silica-gelt to remove moisture and other vapors, Figure 83. After being metered, the air was sent to the frothing column, and subsequently vented to the atmosphere. Rotameters The dry air was metered in one of two Schutte-Koertting HCF Rotameters with 10 psig, back-pressure. Temperature corrections were not made, The small rotameter was calibrated by a water displacement method, and the large rotameter was calibrated by the heat dilution technique. The calibration of the rotameters appears in Appendix Go Heater A one-kilowatt, electrical heater, consisting of two flat G.E. Calrod units was included in the air flow system for drying out

VENT PRESSURE REGULATOR FROTHING COLMN AIR IN'' SILICA GEL DRYING COLUMN PRESSURE GAUGE I ro H!u I KW ELECTRIC AIR HEATER ROTAMETERS Figure 83. Flow Diagram of Froth Measuring Apparatus.

-122 the columns, etc. Because of the very long "lag" in temperature response of the system, it was impractical to attempt to control the liquid temperature by use of the air heater. Thermocouples All gas and liquid temperatures were measured with 24-gauge copper-constantan thermocouples in shields of 1/8-inch diameter stainless steel tubing. The thermocouple EMFEs were measured on a Leeds and Northrup No. 8662 Precision Potentiometer. Top-Column Trap To avoid contamination a stainless steel weir-type trap was placed at the top of the column to prevent entrained liquid from draining back down the exhaust line into the glass column. OPERATION OF TEE FROTHING COLUMN Measurement of liquid frothing properties was initiated by allowing air to pass at a low rate through the empty frothing column, Liquid from the reservoir was then siphoned into the column through the feed hole in the tray. Air flow was necessary to prevent liquid from "dumping" through the tray. When the desired liquid level was attained in the column, the liquid feed was stopped, and the air flow rate was increased to the desired amount. After the back-pressure on the rotameter had been adjusted to 10 psig., the average height of the frothing liquid-air mixture in the column was observed and recorded. At low gas rates the clear liquid depth could be read directly from the clear

-123 liquid manometer (care having been taken at the start of the run. to eliminate all air bubbles from the semi-transparent polyethylene tubing connecting the manometer with the floor of the tray). At higher gas rates however, the manometer gave erroneously low readings, so that it was necessary to almost stop the flow of air occasionally and record the depth of the un-aerated liquid on the plate. The temperature of the liquid on the plate, as well as the temperatures of the inlet and outlet gas from the frothing column were recorded at frequent intervals during the run. The air rate was progressively increased until the delivery capacity of the air line was reached (about 0.5 ft3/sec). The frothing properties of the liquids were influenced quite markedly by slight contamination caused by entrainment of liquid which had' wept" through the plate and accumulated in the air chamber below. It was therefore necessary to bleed off this liquid at frequent intervals to minimize contamination of the liquid on the plate by carry-over. With most liquids no carryover was detected at air rates lower than about 0 1 ft3/sec when drainage is not allowed to accumulate but it was not possible to prevent contamination by entrainment at higher air rates, For this reason, it was necessary to obtain froth data at the lower gas rates first, postponing the high-rate measurements until the end of the run. When entrainment of the accumulated liquid was suspected, it was necessary to flush out the column above the plate and feed in fresh liquido Before attempting to froth a new liquid, the column was rinsed several times with distilled water (or acetone) above and below the plate, and dried completely by passing heated air through the columno

Because of evaporation and weepage losses, it was necessary to occasionally add liquid from the reservoir. When aqueous solutions were frothed in the column, it was necessary to maintain a continuous throughput of liquid into and out of the column so that the composition of the solution was not altered significantly by the differences in volatility between the two components. This was achieved by adjusting the pinchcocks on the inlet and outlet tubing so that a constant clear liquid level was maintained during the run. The column pressure and the pressure drop across the tray indicated by water-filled manometers were recorded for several of the frothing runs. A small bottle was placed below the tubing leading from the top-column entrainment trap to collect any liquid draining from the trap, Even at the highest air rates liquid was very seldom observed to drain from the entrainment trap, indicating that there was little tendency for entrained liquid from the column to drain back into the column,

B. OSCILLATING JET STUDIES 1. PREVIOUS WORK AND THEORIES THEORY OF THE OSCILLATING JET Rayleigh(128 129,130) derived an expression relating the frequency of the oscillations to the surface tension, assuming infinitesimal Bor(27) (118) wave amplitudes in non-viscous liquids. Bohr7) and Pedersen( refined the theory from considerations of the behavior of real liquid jets. Probably the most complete theoretical analysis of the oscillations is that of Bohr. His modification of Rayleigh's equation includes terms representing not only the surface energy forces considered by Rayleigh, but also the effects of viscosity, finite wave amplitudes, and the inertia of the gas phase surrounding the jet. The terms pertaining to the gas phase inertia are usually omitted since Bohr has shown that this effect is negligible. A brief outline of Rayleigh's derivation appears in Appendix A, and an outline of the derivation of Bohr's corrections for viscosity and finite amplitude is presented in Appendix Bo The equations of Rayleigh and Bohr have been reported in a variety of forms, As shown in Appendix A, Rayleigh's analysis of the oscillating jet from an elliptical orifice yields the following expression for the frequency of oscillation, f 2= + 3 )(+ 2r2 (39-A) 2it2pr5 XK 3 5 where f = frequency of oscillation X = wavelength of oscillation r = mean radius of the jet -125

-126 and p = density of the liquid. In order to permit the use of the oscillating jet as a convenient (2,4) laboratory tool, Addison(2) treated the small terms jr/X as constant, to employ Equation (39-A) as f2 K'( ) (6) or, expressing the frequency as c/X, where c is the linear velocity of the jet, a _ K c2 (6a) cP2 Rayleigh has shown that Equation (6) is the relation for oscillations in two-dimensions only, whereas Equation (39-A) depicts the oscillations in three-dimensions. Addison has indicated that if the wavelength is sufficiently greater than the diameter of the jet (ca. 10 times greater) Rayleigh's two-dimensional expression will be valid. This equation offers only convenience, the accuracy probably being limited to several percent, especially when applied to liquids having appreciable viscosity, Bohr's analysis of the elliptical oscillating jet leads to the solution (Appendix B, Equations (29-B) and 55-B)), pk2r c In(kr) 1 1 (3+ k2x In(kr) [1+ (p )5(3/2 3 )2 ] [1-37 where p = coefficient of viscosity b = amplitude of oscillation in an elliptical section, r = ro + b cos 2~, k = 2/X

-127 and In(kr) = Modified Bessel's Function of the First Kind, of order no For large diameter jets where kr is very small, Bohr suggests the following approximation of Equation (7) (see Appendix B), pk2r2C2In(kr) [1 2(p 2 - / + 3( -- ) ]1 3+ (7a) (3+ k2r2)In(kr) pcr2k pcr2k 24 r In order to arrange Equation (7a) in small dimensionless groups, Hansen, et al. (7778) expanded the Bessel Functions and other terms in kr as a power series, yielding (Appendix C), C =pk2r2c2 [1 k- r k85 k4r4 +2( 2 )3/+ 3( 2 2+ 37 b2](9 6 L 12 576 pcr2k 24 r2l The analyses of Rayleigh(l28), Pedersen(ll8), and Bohr(27) are based on the vibration of liquid with a constant (i.e., time independent) surface tension, whereas the usual use of the oscillating jet equations based on their analyses is that of calculating surface tensions of liquids in which the surface tension is changing as a function of time(2'4, 3342 ) (138,141) While charging that such use of the theoretically time-independent equations is somewhat rash, Hansen(77) has shown that if the surface tension changes with time in such a manner that its change can be represented as linear over a single wavelength, then the wavelength on the jet will be approximately that predicted by the time-independent equations with the surface tension equal to the mean value over the wavelength. Hansen's derivation employing a non-constant value for surface tension predicts a high-frequency, low-amplitude oscillation superimposed on the principal low-frequency jet motion. The amplitude of the secondary oscillation will be small enough that under the usual experimental conditions they will offer no complications.

-128 Since the surface tension can be determined only at those positions along the jet corresponding to the midpoint of each node of oscillation, it is necessary to adjust the frequency of oscillation so that a sufficient number of nodes are formed within the time span during which the surface tension of the liquid is varying, The approximate relations, Equations (39-A) and (6) indicate that the frequency of oscillation is relatively insensitive to the jet velocity and for a given surface tension, the frequency is determined primarily by the mean radius of the jet. Therefore the time scale for the measurements can be selected merely by choosing the appropriate orifice size, with the frequency increasing rapidly with decreasirg radius. EFFECT OF OR i:CE ON THE OSCILLATING JET Because of the entrance effects the liquid movement in the jet near the orifice is complex. In passing +through the orifice the liquid develops to some extent a typical l.aJinr-flow velocity profile, After leaving the orifice, the free liquid surface of the jet is accelerated by viscous shear for:es until plug flow is attained' 4 1 4) The resulting non-nmiform vvelocity di.s-ribution in the initial portion of the jet complica*tes not only the determination of the mean ege of the jet surface at each node, but also t> calculation of the surface t;ension as a function of wavelengtho The influence of surface velocity upon d.etermination of the surface age at each node is readily seen. Early investigators reported only the "apparent'1 age of -the surface, z/c, where z is the distance from

-129 the orifice, and c is the bulk velocity of the jet('33) The inacduracy inherent in this procedure has been shown by Rideal and Sutherland(l38) who compared dynamic surface tension data for the same ketone system obtained from four different orifices, two of their own, and those reported by Addison(4), Posner and Alexander(123). They found extreme differences in the rates of surface tension lowering indicated by the "apparent" surface ages. It may be observed, however, that three of the orifices (those of Rideal and Sutherland, and that of Posner and Alexander) were very thick compared to that of Addison (Table III p,138). Posner and Alexander employed a circular orifice, measuring dynamic surface tension along the jet by electric surface potential instead of oscillations. It is possible that some discrepancies may be attributable to this difference in technique. It is significant that in every comparison Addisonts orifice indicated a markedly slower rate of surface tension lowering than did the three thicker orifices. Since the thinner orifice would be expected to create less decrease in initial surface velocity, it would then be expected that the "apparent" age of the jet surface for the thinner orifice would be closer to the true age than that of the thicker orifices, This is supported in that the thinner orifice indicated much slower rates of surface tension change. Any deficit in surface velocity causes the "apparent" surface ages on the jet to be less than the true ages, indicating a faster rate of change than actuanlly occurs. Rideal and Sutherland(l38) attempted to calculate the true surface age by determining the velocity distribution along the length of the jet. They analyzed the effect of orifice thickness by analogy

-130 to the wake created by a flat plate in an infinite two-dimensional stream of liquid showing that the true age of the surface at any distance z along the jet, t = fz dz/cs, as calculated from their 0 values of surface velocity, cs, is probably always at least ten percent higher than the "apparent" age, and may be as much as thirty percent higher near the orifice. As their analysis is based upon a two-dimensional analogy, considering only the length of the orifice wall, there is some doubt as to its applicability to actual, threedimensional flow through an orifice. A recent treatment of the problem by Hansen, et al. (78) is not limited in this way. Employing Bohr s(27) equation for the velocity profile in a free cylindrical jet, evaluating the initial velocity profile (a boundary condition for Bohr's equation) from Schiller's(l44) approximate solution for the development of laminar flow profiles in cylindrical pipes then solving the resulting equations on a computer, they obtain a family of curves relating jet surface velocity to axial distance along the jet with orifice dimensions as parameters. It follows from these curves that thinner orifices yield "apparent" surface ages more nearly equal to true ages than thicker orifices. It would therefore appear that if a thin enough orifice were used, the jet would exhibit plug flow, even near the orifice. Hansen, et al, warn against this approach, citing Schiller's view that the entrance of the liquid into the orifice sets up turbulence in the liquid stream. This turbulence will damp out eventually if the Reynold's number is less than a cirtical value but requires a longer distance the higher the Reynold's number. They caution that

if the turbulence persists to the orifice exit erratic oscillations are liable to result. The influence of non-uniform velocity distribution in the jet on the calculation of the surface tension as a function of the wavelength is not as well defined as the effect on surface age. All of the theoretical expressions relating wavelength to surface tension have been derived on the basis of plug flow in the jet(27, 128,152) Although this basis was known to be inaccurate by at least one author(27), it was not considered practical to treat the problem in any more complicated fashion. The recent work of Hansen, et alo appears however, to provide a satisfactory empirical approach. Considering the possible effect of non-uniform axial momentum near the orifice, Hansen found that a correction factor aCalc cs -o.63 K..... ( -,C (63 8) H Known where cs = surface velocity c = bulk liquid velocity, at each node satisfactorily correlated surface tension data from four different orifices for water, benzene, carbon tetrachloride, and methanol. Equation (8) was employed with values of (cs/c) determined from Hansen's analysis of velocity distribution in jets, Since Rayleigh's original analysis concerned oscillations with infinitesimal amplitude, and Bohr's derivations postulate very small, though finite, amplitude, early investigators stressed the importance of employing an orifice with a minimum of ellipticity. Pedersen indicated, by use of Rayleigh's original equation, that the orifice must

-132 have the exact shape expressed by r = r + b cos 2, (9) where ro = arithmetic mean radius b = amplitude of oscillation in order to produce a jet executing pure sinusoidal oscillations without superimposed secondary oscillations that could lead to significant errors in observed wavelength. Bohr, however, concluded that the jet should execute pure oscillations with the cross-section, b2 2 r r - + b cos 2 + - cos 4 +... (10) 12 ro He suggested that the first several nodes after leaving the orifice might result from "impure" oscillations imparted by the shape of the orifice, but that further away from the orifice the oscillations would become pure. FORMATION OF FRESH SURFACE WITH OSCILLATING JET In the measurement of dynamic surface tensions, it is desired to achieve a freshly formed liquid surface closely resembling that which would result if a large bulk of the liquid were hypothetically cleaved to form a fresh surface displaying the same composition and orientation as the bulk liquid. The liquid surface formed on the oscillating jet can only approximately compare with this hypothetical new surface. In order to form the jet, the liquid must first pass through an orifice, at which time some of the liquid will come into contact with the wall of the orifice. Because of the energy relationships involved at interfaces either the solute concentration or molecular orientation will

change near the wall. The extent of this change will depend on physical properties as well as upon the time of contact, Since the surface of the free jet leaving the orifice will be composed of liquid which was influenced by the orifice, the freshly formed surface of the jet will already exhibit some differences from the bulk liquid. Present knowledge of surface effects does not permit estimation of the magnitude of these differences. ELECTROKINETIC EFFECTS WITH OSCILLATING JET When the oscillating jet is used to measure surface tension of very dilute ionic solutions, electrokinetic effects may possibly further complicate the surface of the jeto It is well known that when a liquid with poor electrical conductivity flows through a capillary a streaming potential and streaming current is generated across the ends of the capillary, The development of this potential as a result of the electrical double-layer between the liquid and the solid wall was first explained by Helmholtz(84), and is treated extensively in textbooks. In the classical theories by Helmholtz and by Smoluchowski(l56) it is assumed that the entire flow of current takes place in the liquid, the wall of the capillary being a perfect electrical insulator. If the liquid flows through a metal capillary, the situation is altered by an appreciable flow of current through the metal, but a streaming potential of considerable magnitude may still result(5758 92 02) Since classical theory indicates that the streaming potential must be proportional only to the pressure gradient through the capillary and independent of the total length, it is apparent that the flow of liquid

through even very thin metal orifices is capable of generating an appreciable streaming potential. It is possible then that the liquid in the free jet leaving the elliptical orifice may have an appreciably different electrical potential than the bulk liquid upstream, The theoretical proportionality between the pressure gradient through the capillary and the streaming potential EMF assumes fully developed laminar flow in the liquid(5' 5 ). Because this condition is not fulfilled in a short orifice, the theoretical relation will not apply to such orifices. However, since the basis of the theory depends only upon the existence of a velocity gradient in the liquid adjacent to the wall, a condition existing in any smooth-edged orifice, it is expected that the magnitude of the EMF developed by flow through a smooth edged orifice in a thin sheet of metal will be comparable to that for flow of the same liquid through a longer capillary. It can also be deduced that an appreciable electric field may exist at the surface of the liquid jet issuing from the orifice. The effect of electric potentials on surface tension at metal-liquid interfaces is well-known from electrocapillarity studies.. The familiar electracapillarity curves show that interfacial tension at the metalliquid interface passes through a maximum value as electric potential difference between the liquid and the metal increases.. At zero volts applied potential, a small positive charge exists on the metal side of the electric double layer. As the applied potential is increased, this charge is neutralized by the flow of electrons to the metal through the external circuit, and eventually, at higher potentials the metal side of the interface becomes negatively charged. Because of the repulsive

-135 force exerted by charges of like sign, the surface energy of a charged surface is lower than that of the uncharged surface, so that the existence of an electric charge on the surface corresponds to a decrease in surface tension at that surface, regardless of the sign on the charge. Although metal-liquid interfaces have been extensively studied, little is known about the effect of electric potentials at interfaces of gases and liquids. Bikerman's work with insulating liquids(20) indicates that their surface tensions are unaffected by changes in applied potential. This appears to be in agreement with the principal equation of electrocapillarity by Lippmann(l06), /dy ^ /de d)S l dS' (11) where y = interfacial tension = voltage e = coulombic charge S _ area of the interface. Equation (11) indicates that if expansion or contraction of the interface requires a flow of electrons to or from the interface from the bulk phase, then the interfacial tension depends upon the applied voltage, *\ In view of this it would seem that electrolyte solutions should be influenced by the presence of an electric field at the liquid surface. Consequently, the surface tension of the "freshly-formed" surface of the oscillating jet may further deviate from that of the hypothetical "cleaved' surface by virtue of the existence of an electric field.

2. EXPERIMENTAL THE OSCILLATING JET FOR HIGH-FREQUENCY MEASUREMENTS In order to employ the oscillating jet method for measuring dynamic surface tensions of the dilute electrolyte solutions in this frothing study, several factors had to be taken into account. Orifice Dimensions First, it was necessary to select the size of the orifice to yield oscillations with a frequency range corresponding to the span of time in which the major part of the surface tension changes occur. As discussed on page 128, the frequency of oscillation is primarily a function of the surface tension and the jet radius, All of the previous dynamic surface tension investigations in the literature concerned surface-active organic compounds, such as soaps and alcohols. These compounds generally have rates of surface tension lowering such that the static surface tension values are attained after 30-200 millisecondso For example, using an orifice with a mean diameter of 0 179 cma, for studying solutions of long-chain soap solutions, Burcik(33) was able to detect changes in surface tension over a time range of about 30 milliseconds, with an average oscillation period of 4 milliseconds. Similarly, Ross and Haak( 41) obtained periods of about 3 milliseconds to measure surface tension changes in soap and detergent solutions over a time range of about 20 milliseconds. Their orifice diameter was 0,0868 cm,, Using a 0.106 cm. diameter orifice Addison(2,4) observed changes in surface tension of aqueous alcohol solutions also at intervals of several milliseconds. -136

-137 Because no quantitative data on rates of surface tension lowering in inorganic salt solutions are available, it was necessary to determine the proper time range needed by experimental trial and erroro As discussed earlier a reduction in the mean diameter of the elliptical orifice causes an increase in the frequency of oscillation along the jet for a specific surface tension. Preliminary investigations with sample orifices of varying sizes showed that no change in wavelength (corresponding to a decrease in surface tension) could be detected in dilute electrolyte jets unless the orifice diameter was less than several thousandths of an inch. The orifice chosen for measuring surface tensions in this study was therefore the smallest size that could be made in the laboratory and still have an approximately elliptical shape and smooth contourso It has a major axis of 0.00260 inch and a minor axis of 0.00123 inch, with a geometric mean diameter of Oo00179 incho The periods of oscillation along water jets from this orifice are of the magnitude of 3 x 105 second (0.03 millisecond). In Table III are listed the principal dimensions of the orifice used in this study, along with those for orifices reported by several other investigators. It can be seen that the deviation from circularity of this orifice, as indicated by the "axis ratio", is much larger than that used by other authors for air-liquid surface tension studies. In early attempts at measuring the wavelengths on jets from such small orifices, small deviations from circularity were employed in an attempt to approximate the conditions set forth in the theoretical developments by Rayleigh and Bohr. It was found, however, that in such minute jets it was not possible to accurately measure the wavelengths unless the nodes

-138 TABLE III DIMENSIONS OF ORIFICES USED IN LIQUID-GAS INTERFACIAL STUDIES Mean Diameter Axes, cm, Axis Ratio Author Maj or Minor Mean Diameter Orifice Length cm. o0 0045 41 0. 106 o, 0674 0. 0802 0. 179.o0944 0.1299 o. 1407 o. 1415 o. 0825 0. 1385 0. 1556 o. o40 o. 0620 o. 0346 o. o868 o oo6604 o.003124. 1183 o 0947. 0692 0o0655 o.0826 0. 778 0.170 o 140 0.1002 0.0890 0.1671 0.1009 0.1545 o.1281 0.1424 0.1303 o 0830 o. 0820 0.1386 O0.1384 0 1556 0 1530 (circular) o. 0914 o, 0824 2.114 1.25 l.o6 1.06 1o o6 1.214 1. 126 1. 66 1 21 lo 09 1. 012 1 002 1. 010 (Glass (Glass 1o 79 5.50 Capillary) Capillary) 14.09. 106 5.20 5.63 5. 66 5.50 5.54 6.22 4,.0 0.155 0. 346 6.83 This study Addison( 4) Bohr(27) Bohr(27) Burcik(33) Hansen( 78) Pedersen(118).. tl 1. Posnerl123) Rideal(138) Rideal(138 Ross(l41) 1. 11

had an appreciable amplitude, even though the nodal peaks were illuminated in the manner suggested by Addison(4), and described in Section II-Bo of this report. Due to the extremely short wavelengths encountered in the small-diameter jet, sharply illuminated nodes are essential for acceptable accuracy of measurement, and distinct lighting of the nodal peaks can be accomplished only when the amplitude of oscillation is moderately large. To this author's knowledge the only previous use of an orifice with so great an ellipticity is that by Addison(4), who employed an orifice with a mean diameter of 0.034 cmo, with an axis ratio of 350 to measure interfacial tension at a liquidliquid interface. The orifice in the present study is made from stainless steel foil, 0,001 inch thick. The use of the thin foil was dictated by several considerations. First it lent itself readily to the method of producing the minute orifice by puncturing the orifice plate with a small needle tip, as described in Section II-B. Secondly, it was felt that the use of 0001-inch foil would offer a sufficiently short orifice that the velocity profile across the jet leaving the orifice would not be appreciably developed, thus minimizing errors due to deviations from plug flow. Because of the smooth, rounded contour of the orifice, shown in Figure 42, it is felt that the danger of turbulent entrance effects (see page 150) is minimized. Calculation of Surface Tensions In calculating surface tension values from the experimental jet dimensions, it was found that because of the large amplitudes produced by

the micro-orifice, it was impossible to obtain accurate results using either Rayleigh's relation, Equation (39-A), or Bohr's modification, Equation (7). These relations are the results of mathematical analyses into which many simplifying approximations have been introduced to obtain analytical solutions from the complicated relations. Most of these approximations are based upon the assumption of very small amplitude. Rayleigh's derivation is outlined briefly in Appendix A, while a short summary of Bohrts method of modifying Rayleights equation to account for the effect of viscosity and small, finite wave amplitude is presented in Appendix B. Because of the inapplicability of these idealized equations and the availability of high-speed computers the more accurate relation, X k t z= Q2 -r 2 _ _ _ __ _ LT^ (7z) I2(kr)r 6 2 1 6r/2 /r2 1 6r)2 1 r)2 r2 p 0 k4(kr).... (-) + (J) -1+ (- )+' () + (' ) (.) _ L kl(kr) 6z + d6 6 dZ r2 6g r2 6z XQ 2 2 I Vr 2 1 6r 1 6r 2 6r 21):rgX o o 1179. 867t rg Li j r + ( +)O + (-) + _ (-)(V)j (I 0 0 (23-E) was developed (based on Rayleigh's method of attack) for use with the microorifice. Surface tensions were calculated from Equation (23-E) by summing the terms on an I.B.M. 704 digital computer (at the University of Michigan Computing Center). A detailed development of Equation (23-E) is presented in Appendix E. The terms included within the double summation signs are summed over the intervals, 0 < z < X/4, and 0 < @< < /2, in small arbitrary steps

-141 of Az and AG. In Equation (23-E), k = 2t/X, rg is the geometric mean radius of the jet, in inches L is the volumetric flow rate, ml. per min., and r is the actual radius of the jet at any point (G,z) and is expressed as a function of Q and z according to Equation (19-E), Appendix E. It was found that the increments Az < X/24, and AG < It/28, were small enough so that no significant improvement in computing accuracy could be attained by use of smaller sized increments. Noticeable loss in accuracy occurred if slightly larger increments werd attempted. DESCRIPTION OF THE MICRO-ORIFICE APPARATUS The liquids under consideration in this study achieve their equilibrium surface tensions extremely rapidly, so that it is necessary to produce oscillations on the jet having as short a period as possible. This was accomplished by employing a micro-elliptical orifice with a major diameter of 0.006604 cm. (0.00260 in. ) and a minor diameter of 0,003124 cm. (0.00123 in. ). The oscillations produced by this orifice have a period of about 30 microseconds, depending upon the surface tension of the liquid. The orifice was produced by piercing a sheet of l0001-inch thick stainless steel shim stock (type 302) with the tip of a fine sewing needle. The tip of the needle was first shaped to the desired elliptical dimensions by successive polishing with fine emery paper and inspecting under a microscope. When the proper shape was achieved, the needle was used to puncture the sheet. This was accomplished by first applying only enough needle pressure to indent the surface of the sheet, following which

-142 the reverse side of the sheet was abraded with fine metallographic polishing paper to remove the resulting bulge. The tip of the needle was replaced into the indentation and the process was repeated several times until the sheet was eventually pierced by the tip (the elliptical axes of the needle were kept aligned during this procedure by mounting the needle in a rubber stopper marked to indicate the major diameter). The edges of the orifice thus formed were first smoothed by polishing the faces of the punctured sheet with fine polishing paper. This was followed by polishing the faces by hand with wet alundum abrasive powder. When the edges of the orifice appeared smooth under the microscope, a 1 1/4-inch diameter disc containing the orifice was cut from the steel sheet. This disc was stamped into the shape shown in Figure 88. The stamped disc was placed into the jet assembly and dry alundum powder (type 400 B, Norton Company) was blown through the orifice for about 24 hours. At the end of this time the inside surface of the orifice displayed a very smooth contour. Final polishing of the inside surface was accomplished by blowing Linde abrasive powder (type B, Linde Air Products) through the orifice for 24 hours. The orifice was finished by wet polishing the faces of the orifice disc with a paste of Linde powder applied on the tip of a finger. Figure 84 is a photomicrograph of the elliptical orifice used in this study. The cross-section through the orifice plate, as determined by sectioning and polishing a typical orifice made in the above manner, is sketched in Figure 42, p. 53

I. "X oo. (vD,;JTJO-OjZTx J:0 O'DULE 14 jo qdv-iBoxo-ywo-.-pqj I I I 11.:L.....L,::.:.L'':::::':::i!] ]:,i.:. i,:::i i:j:L.::],., i,::: i:L'.,L',LI,L:I:,I:: ]:::.:L'....I.L'.L.IIIIILIL'...IIIIL.1.....L.'...: i:, ],::,:'L,:::L:''L:,::"::L'LLILL:,,,'L'LLL'IILIL'.LIII.L.,..I,",', L',':'L:'.I.L'.:''',I..II,..L::II'L.1,.i':.-::.:,:,L.'L,,,,.,..,,.,,LIILL I,].,,::''', i''.',:.L:L',.'.LLL,,..IL.L.. I. I':'L':',."IL'.,.::.L'.-:I::L''..,L.,::L':LL:"," "".L:':.L::.L''.L:LL:L'...,:.':4LL::L::. L''.... '-,: :;]:]::;:i ]::::]] i::,ii:,:. I...1 I....,,LI'L.,::::::;, :::,L::.::::::,::'.'.L':L.'::,LL.::.::' L:.,........L,:.::,L : :i.Iii:::::: :i i!,:L',::',,::.L:'L::L,,I,.LL':::.:iIL'.,L'._.L'',",,.:L'.L.':':L'I:II.,."I.LL: ... L:',.IIL,:...1:::]i: :: L::': :]]i:!:::: ;::'.L:L''..:...::"..:::L:::: ',]:;;.iIL.: LL:.,:: L:' L:':'::: i::,:::,7:::'.:L:':'.L.':', L:L]: :Li; j'$:: ii::i.-,.Ji,: i:;;,":..1.1 1.,.:L:,.L'L.LL'L.::I,.:.L,: '.':L.'L::..,II I:L': I...,I,:,L:'.,:.:".:,.:L':.:'',:,,LLLLLLL.....I...I,IIL:.L'I'''L,'L'I... —i iiii:i :: i:I::,:::::ii:i ::.::, 1.'., iL,.I.I,.,...,...:, i:. iii::]::ii;l ::]::,::...::.LI:::.:::II:::.:.,.;.,:::L.,.,:,..I.IL"L'L.,.L..I..:'::';:::':,.:: I,..L'.IIILL'LL,'.L'.L'.::.:::I.'..:. L,::::L::IL:::'::::::::XL:::.,"L'L::, L:::IIILI...:L:L:,,:,:,::, LL'.LL:L:...:1.I. I,." 1,:...:...IL..,.L.. L."','L":L:: ::] .'::',..,.'.,......Li:i':i.::: i:]',':i,.L.:iL::::;]: L::] ::':',':''::..,.LI.LLL,.ILL,....II...L-:L:.:'LIII.IILLL.,:,,''::'!L,: L..'.:-''.':I........$::],: :::::: 'L],:::,:;:,:::':]:iLLL"L...L.:L...:,F..:,:,:::::::::::.:,::::,':::::;:: L.'.:::. IIL:::]:L:..:,.:..,L.,''L:.L',"Lii i.I::,I.,:, ::,L L.:.::1I1. L.',.L'LL.:L'L::::'LL'LI%,,::..:,L.....l. "::L.'L::::I, I L':'.I:::..,L1,IIIL'I::L]: L::]': L ::L-L]i: :.'iL:L:i:: :.IL:::i::::::':L,:L.1:",..II I.L'L'I.IIII.LI.III. II.I.,II...,,I.I.L..1...I.1. L::II:':::L'..,L:.:,:L.L...,,:.:.L.,:::,,.,LL:':..."L.L",'.,,L''':':'iL:':L,:LI L...L.L.,.,,,.L'L:I..1III.IL'IIIIII:'L' L, 1, L.':::: L:::'L::::':'i:::: LL:L:LL:L:''''II,.L'IILL,,.IL''L'I.... 1,...:,i:-::, —:i'''L:':.:IL,.:I1, LL.IIIIL',L.:LL'',,:L'.::ILLL:,:::',:.",,"":''.L:.,.,,'::::''LjL:'L.: L:'::L.,::::::L''....L.."II L:........,::LL'L...:'':,IL'.II'L'L. L.L. L:, L.:::' ".," ":,'L:''".:,IL:L:.1LL,,.L.ILI::::.:..LL,'...L:."'L,',.1::,L:,::'' L.I. I..L' L':I:.ILLI..",., ".L,..,LLL:.1::...:: LIII.IIL. I_.......,.,,, L,:.:'.:.,:::::.:::.,L..IIIIIL.,.:: L::]'II.,L.I:: I.I. L:','''.,L'LLI.L'.'L" L...::::L:'I,.:':''.,:.::::::L:::L::,:L:::.::.:..:"::., :::] L:::; L:];;;:L iLi1:':::L'':'::L:''''L'%:L:,.''LLL'''LL L''L'LI.1.I.,:::':,,LLLL'L'L'',:,.,:,:::.L,:I::LLL:::L:..:::L_::,::....::L:::,:::: .,:,,:,:L:L..'',,,:.,:'LLL','L.LL''II1IIII.1,.1,LI..II.I..LI.LL.::..:.I.I..L':::L, L'III I. ILLL''::.::ILL'..IIL'L''. ""'L'IL',...:,:::.::::'. L.:: LL:,:L.': I,,,:L'.IILII,:,.., L::LL:I.:L':'.'.::...L.L',I.,L.LL,.II,.1.LI.LL.I::.,"',.'L'LLL'..."'::,]]L::':' L:' I:: LL.:L'.:,-L"I,.1IL:I.I..I I.,LL. I.I.,.,.,. I ..II: L.ILI,.II::.:::::'l,::::'::':::L,.IL..II.I-L'::...1I..L.::.,IL','L.1,.:::: LLLLL.,,I.I.IIIII. I:IL.::'IL::::L.:L',,I.:,.LIIIL''L.I.L::::'::L:::L':::':'."'L',,L'L.L.I.IL., LL'I, I1.,ILIII:I.'L:.,I.,I.L'II.II.II. I:,L,....,''L...'''L.IL,..L..III..,I L'' L'L:::.ILL, L' I......,.,L;' ']:]:::':L.L:L,,",,LI1..IIL...L, LL.I I"ILIII I.I: I,.::,:.,.':L:.IIL::IILILLL'LI LI.IIII.1L"..LL:LLLL: ::1I'LL':::::L'':L-L:.,':L::.':::i:::::::,.I.:.: ":.::,:.: L: L::L:'' L.L'L.I","",.''L'L:L,' L'LL:.I:,': : .: L.,,' L:I LL Li::,::: L:] :,.,LLL'LL"'. L:, ' L.:L:]::]':::i,:L:IL:,..,.,LILI L.I."L.I. II....,.L'L:.....::,',:.%.:::::.::::..::::i::L:L' L::: i:,.II I...:,L'''LIL.:L. LL:,L::L'''L''L.:pI.I.L:]L: I::L',LL.L,...,L"II1,...L.' L,'II.I. L'..,I::IILL:L::"::iLL::,:::::::L''L.,,:,::L:::,::.::::..,:.' ,.,,.,,,".,L:.: L''''.I L:' : LL: LL:,L::":,IL:, I ILL'.,L",II1,LI.III.L.I'LI."ILL..I.1 -...I%:::".LL:''.'LLL'.ILII...,IILI.,:.,L''LL:..,'::L':::LL':L'IL,".L', -i:']i:L 1.II::::: -:::.L,:.:L..ILIIIL'LLL.LIIII, L LILL'I,.::':IIL''''' L''L'I L;::']:i..' i,". ::,:.,,.I..,LL..IIII.II.1..II,,LL.I:..,,, L'1,.1ILLII.IL.II IIIL'"..I..IL'.:L:4:L:':'L."':".."IIIII...IL'IIILL..:LI I.IIL':L,:.IIL'.,.I..,...".".'L L..::::,'. .::'L':'.L,'L:,",."'': -:'.:::::L'L.II..I IIL'.II..,,,i.::,: L::LL.:.'LLL:....IL",L:,IL..:::LL''.:,',.L.:LL:'L::' L...LL.,.'..I..II.IL:IL::''I:::L::III,''L....'...'LLL"',ILLLLI.IIII.'L::::::, "'::L'L' LL:..I.IL.ILL'LL'I..IL,:L'LL:,'..,". "''L:.1:::..'L:L::::::,L L::LII'L.IL.,.IIIIL.L',I..IL.:::::::....L'''.I.I ....ILILLIIIII.I"'''L''... II,:,L..,I"LIL' ''.I.:L:'L'::1.,.III,.L,.L',L::.II.II.1.IL.IL:L'::.",LL::I::L:'::: L:::L:,:II.I:...L..1I..:,,L'L'I...ILL'. I I.ILI.IIL.LL.'L,,.L::...%",..",..:I.II.IILILLII",I....L,'.L.ILIL'L'IIIL,:,LL..1.:I:,L."ILL.'...L'IL.I.L.LI.LLIIIL.LLL'I%.L'.:.I..'..,I."L....1..I.....L'.:,L:,,L::.'LL:::,:,,.IIILL,.L.,.III.'ILII,'' L..IIL IL...1.L1LLi::: L:''L:: i:$::i,,i.:::::] i..qL.IL:'.'::::::'.',:.I'L..,.I..L',.,IL..I....L,LL',II"IL...I..L,.L.LLL.,.II.I ILII.LIL.I:].:::::'.I.I'LI.,L'.IL.IL:':.:::':L::L:%::::i::i:::.......L.'..:,L:::..II.I.I1 I I,...1IL:..LLL'''':,',L:II.. L''::II.,::LL ".''L'L.,IL.I.IILI.,L.L,:LII...:I.".II:':LLIILLL. I I..IIIL..I::.,%:,'::: L:::.::::::::::::::::....,I..:::::: L::::L:.:'L;'';L:: ".:..L1.L%.L."IL'.,.II.IIII.ILLLI1.I.IIIIII.i:':::::-,::,,::: i%%::::L'::::..%I:'L,',LII.ILIL.,. I.L...%.L'I.IL'L..IIIILILILI. L.I.IIIL:LI-IL... L. ","......I.L...I IIILIII.IL',..,IIL LL:,,.: IL,.:.I:'L.:LLI,.,LLLLIL. I.ILI.I1.IIIII L.L]:::::i:. ii::]:;iLL:.:::!:,L:L.:.., i.LI.. 1. L:'.....L'IIL''L'. I. IL I.LI..1LLI, I.. LLI.I..I:.. :i:!:.:',:,:.L,:".:.::L...I.I:IIL::,:,:::..,LI.,,.I1.IIIL::L:ILIL.. LIIIIIL,:L..:: ]:::iL.: ;::::::]i..,..i:ii,:..ii'. L.:I:!:'. L.'.:.::L:L' II,".L:LL::,.,.,,"LIL'.II1,IILLIIIIILLI.LI:L'L::,:LL::,:.',':L:::':':LI.I.1I...L'L''L'LI:::'LLLIL:: L:I:,,LI1...,L.II1,II.,.::;::::::: i::'::L..IL:::, ii.:::iL:]],:' i::L:']:ii,I..I.,L,..,IIILL...L':I..1,' L'. IIII II II.L..I.II I.I.III IL....ILI.ILI....I::I IL;L:L:L::::::i.LLLIII.::..1,LLI.:: L:':.::::::.:::L::] ;]::]:::::::']:i ]: L::i:::]:':::::::::,L L:I1:..L'IL'".LLL.,.ILILLI.II. I... I..L::..:.:,::'iL:LL'.I1..,IL'I.I,... ",L"..IL,' L: L'.1LI:..LLI.I.IIL'L'..LLI.. 1...I..L,.... 1".IL'I.IILI.L'LILI.I.,..1 L:Li:]: :i i]] iL::i:i'::':...:':.:Li.::",,.,. L:".L'''.' II...IL.L'I.L:L'IIIL.IILILLL.,I':::: .: :;i:I...1.. L.',II:LL:L:L.....L' L'I.I.I..I L,,-...L,.L'.....IIILILi'L.1. LIII.,..L'I1, L'IIL'IL..L'I.I.IIII:.'ILLIL',.IL'II:IIIIL'.I....',LIL:I.,...' L',',.:'LLI:,IIIL:,..L;i:::!:.:::,:,:L,:':::::.,:,L'.L.L:LLI:L: L:,..,L' L:'III:LIIIILLIIIIL.::::::L.::: ;i:j:;"..:iLLL..L::LL:::"L:.,::::::::::::.....,.'...IL,:'L.'"",LLL.III.I:IL.ILL'ILLL....III.I.L'...., I.".,.1 1, L,.L,','..... I1..:L:::..,...L'L''.I..,,ILI.I I.,L. I ILI,:'L''IIIL,, L:],LL: :::LL'L:LL:::::::::'':':::L.L. LILIL:,L1.., L',' L'".. IL'.1.ILILIIILLL:. IIIII..,,I'L::::::.L:L::L::::LLI:Ip.:L':IL..L".1,.LL:L:..L:',''.',...I......:::' L%::. L'L,."".1I,,.IILI::*I.LL,::::,::,L,.II,::::.IILL,.I..L''L...I.IIILL'IL:LI.LLLL..-:,:,:.:L::i:",' ".',L'LL LL.IIIIII....I'L.,:I.IIL.IL,,':LL',L;"L:I:,.::.,Ii:L:'::%,L::L:::::.L:L:,,:.''.'.::L:L:." L,,LILL1.LLIIL'.IIIL,,:L.,I1,::"I.... :i i!ii:::.,i::i1:1:;:;;::.:::::i:i-:::.L'I.III.I..III.1.,::, L.:,:,.'L..., II.1.'L..L %.%,.,,."..,L':'L':,..,'L'L'.'L.ILIL...ILIIL,:%:,,.....,:::,:L::IILL',..IIIL.,L.IIII%,IL...I.LLL,:.%.:.I.I'....:,LI.I.IL::X:::::::.....,...,.' L.'. L'I..:.:::,,:'LL:L:', L'L''.,I.LI.LIII1, I I:,''.,,:..',,,.L,'"'L':I.,:L.,,L...",..,.L'L'L.IILILI.,.1II.L'.1::"I,..1':]:L]i:: li II' L'L'LIILL'L'I:ILI.11,LL,..LLIIIL.IIII1, LL'IL:: LL,"::.L,:L:.' LL:::::'LLL:: i..::L.L::.7::]i::i -::' %LL:II.."I.LL"II.ILILIIL.IIL...IL'.I..ILL:::,: L1,:LL"..L''.1I. L,.,.IIL.I":ILI.LII..IIILL'L...L.,_. LL LL....IL:,'.,,II.:,:L,::;L.LI::,:. L.':L:,.L"L,':'L::::L:::LLIIIIIILIIII I I:L.IL:.I::::'::L.::L:L::L..,...,L'L,.:.,:, L:IL'..I.LLII.LLI1.,:' L:':'LL': L:L:L.,:,..:,.':.":,:.:' L:':',:,'.:.:, I IIII'L.IILILL LI.IL'L:''L.:.:,,,:L:::-L.....II..L...III.: I.L:L,.i:.LL.IIL".L.I'L.L..I.I.II.ILILII.L"I::: 11 I.,,,L I I:',IIL::L'L'::','L:].:..,.:::.::":::::: '..,iii:i::iLiL.",',':II.ILL,'.:::.,I::LI..L.IL.II.ILI.ILLLI:'LLILL.'I: :i :,.:] LL:,X::: L.L::::::: iL''.IIL'..I.I..II I":,L::::LI.:1,ILLLII:1 1,.::::.'':.!.::.:::.. L.:.:,:.:::,'!.:IIL,,:'IL:::L,'L:::,,IILL'IIL....I.I'I..ILL'LL::.:".:'L'.:'L.::LL''L,..';;L.:.:.I::.:L'L:ILIILIILIILIL.II,,:L::::L'L::,:::,,.:::::Li'i.:i iLL....... L.L:i::L... I IIII.IIII.I.L',:,:L':'::::':'L':'L: i:,L:::::L::L...... IIIIIII.,.ILI..IIIILIILL'L'.IIL.III:L:I..1I.:.], :].:::::::ij:;: : ",...,..1I. ILi:1,I.1IL:L'I' LILII.,LI.,.,ILLI.I.I.1,L:IIL''L'LI.'L'.."III LIIILIII.,,::,::..':.%......,,'L.::. L'L'...III:..::,LL' L:L:':''::'LL'L I.L',LL.I1,L.1,L.IIIILII'L.,LL'...L'.I::I,:!.,:".:.L::'L:::::,::::: LII.. II LLILI.L'II.II,, IL'LLI.II'L'...I.,'LL'L':,..L IL.L1.., I L'II, II I ILLLIIIIIIIIIL11I.LL.".1LLL:,::::..,,.::::':.:.:.:,:,:,'LI.' LII:::..I.I."LI.I.ILL'::LL ILL..,IIIII.II"L.I:.',':,::::',' ':L'L:L.L'..:I.L:'::.1.:::LL'LLL :::,::::.::":: LIIIIILLII.IILLLI'L:,:,:LLL'., LL'.I.,..::,:L.:.', L.LIL',LILL.,,LI:':::,L:'::.:L:''.:':L::.' L%'L::: IIIII.LL,. ILL:L'i:: 1, L.".L'.::,:,... I I I I. IL'' L...I.,IIII.. I I I IL., ILL.I.L,,.L..::L'::: "''L.L':':',.ILL'L'.II'LLL'L.''',,''' ILILI,.L:::,:L:' L::L.',L':''LL L :L:.L:L''.L,....., ".....,I 1II11IIL... II. I:::,:..II'LL,.I:.II IIIL.LLLL,.I.LL'L:L'':.L::.::, :: L::I:I:LL:.LL:':':'']:::]::i 1::i':.',".L'.IL,.IILL'LIII:L".,:.:LL'L':1::]::.I..I ILIIILL,,LLL,III.LII..L'L':LL':': L,',.:'LLI, IIILILIILIIII'LL:..,:,:,:,:':': ":. L:':...: L,,LIIL.LL.1,,LI..:L:L,..LL'.ILLI:;]::::',:L II.IIL LL1.ILILLLI..II:L:,LLL',:,::.'L'L',,,,I..:::, L:LLI.IL''L:::::,::::'L:,:::::,::,'::.:::''L:L:L'.:.:,.::':I",I.L,.LL,,.,.,L,.LI.I.I::''L'L'.IIIIII.IILL'L:L'., 1, LL..:::::::,:.L. L:L::,,:L,'::, ...,.::.::i:'::::..'L''..L' L'LLLI,.I.%,.1.,...q'L",.I.:L.,LL....L I.,LIII.L....ILII.I.IL.I..,LL'L'.. LL'.II.IIIL.I...I..II.LIL,.L.IL'..'.LL ILLIIII11L.I.L'.L'LI. III.,.LIIL':.:L:','.I.I.LLI.IIII;L,. I:.::: I.1.1: "I'ILL.::'.":..,:::'.L'L IL:L: ".IIIL,,.IILIIL:..L...L::::::,,...L:I..,L.II..1I.I:LL:L.II.....,,I:LL'".I::,.::.L:,.':::,'::::.:L".L.'-'L LI,.II.ILII:IIL'..I.I.,.II:::'L,.....I..I....I..L.LII.IL'..",,L',I".I::::.I:I III.II.:,.,i: j!L::ji::ii';:::: ;: j;: ::]ii::iii,iL''.L, LI IILII.I.III.IIIIIL.L''', III.I...IILI.1 L.IL.I:L "'::] I I. I..IL'" L.II.IIII.IL'II LIL..LLII...L'':.:L:::::,:L',:L L'.,III I.. IIIL'.LIi:,:,:LL::"'.II...ILIII.IL'II.:L'::LL:,L:''::I.;.L..,.IL1,..:L,,,:..1I.ILLL,::::,.'. LIIIII. I,:.,L,.L'L'L''L.....III...IILI'LL''IL.ILLII.ILL'....L.,,LL..IL.LIL::: L::'LLI.L.,L...,:.:,L.IIIII.1,.I I' LII.L.L'L'L'IIII.. ILL, L.IIIII.L'.'LI.L,.,.I,, L'.II..II..IL''IL''LL.::'L:L:L''..I.,LL,.,,:iL:::L:.LLL.::.....L'.I..L'LL'L'I::",:,.,L,:.:,. I IL'LIIL'L", II. IL. I.IIIIIL..:".I.II. IL..IL.L' I.LWLIIII:L'',L':':'.,,",..,".L..1,ILLIIII1.I::.L:':,:L'L'.::i.,'L':L.L,..., ".',L'L, IL'.LI:L"''L':::':L:LI..LLLLL'' L'.I.I.I wIILI1I.L''".I.L:''I......L, I I,.:, L "Li:::i',L:i:.":.:':,:L:LL.I.IIL....::L:'..:,.1.I,.:".:.:: ::q III..IL.IL.',IIII,:L:.,:.,"L:-,LLLL'::L:::,:IL.::L:L.;::: L:;: ] ::I::::]" ::: ]::::::Li::.IL.I I,I1.ILI....I.L'I::.III1, I IL:', L','L-...,:,'.''.L.' I' I.L1."I.." I.L'.L..,.LL::::L,:'::.: ".L,:":"L I I.LL,L. IIIII,IIL'I. I II.I.I..I., 1,IL.:.LL"',';..ILI:,:::...L,:.L' LILIIIL..I.L',,.L::::.,L IIII,.LLL''.L'LI.,LLIL:L' L,,LI....,1. 1I.L..LLIII.III.,,,.,......,L,LI.ILL'L'IL,..::II.... II.ILL'.IL'L'LI..,IIII.,LL'::..L::......... L',L IIL.LI II LI.I.....I.LI:::L.:: L::::: "::::4':Li':::.:,,::L: I..IIL.III::L:'LI...I4,,,.:::..L: IIL, IL'I LIIILLI.,IIL.,L. ILIIi L:.L:;i : ] i: :: iii:.'. .,L ILI.IIII,.,IL. LLIILL.I IILLL.ILLIL'LI IIIIIIIII.'L'LIIII.II IIIIL.. I.,' 1,IL'LL..::]: : .. IIIIIL'III.L.,L.ILI.III.,I.,L"i:i:: LI:.II.IILII.IL III.LI,,IIL;;i,.: ::i,! :: i: ii,:: ILLI.L..LI..I LIILLL,'LL"L:!',:I1,IL, v.:.":,.,. IIIII..L.I.ILI.I...IIIIIIL.I.....,.".'L:..::::: :i.-:] x :! :::i. ]." LIIL..I:L'LLIL'.....' III.IIL.L:L:i::.LLL'IIL'IL'IL'IIII. L,....L.LLLII, II.,L'I1 ,LLLL:':L:'LI:.:L..:.:,..,:L: IIIL.LII.LILIL,:.L:L:':IILIL'L'.. ILI..IILIII.III I.I:LLI.I.II, II:':' L.','. ILI.1LL,'LL.'L:.': I.,L.L''' IL'I' L.LL,.L'.L,'.:j!,L..,...,:L', ILIII,..."I:L.::.. I.:':::'L......L,,"'L L.II.IIIL.....I.I IL.I.III."LLL.,I.,..::I.IL,,,..L.LII.ILIII LL'II:LL:..:'':::::::::::.L:' I..L.I. I.IIIIIIL,II.LL:L:L'L'L:':L"'':.:.,,".:.IL,.ILIL'II:'L'''L'' I.,LLI,::' L, L:'.IIIIL''...., I I.LL'L.,,L IIIILL'. I..I..LI., II1,IL.:L::IL..LLL' IILIL'I...L"""' I.IILLILLL.::;:':: i,..,.,.,.:,.:L.'. IL.IILLL.IIIL'L".II.'L" L,.:,4,L:' LL: III ILIIL....II,,,.,, LI.,III.LLIIILL."..;1,...LL''...L. III.IIII.LL'.. LLLLL'.II.IL'.III:LLII.ILL',I1,,L:: Li, YL:L..:.,,:,L.:I:.: I1..LL.IIIILL.,::L''''L''' III.L...I.L..I.,,:..:::L.IL'.LI.L:I,.L, ILLILIILII.'LI..IILI'LL' I.LLLLI L...L, LI,..,,.,.':.:L, III.LI IIIIII,.L.':"::::' i' ILI,L.I,...L,::L II11.I.I:L I.,I....,II::L I.I.I' L::L:' L:L IIILL.IL'L LLILL' IIIILL.,L:,: LL':,.''.,:::,'L"Ll'.' LI IIL'......L ILIIL.....IL.....I L.IL. ILI..IL':.:. L:' L''L II.,L I...,:'. 1.::,:L,:':::::,::'L: I.L.. II.IIL'I...IIIII..,I...,L' II.LL.,::: i:i:::,' I.L.III.IL'. III.,%%%%'%'%L'.I.L II.III I.L... L.I,L....LI. .L.L'.,L'... II.I.I.L'L'.:,IILL:'IL:::L:,L:':' L.IILL':IIIIL'L:: :':':: I.IL":L:'. IIILI,:,,LL..II L'.I.LL':':'L'L'LL''..LI..LL..IILL::.:: :. : ILILL.IIL'L. II.II..LIL,,:L:::,:: IIL,I.IIIII-L:LL'"'...,:.,:,L''I:,L:,L:'::'.I.ILL1, 1,:',LLL.::.:..I..,IILL..IIILIIIIL' I.IL..,,ILL:'::L:: II.ILI., LLIIII., I.ILLIIIIIL I.LL,.,ILI":LLL:'::L, I..I.IL:LIII,,.IILII.I II.,,L.,,III I.I'L'.L.L'.II,,IILIIL'II,,L'.I.IILI.I,..,L' IL.L.LLI,.::L LI....., LIIII.LIL:...LL:'L'::L IILL.., I.IIL'I II,...IIIII IL.II.1,.I I.I..,:::'L" IIL I.I.I. ILL..I..I.II..I.I., LII.II.IL.ILIII,,., LI.I..I LIIIII.IL, IIILLL:L:'I:LL' L.,L. LI.I IIL.II I.I.L I.. LILI.IIII L.LLILL.:.1 I,:,I.,,II.I LILII

MATHESON" PANCAKE" PRESSURE REGULATOR AIR - FEED STOPCOCK AIR INLET 50 PSIG MERCURY MANOMETER 6-VOLT LAMP I \ w —M ~ - % VYCOR RESERVOIR VYCOR LIQUID- FEED LINE ELLIPTICAL ORIFICE ASSEMBLY TO WATER JACKET MICROSCOPE CATHETOMETER Figure 85. Flow Diagram for Oscillating Jet Apparatus.

Oscillating Jet Assembly The oscillating jet apparatus for measuring dynamic surface tensions is shown in Figure 85. Liquid contained in a one-liter, pressurized Vycor reservoir was fed to the elliptical orifice through Vycor tubing. The use of Vycor (96% silica glass, Corning Glass Co.) was necessary to prevent contamination of the liquid by leaching of the glass, as explained in Appendix D. The reservoir, Figure 86, maintained a constant pressure head at the orifice during the time required to measure wavelengths and diameters along the jet (the time for these readings ranged from 30 to 60 minutes). Any slight drop in static head below the desired pressure at point A permitted air from the pressure regulator to enter the reservoir. In this way a constant static head was maintained at the tip of the surmerged delivery tube regardless of the depth of liquid in the reservoir. The tip of the air tube was fire polished to a small diameter in order to reduce the size of the bubbles generated at A. Large air bubbles would be released from the tip at longer intervals and would cause wider pressure fluctuations at A than would small bubbles(2'4) Because of the small flow rates employed with the "micro-orifice", the rate of air discharge at A was very low, and those difficulties (pressure vibrations, etc.) observed by Addison were not encountered. Therefore investigation of an "optimum" tip diameter was not necessary and a convenient I. Do of about 0.5 mm, was employed. The orifice disc was supported by a threaded stainless steel retainer ring at the head of a stainless steel barrel, as shown in Figure 87. The inner surface of the barrel was polished to a mirror finish to

-146 BALL a SOCKET CONNECTION TO AIR LINE, VYCOR VYCOR TAPERED GROUND JOINT BALL a SOCKET CONNECTION TO LIQUID FEED LINE, VYCOR ONE - LITER VYCOR FLASK VENT STOPCOCK eZ2K CONSTANT PRESSURE LEVEL Figure 86. Detailed Construction of Reservoir Flask.

STAINLESS STEEL BARREL, I.D. SURFACE POLISHED TO MIRROR FINISH RETAINING WATER JACKET RING NEOPRENE 0- RING ORIFICE DISC Figure 87. Diagram of Oscillating Jet Barrel Assembly. Exploded View.

improve its resistance to corrosion. The orifice disc was "stamped" outward at the center to gain rigidity, and also to render the orifice visible beyond the 1/16-inch thick retaining ring. A 1 1/8-inch O.D. x 1/8-inch thick neoprene "O"-ring provided a leak-free seal against the face of the barrel. The barrel was surrounded by a water jacket, with which it was possible to control the temperature of the liquid leaving the orifice. Measuring Equipment The wavelengths of oscillation along the jet were measure with a 300-power microscope mounted on the barrel of a Pratt and Whitney Model M-1471 "Super-Micrometer" so that it could be moved horizontally parallel to the axis of the liquid jet. The distance moved by the microscope was read on the micrometer spindle, which reads directly to 0.0001 inch, over a range of 2.0 inches. Because of the dimensions of the retaining ring on the orifice assembly, the closest the microscope objective lens could approach to the jet was about 3/4-inch. The use of a standard 16-mm focal-length microscope objective would impose too low a magnification (lOOx) on the microscope for accurate measurements, where higher magnification objectives have focal lengths which are too short to allow focusing on the jet from as far away as 3/4-inch. However, by using an additional lens of moderate focal length as an "inverting1 lens in front of the objective lens, the effective focal length of the microscope was lengthened with no loss of magnifying power. Figure 88 shows the lens arrangement employed with the microscope in this study. The "telescoping" barrel of the microscope permitted flexibility in the object-to-lens distance, and also in the magnifying power.

I. 13Tr' I g 0o - 3" - Ar /1 - — x 1 I... U Ia — w —fl-MiRA n n n V * A _ ***"III I~~~~~~~~~~IL~ 1x EYEPIECE WITH CROSSHAIR W-I —-Yw 0 ELESCOPING BARREL "OBJECTIVE "LENS 5X, N.A.20 MICROSCOPE OBJECTIVE (16mm. FOCAL LENGTH) "INVERTING" LENS. 5X,N.A.20 MICROSCOPE OBJECTIVE (16mm. FOCAL LENGTH ) I I-',, Figure 88. Optical Arrangement of Cathetometer Microscope.

-150 The eyepiece of the microscope contained two cross-hairs at right angles to one another. Wavelengths were measured by alligning the vertical dross-hair with the midpoint of each node. Because of the small curvature, i.e., small ratio of amplitude to length, of the standing waves, it was impossible to determine the exact midpoint of the node very accurately unless the points of maximum amplitude along the jet were "pin-pointed" by illumination from above by a small, bright light source. This was accomplished by a 6-volt, 18-watt microscope-illuminating lamp with a 1/16-inch x 1 1/4-inch slit aperture (parallel to the jet), mounted above the jet. Because of the different angles of reflection and refraction along the jet surface as a result of the changing shape of the jet cross-section, the lamp could be positioned so that a distinct, sharply defined bright spot appeared exactly at the bottom of each nodeo Since the amplitude of each node was different, due to damping of the oscillations along the length of the jet, it was necessary to change the position of the lamp to obtain optimum illumination at each node measured, In order to measure the diameter of the jet at each node, the mount by which the microscope was attached to the barrel of the "SuperMicrometer" was constructed to permit very fine movement vertically, independent of the horizontal movement of the micrometer, (Figure 89). The distance moved vertically was measured by means of a Linear Variable Differential Transformer (LVDT). The construction of this sensing element is shown in Figure 90. The LVDT is a small, annular-wound transformer with a center-tapped secondary and a moveable iron core. A high frequency AC voltage applied to the primary winding induces voltage in the secondary.

ZERO ADJUSTMENT - FOR LVDT LVDT SENSING ELEMENT TRACK FOR _ MICROSCOPE BARREL "SUPER - MICROMETER " SHAFT FINE ADJUSTMENT MICROSCOPE FOCUS Figure 89. Microscope Mounting with LVDT Sensing Element.

-BRASS LOCKING NUTS r-FLEXIBLE BRONZE ARM wfUf I ASS HOLDER RING / 4X50 BRASS SCREW WITH IRON LVDT CORE IN POSITION Figure 90. LVDT Sensing Element for Measuring Vertical Movement of Microscope.

The windings are so constructed that when the iron core is positioned symmetrically in the hollow core of the LVDT, the voltages in the two legs of the secondary winding cancel one another, yielding no outputo Any slight displacement of the core from this position will, however, cause unequal induction in the two secondary windings, resulting in a net secondary voltage. The direction of the displacement is indicated by the phase shift of the secondary output signal, and the magnitude of the displacement is linearly proportional to the output voltage over a specific range of displacement. In this way the LVDT is capable of measuring extremely small movements with excellent accuracy. On the microscope mount, the LVDT measured the displacement of the moveable section of the mount relative to the fixed section. The LVDT used in this apparatus was a Schaevitz type 005 ML, which has a maximum linear range of 0.005 inch. This was used in conjunction with a Dyna-Myke Model 129C control unit (Industrial Electronics, Inc.) which supplied the 8-kilocycle carrier sygnal and measured the output signal. When calibrated for the specific LVDT used with the Dyna-Myke unit, the Dyna-Myke read the displacement directly, in micro-inches, on a meter dial. The unit was calibrated by displacing the core in the sensitive element with several "feeler" gauges which had been previously verified with a micrometer. With extreme care, the "feeler' gauge readings could be reproduced with an accuracy of about + 10 micro-inches, which probably corresponds to the accuracy of the gauge thickness.

-154 The diameter of the jet at each node was measured by moving the microscope vertically to allign the horizontal cross-hair with the top and bottom edges of the jet image and reading the vertical displacement of the microscope from the Dyna-Myke meter. During these measurements, the jet was illuminated from behind to give a sharp silhouette. A 6-volt, 18-watt microscope illuminator lamp, mounted vertically behind the jet was used for this, the light rays being directed on the jet by an adjustable mirror. Both the back-lighting lamp and the front-lighting lamp used to illuminate the nodal peaks were fitted with bi-chromatic filters to reduce chromatic abherration, thus rendering a sharper image in the microscope. JET THERMOCOUPLE The temperature of the liquid in the jet was estimated by allowing the jet to impinge upon the fused junction of two 40-gauge Chromel-P and Copel-X thermocouple wires. The junction was small enough so that it was completely enveloped by the impacting liquid, so that cooling effects due to evaporation were probably negligible~ The thermocouple EMF was measured on a Leeds and Northrup Noo 8662 Precision Potentiometer, with an ice-water cold junction. The thermocouple calibration appears in Appendix Go OPERATION OF TE MICRO-ORIFICE Before each run the orifice was thoroughly cleaned to remove any deposits from the previous run (see Appendix D) by immersing it in

warm detergent solution in a "Sonogen" ultrasonic bath until the orifice edges appeared clean under a 500-power microscope. The orifice was then rinsed with distilled water and dried in warm airo Because even the smallest particles will lodge in or near the micro-orifice, extreme care was taken to fill the reservoir with liquid containing as few solid particles as possible. For most liquids this was accomplished satisfactorily by distillation directly into the closed reservoir flask through a fused quartz condenser with Vycor joints. When charging electrolyte solutions into the reservoir, it was necessary to pipette freshly filtered concentrated electrolyte into the reservoir flask, Double distilled water was then re-distilled into the reservoir through a quartz condenser. The amount of water added to the reservoir was determined by weighing the reservoir on a Seederer-Kohlbusch analytical balance, which is capable of accuracy to + 0.005 gram at weights of about 2000 grams. Filtration of the electrolyte solution was performed through a microporcelain bacterial filter candle. After the reservoir had been loaded, and the air and feed lines had been connected, the reservoir vent was closed and the air regulator was adjusted to the desired pressure. The orifice and retaining ring were removed from the barrel to allow air and liquid to discharge rapidly. When sufficient liquid had purged the feed line and barrel, the retaining ring was replaced and slowly tighened, so that the last traces of air were allowed to bleed out before the orifice was sealed securely. The barrel was rotated until the inscribed line on the orifice plate, indicating the major orifice axis, was parallel to the axis of the microscope,

-156 The barrel was then adjusted so that the liquid jet; was horizontal and parallel to the axis of the "Super-Micrometer." Next the Dyna-Myke was adjusted for phase allignment, and the meter calibration was checked and adjusted if necessary. The microscope was placed into its mount and focused on the jet, near the orifice. After the levelness of the jet had been verified by a lengthwise traverse with the microscope, the liquid flow-rate was measured by catching the jet for exactly two minutes in a 5-ml. capacity pycnometer bottle. As soon as the sample had been collected, a ground glass cap was placed into the mouth of the bottle to prevent evaporation losses before the bottle could be weighed, Following this, the front-lighting lamp was positioned to best illuminate the peak at the first node and the mirror for the back-lighting was adjusted to produce the sharpest contrast in the silhouette of the jet. The wavelength and jet diameter were now measured alternately at each node; the back-lighting alone being used for obtaining the diameters, and only the front-lighting being used for locating the nodal peaks. Four separate readings were made of each d1imension and the average recorded for each, Measurements were taken for as many nodes as could be illuminated sharply enough to permit satisfactory accuracy of measurement. The separate wavelength measurements at each node usually agreed to about + 0.00005 inch. The separate diameter measurements usually agreed to about + 0,00001 inch. After the final wavelength measurement, the thermocouple was positioned to intercept the jet and the t liquid temperature was recorded. Early experiments showed that the temperature of the liquid in the jet did not decrease perceptibly along the length of the

jet, so that cooling of the jet surface by evaporation appears to be negligible. The liquid jet was again collected in a second pycnometer bottle for a period of two minutes. The liquid flow rates were then determined by weighing on an analytical balance. The initial and final rates were usually found to agree within one-tenth of a percent. A run usually required 45-60 minutes, CALIBRATION OF THE MICRO-ORIFICE Before using the micro-orifice for determining dynamic surface tensions it was first necessary to investigate the following: (a) applicability of Equations (7), (9-C), or (23-E) (b) effect of liquid rate (c) effect of liquid physical properties (d) effect of jet dimensions. For this reason it was attempted to calibrate the jet by measuring the dimensions of oscillations produced at various liquid rates on jets of seven pure liquids having known surface tensions and widely varying physical properties. They are as follows: Nominal Nominal Nominal Nominal Liquid Surface Tension Density Viscosity Kinematic Viscosity dynes/cm. g/cc. cps. centistokes Water 73 1.00.95 O95 Nitrobenzene 43 o 20 2.00 lo 67 Diethylaniline 34.93 1.93 2, 08 Carbon Tetrachloride 27 1,60.99 62 Acetone 24 o79.33 o42 Methanol 22.79.58.74 Isopropanol 22.79 2 30 2o 91

-158 The water used for calibration was double-distilled in a Barnstead tin-plated copper still (School of Pharmacy Laboratories, The University of Michigan), followed by redistillation into the reservoir bottle through a fused-quartz condenser. Reagent grade carbon tetrachloride, acetone, methanol and isopropandl were each redistilled into the reservoir through the fused-quartz condenser. The diethylaniline was Eastman Chemicals Company, practical grade, twice vacuum-distilled through the fused-quartz condenser, with only the middle fraction of the second distillation being fed to the reservoir. The nitrobenzene, reagent grade, was used in the jet without redistillation. Correction factors were obtained by dividing the calculated surface tensions by the corresponding known surface tensions. It was discovered early that Equation (23-E) gave calculated values more closely agreeing with the known surface tensions than the classical equations (7) or (9-C). Efforts were then placed on correlating the correction factors resulting from Equation (23-E) with operating variables for the jet. In calculating correction factors for the calibrating liquids it was necessary to assume a time-independent surface tension equal to the known equilibrium surface tension, Although it is possible that small changes in surface tension may occur along pure liquid jets because of molecular re-orientation, absorption of air, electrical effects, or contamination, such changes should be minor, Calibration measurements obtained with the seven pure liquids are presented in Appendix Z along with the resulting correction factor, Ko

Although it is possible to correlate K for all seven liquids as a function of jet variables, a more satisfactory correlation is achieved if only the calibration data for water are considered. Since the micro-orifice was to be used primarily for determining dynamic surface tensions of dilute aqueous solutions the following water calibration was developed for use with the frothing liquids. Water Calibration Contrary to Rayleights(128) premise of constant cross-sectional area in the jet (see p. 181, Appendix A), it was found that the geometric mean radius of the jet from the mocro-orifice changes appreciably from node to node. Although the inaccuracies involved in measuring the jet diameters (+ 0.5%) undoubtedly account for some of this observed variation in mean radius, the radius changes do not appear to be random, and have been found to be quite reproducible during the course of each run (an elapsed time of about one hour). The change in mean radius along the length of the jet is shown for several typical water runs in Figure 91. From Figure 92 it can be seen that the correction factor varies as a function of the mean radius, asymptotically approaching the straight line, 5Calc. Kr = aCalq - I + Br (12) ~, = I +Brg (12) aKnown Examination of the calibration data indicates that the intercept, I, for each water run can be satisfactorily correlated as a function of the linear velocity of the free jet, c, so that as indicated by Figure 93, Equation (12) for all water runs was found to be

1.04 1.02 1.00 0.98 RUN 409 w 0.96 U. 0 Ic: 0.94,,06. z L ____ ________ ____ ________ R U N 4 11 Cn iRdslg gtof/ 092 I - tL / ~0~~~~ 0.90 0.88 0.86 0 0.02 0.04 0.06 0.08 DISTANCE FROM ORIFICE, INCHES Figure 91- Change in Radius Along Length of Jet,

1.06 1.02 0.98 0: o I o z 0 U cr 0 U 0.94 0.90 0.86 I H 0.82 0.78 0.74 05 OB7 0.89 0.91 0.93 0.95 0.97 0.99 GEOMETRIC MEAN RADIUS OF JET, MILS Figure 92. Relation of Correction Factor, K, to Jet Radius, 1.01 1.03 1.05

-162 2.52 2.50 2.46 2.46 - u. 1^ 2.44 2.42 2.40 IA SLOPE — 0.0082 —__ I 2.30 -0.0062 C ___ ___ SLOPE - 0.0082 l....... C i!I 2.630 -0.0082 C S I..I.......... ( I, -- -- 11 - - - - - - - 1 11 1___ __ __ __ __ __ __ __ __JzL 2.38 2.36 2.34 20 22 24 26 26 30 LINEAR VELOCITY OF JET, C, FT/$EC Figure 93. Relation of Intercept I to Jet Velocity (Calculated at Second Node of Jet). 32

Kr = 2.630 - 0o0082c - 834 rg o (13) The asymptotic approach of the observed correction factor K toward the Kr values indicated by Equation (13) suggests the use of Hansen's(78) empirical correction K K= (s)-0.63 (14) KH Kr c where cs = velocity of liquid at jet surface, and c = bulk liquid velocity in jet. Bohr's(27) expression for the velocity profile in a free liquid indicates that the surface velocity along the jet can be approximated as Ip~z = c - Ae-7 (pL) (15) in which A is some constant indicative of the initial velocity decrement at the orifice exit, and (pL ) is a dimensionless group. Hansen's correction can then be written: K L A 7l5 -0L.3 (16) - - e (16) or n l - K RH n A - 7015 (L). (16a) L j Jc pL Equation (16a) indicates that if Hansen's correction is applic-1. 588 able to the micro-jet a plot of log [1 - KH1 ] vs. the dimensionless group (-) should yield a straight line with a slope of -7.15o Figure 94 shows that the semi-log plot of the water calibration data gives straight lines with the proper slope.

0.400 0.200 0.100 0.080 0060 0.040 0 0 Ca in I m 2:'___ ___ \^ <___ ___ ___ SLOPE =- 7.15 L~^ 1Y ______________^_____K__.....== %===EE==S^=^= P~~~~ %e~ o~~~~~~~~~~~~~~~~. I I I I, I II ii i I19c I F 0.020 0.010 0.008 0.006 0 0.04 0.08 0.12 0.16 ( pL S Figure 94. Plot of Equation (6a) for Several Water Figure 94. Plot of Equation (16a) for Several Water 0.20 0.24 0.28 Calibration Runs.

-165 Values for A/c were taken from the y-intercepts of these semi-log plots. The constant A characterizes the initial velocity profile at the orifice exit, and should be a function of the orifice dimensions and the Reynolds Number of the flow through the orifice. Because of the rounded shape of the micro-orifice, and the consequent poorly-defined flow pattern at its exit, a good correlation for A as a function of Reynolds Number was not obtained. An approximate correlation is shown in Figure 95, -Lro - 0.000543 A - 17.9 - 41200r -- 1 (17) where L = liquid rate, cc/min. ro - mean radius of jet, extrapolated to orifice, inches (a/ major diameter (a/b) o major diameter, extrapolated to orifice o minor diameter The Hansen correction factor then'becomes K 41 (Lro - 0000[e4 e75( -~e65 Kz = 1 = - 17.9 - 41200 (- -----. (18) H Kr I L (a/b) - 1 C \ c J The combined correction factor then becomes K Kr - KH,|z Oo 0, 0041-37~15(Pr F /Lro-0.00045 e [2.63- 0.0082c- 834rg]- 1 - 17.9 - 41200 (/b- - } \ 5 —-- 9 [ a/b)o - 1 c (19) Values for K, Kr and KH calculated from Equation (19) are listed in Table I, Appendix A. Also listed are corrected surface tensions calculated from the water calibration data using these factors. In Figure 18, p. 355 are plotted calculated surface tensions for several typical water calibration runs. It is seen that although the

'(5T) uoTF8nbai n a v q.eqsuoo rTx.Tidma gIOj UOr8TqaJa.oo aqsmrpxociddv *6 aJn;T,o,[ q-'(] t~~ ) (000' - J1 S~'O 0C0 SZO \ I ~ - -------- ---- ---- -- - ( 01 )01' - ~ 0O0t;' I - — ""-"= 3d01S 8ef~ + 9'L1 ~z - ---- --- ---- --- --- --- --- ---- --- --- -- - - 9 ~- S~~~~~~~~~~~~ -99T

absolute value of the calculated surface tensions may differ from the known value by as much as four dynes per cm,, the scatter between the separate values calculated for each run is usually less than + 0. 7 dyne per cm,. The surface tension calculated at the first full node shows a larger deviation than this. Surface tension values calculated using the correction factor K, and the CONCLUSIONS derived from them are found in Sections I-E and I-F, pp 34 and 74 respectively.

NOMENCLATURE A a b c Cs e f I,(x) I'(x) n Kn(x) K KH Kr k L tapp ts r,rs ro r vS V xo xs constant in Bohr's velocity distribution equation major axis of ellipse minor axis of ellipse bulk liquid velocity liquid velocity at jet surface base for Naperian logarithms frequency of oscillation, per second Modified Bessel Function of the first kind, order n derivative of In(x) Modified Bessel Function of the second kind, order n empirical correction factor Hansen s correction factor empirical correction factor due to radius wave number, 2c/X Liquid flow rate, cm, per minute "apparent" jet age, z/c jet surface age radius at any point on jet surface arithmetic mean radius of jet geometric mean radius of jet superficial gas velocity volume bulk liquid concentration surface concentration of liquid -168

z distance from orifice, along jet zc depth of clear, unaerated liquid, inches zf depth of froth mixture, inches a amplitude of oscillation G angle of rotation about axis of jet X wavelength of oscillation (I ~ liquid viscosity p liquid density a liquid surface tension relative froth density

BIBLIOGRAPHY 1. Adams, N. K., The Physics and Chemistry of Surfaces, 2nd Edition, Oxfor d UT:iJ'ers- t.y Prec,.Tondo.l (_'.i. 2o Addison, C, C., J. Chem. Soc., 535 (1943) 35 Addison, C. C., J. Chemo Soc., 252, 477 (1944). 4. Addison, C, C., Phil, Mag. (London) Series 7, 36, 73 (1945)o 5. Addison, C. C., and T, A. Eliot, J. Chem. Soc., 3090 (1950). J. Chem. Soc,, 2789 (1949), 6. Ader, J,, J. Phys. et Radium 11, 196 (1950) 7. American Institute of Chemical Engineers Research Committee, Bubble Tray Design Manual, AIoCh.E., New York (1958). 8. Ashby, B. B., Ph. D. Thesis, University of Michigan, (1956). 9. Ashraf, F. A., Cubbage, To L., and Huntington, R. L., Ind. Eng. Chem., 26, 1068 (1934). 10. Axelrod, L. S., and Dilman, Vo Vo, Zhurnal Priklad. Khim,, 27, 485 (1954), Also J. Applied Chemo, (USSR) 27, 449 (1954), (English Translo). 11. Bagnoli, E., Ph. D. Thesis in Chem. Engrg,, University of Delaware, (1950), 12. Bailey, R. Vo, Taylor, F, Mo, Zmola, Po C,, and Planchet, R, JT,, Paper presented at AoIoChoEo Meeting, New Orleans, May 8, 1956. Also Trans. Amo Soc. Mecho Engrs 78, 881 (1.956) 13. Bakowski, S.O Chemo Engro Scio, 1, 266 (1952). 14. Bartsch, 0, Kolloidchemo Beiheft 20, 1 (1924). 15. Bartsch, 0., Kolloid Zo 38, 177 (1926). 16. Begley, J. W., Ph, D. Thesis, University of Michigan, (1959). 17. Benzing, R. J., and Myers, Jo E,, Ind. Engr. Chem. 47, 2087 (1955). 18. Berkman, S., and Egloff, Go, Emulsions and Foams, p. 116, Reinhold Publishing Corporation, New York (1941) 19. Berry, V. J,, J. Chem. Physics 20, 1045 (1952).

-171 20. Bikerman, J. J., Journale de Physique et Radium [6] 9, 386 (1928). 21. Bikerman, J. J., J. Phys. Chem. 56, 164 (1952). 22. Bikerman, J. J., Foams --- Theory and Industrial Applications, Reinhold Publishing Corporation, New York (1953). 23. Bikerman, J. J., Surface Chemistry, 2nd Edition, Academic Press, New York (1957). 24. Birkhoff, G., Hydrodynamics --- A Study in Logic, Fact, and Similtude, p. 49, Princeton University Press, Princeton (1950). 25. Bocquet, P. E., Univ. of Mich. Eng. Research Bull. 33, Two Monographs on Electrokinetics (1951). 26. Bocquet, P. E. and Sliepcevich, C. Mo, and Bohr, D. F., Ind. Engo Chem. 48, 197 (1956). 27. Bohr, N., Phil. Trans, Roy. Soc. (London) A 209, 281 (1909). 28. Boys, C. V., Soap Bubbles and the Forces Which Mould Them, p. 131, Society for Promoting Christian Knowledge, London (1890). (Reprinted 1959, Doubleday Anchor Books, Science Study Series). 29. Brady, A. P., and Brown, A. G., Monomolecular Layers, Symposium edited by H. Sobotka, American Association for Advancement of Science, Washington D. C. (1954), 30. Breitner, H., Kolloid Z. 100, 335 (1942). 31. Breitner, H., Chem. Zentr. I, 134 (1943). 32. Brown, A. G., Thuman, W. C., and MCBain, J. W., J. Colloid Sci. 8, 508 (1953). 33. Burcik, E. J., J. Colloid Sci. 5, 421 (1950). 34. Burcik, E. J., J. Colloid Sci. 8, 520 (1953). 35. Camp, M., and Durham, K., J. Phys. Chem. 59, 993 (1955). 36. Cassel, H. M., J. Appl. Physics 15, 792 (1944). 37. Chaminade, R., Compte Rendo 228, 480 (1949). 38. Chu, J. C., Forgrieve, J., Grosso, R., Shah, S. M., and Othmer, D., A.I.Ch.E. Journal 3, 16 (1957). 39. Colburn, A. P., Ind. Engr. Chem. 28, 526 (1936).

-172 40. Crozier, R. Do, Ph. D, Thesis, University of Michigan (1956). 41. Cullen, E. J., and Davidson, J. Fo, Trans. Farad. Soc. 53 (Part I), 113 (1957) 42. Cutler, W. G., and Martin, A, Ro, Paper presented at AoC.S, Meeting, Boston, April, 1959. 435 Davidson, Leon, Ph, Do Thesis, Columbia University (1951)o 44. Davis, R. F., Proc. Inst. Mech. Engrs. 149, 198 (1940). 45. Derjaguin, B. V., Bull. Acad. Sci,, U.RoS.So, Serie Chemique 5, 1153 (1937). 46. Derjaguin, B. V., Acta Physicochimica, UoRoSoSo 10, 333 (1939). 47. Derjaguin, Bo V., Trans. Farad. Soc. 56, 204 (1940) 48. Derjaguin, B. V. and Titievskaya, Kolloid Zhur. 15, 416 (1953). 49. Dewar, J,, Proc. Roy. Inst. Great Britain 24, 197 (1925)o 50. Dombrowski, N. and Fraser, Ro Po, Phil. Trans. 247A, 101 (1954). 51. Donnan, F. Go, Jo Soc. Chemistry and Industry (London) 42, 892 (1923). 52. Dunstan, Ao Eo, The Science of Petroleum, Vol, II, po 1366, Oxford University Press, London (1938). 53. Dupre, A., Theorie Mecanique de la Chaleur, p. 352, GauthierVillars, Paris (1869). 54. Dyakonov, G. K., J. Tech. Phys. (USSR) 12, 302 (1942). 55. Eberle, C., Archiv. Warmewirtshaft u Dampfkesselwesen 10, 339 (1929). 56. Elton, G. A. H., Proc. Roy. Soc. A194, 259 (1948) 57. Eversole, W. G., and Boardman, W. Wo, J. Phys. Chemo 46, 914 (1942). 58. Eversole, W. G., and Deardorff, D, L,, J. Phys. Chem. 45, 236 (1941). 59. Eversole, W. G., Wagner, Go Ho, and Stackhouse, Eo, Indo EngYr Chemo 33, 1459 (1941). 60. Ewers, W. E., and Sutherland, K. Lo, Australian Jo Sci, Research A5, 697 (1952),

-173 61. Faraday Society, Symposium, Trans. Faraday Soc. 33, 1 (1937). 62. Finzi-Contini, B., Chimica e Industria 36, 452 (1954)o 63. Foss, A. S., and Gerster, J. A., Chem. Engr. Progo 52, No 1, 28-J (1956). 64. Foulk, C. W., Ind. Eng. Chem. 21, 815 (1929). 65. Foulk, C. W., Trans. Am. Soc. Mech. Engrs. RP-54-5, 105 (1932). 66. Foulk, C. W., Ind. Eng. Chem. 33, 1086 (1941). 67. Foulk, C. W., and Barkley, J. E., Ind. Eng. Chem, 35, 1013 (1943), 68. Foulk, C. W,, and Miller, J. No, Ind. Eng. Chemo 23, 1283 (1931). 69. Geddes, R. L., Trans. A.I.Ch.Eo 42, 79 (1946)o 70. Gerster, J. A., Bonnet, W. E., and Hess, I., Chemo Eng. Prog. 47, No. 10, 523 (1951). 71. Gerster, J. A., Bonnet, W. E., and Hess, I., Chem. Engo Prog, 47, No. 12, 621 (1951). 72. Gibbs, J. W., Collected Works, Vol. I, Longmans, Green, and Co,, New York (1928).73. Grassman, P., Chem. Zentro I, 3179 (1942). 74. Grassman, P., Z.Ver. Deut. Ing,, 28 (1942). 75. Halberstadt, S., and Prausnitz, P. H., Z. Angew. Chem. 43, 970 (193 76. Hancock, J. S., J. Soc. Chemo Industry 49, 369 T (1930). 77. Hansen, R. S., Iowa State College Journal of Science, 30, Noo 2, 301-311 (1955). 78. Hansen, R. S., Purchase, Mo Eo, Wallace, T, C,, and Woody, Ro Wo, J. Phys. Chem. 62, 210 (1958). 79. Harbert, W. D., Homan, E. S., Roseberry, D. D., and Huntington, R. L,, Refiner and Nat'l Gasoline Manufacturer 20, 170 (1941). 80. Hatcher, J. B., and Sage, B, H., Ind. Eng. Chem. 33, 443 (1941). 81. Hazelhurst, T. H. and Neville, H, Ao, J. Phys. Chem. 41, 1205 (1937). 82. Hazelhurst, T. H. and Neville, H. A., Jo Phys. Chemo 44, 592 (1940)o

-174 83. Hazelhurst, T, Ho, and Neville, H. A, Ind. Eng. Chem, 335, 1084 (1941). 84. Helmholtz, H., Ann. Physik (3), 7, 337 (1879). Translation by P. E, Bocquet, "Two Monographs on Electrokinetics", Univ. of Micho Engrg. Research Bull. 33 (1951). 85. Higbie, R., Trans. Am. Inst. Chem. Engrs., 31, 365 (1935). 86. Hoffman, K., Erdol u. Kohle 6, 791 (1953). 87. Holbrook, G, E., and Baker, E. M., Ind. Eng. Chem. 26, 1063 (1934). 88. Holbrook, G. E,, and Baker, E. M,, Trans. AoIoCh.E. 30, 543 (1934). 89. Houghland, G. S., and Schriener, W. C., Proceedings, 6th Meeting, National Conference on Industrial Hydraulics, Vol. 4, p. 75 (1950). 90. Houghton, G., MCLean, A. M., and Ritchie, D. P., Chemical Engrgo Science, 7, 40 (1957). 91. Hughes, R. R., Handlos, A. E., Evans, H. D., and Maycock, R, L., Chem. Eng. Prog. 51, No. 12, 557 (1955). 92. Hurd, R. M., and Hackerman, N., J. Electrochem. Soc. 102, 594 (1955). J. Electrochem. Soc. 103, 320 (1956). 935 Hutchinson, M. H., and Baddour, R. F., Chem, En.g Prog. 52, 503 (1956). 94. Hutchinson, M. H., Burton, A, Go, and Miller, B, P,. Paper presented at Regional Meeting of A.IChEo,, Los Angeles, May, 19490 95. Irany, E. P., J. Am. Chemo SoCo 61, 1436 (1939) 96. Jennings, H. Y,, Jr., Rev. Scio Instruments 28, 774 (1957). 97. Joseph, A. F,, and Hancock, J. S., J. Soc. Chem. Ind. 46, 315 T (1927). 98. Kaiszling, F., Forschung, Bdo 149 Heft 1, p. 30. 99, Kaufman, H. P., and Kirsch, P,9 Fetti u. Seifen 47, 191 (1940). 100. Klein, J. Ho, Sc. D. Thesis in Chem. Engrg., Massachusetts Institute of Technology (1950), 101. Klinkenberg A., and Mooy, H, H., Chem. Eng. Progo 44, 17 (1.948).

-175 102. Kruyt, H. R, and Oosterman, J., Proc, Acado Sci. Amsterdam, (Proc. Section of Science) 40o 404 (1937)o (Proc. Section of Science) 41 370 (1938). 103. Lamb, H., Hydrodynamics, 5th Edition, Cambridge University Press, (1924). 104. Lange, N. A., Handbook of Chemistry, Handbook Publishers, Inc., Ohio (1949). 105. Leibson, I., Holcomb, E. G., Cacoso, A. Go and Jacmic, J. H., Special Report 226, Pilot Plants Div., Camp Detrick, Frederick, Maryland (1955). 106. Lippmann, G., Ann. Chim. Phys. 5 5, 494 (1875). 107. Marangoni, C., Nuovo Cimento, Ser, 2, 5-6, 239 (1871). 108. Marangoni, C., Nuovo Cimento, Ser. 3, 3, 97 (1878). 109. Miles, G. D., and Ross, S., J. Phys. Chem. 48, 280 (1944). 110. Miles, G. D., Shedlovsky, L., and Ross, Jo, Jo Phys. Chem. 49, 93 (1945). 111. Miller, R,, Ph. D. Thesis, University of Michigan (1959). 112. Nakagaki, M., Kagaku no Ryoiki 6, 583 (1952). 113. Nakagaki, M., J. Phys. Chem. 61, 1266 (1957). 114. Nakagawa, T., and Shameshima, J., J. Chem. Soco Japan 64, 360 (1943). 115. Newitt, D. M., Dombrowski, N, and Knelman, F. H., Trans. Inst. of Chem. Engrs. (London) 32, 244 (1954). 116. Nutting, G. C., and Long, Fo A., J. Am. Chem. Soco 63, 84 (1941) 117. Obrien, M. P. and Gosline, J E., Ind. Eng. Chem. 27, 1436 (1935). 118. Pedersen, P. 0., Phil. Trans. Roy. Soc. (London) A 207, 341 (1907). 119. Pinkel, I. I., National Advisory Committee for Aeronautics, Advanced Restricted Report No. E4K01, Washington D. C. (1944). 120. Plateau, J., Mem. Acad. Royo Sci., Belgique 37, Ser. 8, 49 (1869)o 121. Plateau, J. Statique Experimentale et Theoretique des Liquides Soumis aux Seules Forces Moleculaires (1873).

-176 122. Pokhil, P. F., J. Phys. Chem. (USSR) 14, 554 (1940)o 123. Posner, A, M. and Alexander, Ao E., Trans. Farad. Soco 459 651 (1949). 124. Quigley, Co J., Ph. D. Thesis, Johns Hopkins University (1953)o 125. Quigley, C. J., Johnson, Ao Io, and Harris, B. L., Chem, Eng. Prog. Symposium Ser, 51, No. 16, 31 (1955). 126. Quincke, Go. Anno Physik, Sero 3, 355, 580 (1888). 127. Ragatz, E, G. and Baxter, H. A., Oil and Gas J. 54, No. 50, 158 (1956), 128. Rayleigh, J. Wo S., Proc. Roy. Soco (London) 29, 71 (1879). 129. Rayleigh, Jo W. S.o Proc. Roy. Soc. (London) 34, 130 (1882). 130. Rayleigh, J. W. S., Proc. Roy. Soco (London) 47, 281 (1890)o 131. Rayleigh, J. W. So, Proc. Roy. Soc. (London) 48, 363 (1890). 132. Rayleigh, J. W. S.o Philo Mag, 34, 145 (1892). 133. Reinold, A, W., and Rucker, A. Wo. Phil. Mag. Ser. 5, 19, 94 (1885). 134. Rexford, D. R., Ind. Eng. Chemo, Anal, Ed, 135 95 (1941) 135. Rhodes, F. H., Ind. Engo Chemo 26, 1333 (1934) Indo Eng. Chem. 27, 272 (1935). 136. Rhodes, F. H., and Slackman, P. G,, Ind. Eng. Chem. 29, 51 (1937). 137. Rhumbler, L., Ergebo Physiolo 14, 526 (1914). 138. Rideal, E. K. and Sutherland, K. L., Trans. Farad. Soc. 48, 1109 (1952). 139. Robinson, C. S. and Gilliland, E. Ro,, Elements of Fractional Distillation, 4th Edition, p. 415, MCGraw-Hill Book Co., New York (1950) o 140. Ross, S. and Butler, J. No. Jo Phys. Chem. 60, 1255 (1956). 141. Ross, S. and Haak, Ro Mo, J. Phys. Chem. 62, 1260 (1958). 142. Ross, J. and Miles, G. Do, Oil and Soap 18, 99 (1941)

-177 143. Sasaki, T., Bull. Chem. Soc. Japan 15, 517 (1938)o 144. Schiller, L., Forschungsarbo Gebiete Ingenieurw. Heft, 245, 1 (1922). 145. Schmidt, E., Behringer, P., and Schurig, W., VoD.I. Forschungsheft 565, 1 (1934). 146. Schnurmann, R., Z. Physik. Chem. A 143, 456 (1929). 147. Schnurmann, R., Kolloid Z. 80, 148 (1937). 148. Schnurmann, R., Indo Eng. Chem. Anal. Ed.o 1, 287 (1939). 149. Schutt, H. C., Petrol. Refiner 24, No. 7, 249 (1945). 150. Schutz, F., Trans. Farad. Soc. 38, 85 (1942) 151. Scott, P. H. and Rose, W. D., Effect of Fluid-Fluid Interfaces on Flow of Fluid Mixtures in Porous Media, Conoco Oil Co., Developo and Res. Dept. Report No. 137-53-102-30 (1953). 152. Seeliger, R., Die Naturwissenschaften 36, 41 (1949). 153. Sherwood, T. K. and Jenny, F. J,, Ind. Eng. Chem. 27, 265 (1935)o 154. Shkodin, A. M., Kolloid Zhurn. 14, 213 (1952). 155. Shorter, S. A., Phil. Mag. 27, Ser 6, 718 (1914) 156. von Smoluchowski, M., Handbuch der Elecktizitat und des Magnetismus, Vol. II, 366-428, Leipzig, Barth (1921). Translation by P. Eo Bocquet, University of Michigan Eng, Research Bullo 33, Two Monographs on Electrokinetics (1951) 157. Souders, M. and Brown, G. G., Ind. Eng Chemo 26, 98 (1934) 158. Souders, M., Huntington, R. L., Corneil, H. G. and Emert, F, L., Ind. Eng. Chem. 30, 86 (1938). Also Trans. AoIoChoE. 34, 71 (1938). 159. Spells, K. E., Trans. Insto Chem. Eng. (London) 32, No. 35 167 (1954). 160. Spells, K. E. and Bakowski, S., Trans. Insto Chemo Eng, (London) 28, 38 (1950). 161. Spells, K. E. and Bakowski, S., Trans. Inst. Chemo Eng. (London) 30, 189 (1952). 162. Stabnikov, V. N., Khim. Machinostroemi 8, No. 6, 17 (1939)o

-178 1635 Stewart9 Go W., Chemical Rev. 6, 483 (1929). 164o Stone, Ho L., Sc, Do Thesis in Chem, Engr., Massachusetts Institute of Technology (1953)o 165. Strang, L. Co, Trans. Inst, Chem. Engrso (London) 12, 169 (1934) 166. Strang, Lo Co, J. Inst. Petrol, Tech. 22, 166 (1936)o 1670 Stuhlman, D., Physics 2, 457 (1932)o 168. Stumpner, R,, Die Werme 59, 463 (1936). 169. Talmud, D., and Suchowolskaya, S. Z. Physic. Chem. 39, 1108 (1912). 170. Terres., E,, Gebert, F., Fischer, D., and Modak. G., Brennstoff-Chem. 35, 263 (1954). 171. Thompson, A. K. G., Trans. Inst. Chem. Engrs. (London) 14, 119 (1936)o 172. Trapeznikov, A. A., Acta Physicochim. USSR 9, 273 (1939) 173. Turner, G. M., Formation of Bubbles at Single Orifices, Presented at A.I.Ch.E. Meeting, San Francisco (1953)o 174. Verschoor, Ho, Trans. Insto Chem. Engrso (London) 28, 52 (1950)o 175. Villar, Go E,, Boliv. Faec Ing. Motevideo 4, 403 (1951) 176. Villar, G. E,, Quimica Indo (Uraguay) 2, No. 3, 5 (1952). 177. Walter, J. F., and Sherwood, To K., Ind. Eng. Chem. 33^ 493 (1941). 178. Warzel, Lo A,, Ph, D. Thesis, University of Michigan (1955). 179. Whitman, W. Go, Chem. Met. Engro 29, 146 (1923). 180. Wilson, Ro E, and Ries, E, Do, Colloid Symposium Monograph 1, 145 (19235) 181, Yuster, So To, Proc. 3rd World Petroleum Congress, II, 457 (1951)o 182. Zocher, H., Z. Anorg. Allgem. Chem, 147, 91 (1925)o

APPENDIX A OUTLINE OF RAYLEIGH'S DERIVATION FOR FREQUENCY OF OSCILLATING JET -179

OUTLINE OF RAYLEIGHIS DERIVATION FOR FREQUENCY OF OSCILLATING JET The following discussion presents some important points of Rayleigh's analysis of the conditions existing in a free jet of liquid issuing from a non-circular orifice. Rayleigh's original treatment appears in Reference 128. The analysis is based on the following assumptions: a, the liquid is non-viscous b. the amplitude of oscillation is infinitesimal. Rayleigh's derivation employs both the Eulerian and Lagrangian points of view. In the Eulerian sense, in which the liquid is considered flowing past a system of fixed coordinates, the liquid jet is bounded by the surface S(r, G, z), which is fixed in space, and is therefore completely defined by the cylindrical coordinates r, Q, and z. If the deviation of the orifice from circularity is a periodic function about the circumference of a true circle of radius ro, the cross-section of the jet leaving the orifice may be expressed as r - r + b cos nQ (l-A) where n = mode of periodicity about circumference, and b = maximum amplitude of deviation from circularity at that cross-section. The mode, n, denotes the number of axes of symmetry contained in the cross-section. For example, n 1 corresponds to a lateral translation of the circle; n s 2 corresponds to an elliptically shaped section; n = 3 to a triangularly shaped section, etc,, as illustrated in Figure 1-a.

n n 2 n 3 Figure 1-a The maximum amplitude of deviation, b, is a function of the distance z, along the jet, according to the expression b = a cos kz (2-A) where k = 2j/X and X = the wavelength of one complete oscillation of the jet surface. (See Figure 1, p. 11, for diagram of jet surface. ) The equation for the surface of the liquid jet is therefore expressed as follows in cylindrical coordinates: r = ro + cos n cos kz (3-A) The radius, ro, about which the non-circular cross-section is displaced is not a constant value, but varies slightly as a changes so that the volume per unit of jet length is constant and equal to the volume of the undisturbed cylindrical jet, This is necessary to avoid acceleration in the Z direction. If the radius of the undisturbed cylinder is a, then its volume per unit of length is jta2. The volume of the non-circular section may be found from the expression, jZir V= ~7ff~z d 0o =?r (a,?A + si ak (4A)

-182 Neglecting the final term of this result leads to the volume per unit length, V 2 a a V r =:rX = Crn + 1o 0X (5-A) thus yielding the relation between a, ro, and a, fn = aV- I.'Z (6-A) Since a is assumed to be very small, - 462 -- 1 8 oa- and Equation (6-A) becomes R = 0 (l 8- )' (7-A) In order to relate the increase of potential energy to the displacement, a, it is first necessary to estimate the increase in surface area due to a. The area of a surface expressed in cylindrical coordinates can be found from the equation ^ Ba Area = +jj 1 vQ. (8-A) 0 0 Since a is assumed to be very small, the derivatives ar/6z and ar/aG are also small, and the above integral can be replaced by the approximate expression -i 27 Area J | + }ff C 2 ] L (9-A) 0 0 A further sinplication of the integration is accomplished as follows:

-183 ~(^\ t _msinm_ _coke, O si2 S k (10-A) x c<+O Cx cos r05 d5 k* nio In this way the surface area is found- to be Area = - ( r, -4 r), (11-A) Replacing ro by a from Equation (7-A), the area per unit of length is 4 Area _ aMa-2r~ + ~ +~'~' (12-A) Z 4 4.- 32 /4 If a _ 0, and trO< ra Tr o/n 4(L-8~) 4O the area becomes'Se Z.o+ ~ (ka ^ J -1) (13-A) The increase in area due to the displacement a is s - 2ia, and the increase in energy is equal to the excess surface times the surface tension, Thus the Potential Energy of the distorted surface is -E (j -Tc a - (4- A) Next, in order to find the Kinetic Energy of the liquid motion in the jet, it is necessary to investigate the flow potential relations in the jet. The requirements for steady-state flow in a non-viscous liquid yield the continuity equation at} + Z +- + I) + 0 (15-A) 3n' 7 n. ^-n n -L a OZ 3 2

Equation (3-A) suggests that the flow potential be of the following forms 0 = f(r) (cos nG cos kz) (16-A) where f(r) is a function of r which is to be determined, Then Ai = -.-, % = -ke and Equation (15-A) becomes and Equation (l5-A) becomes a 2 -,,, r, aw —- +k (17-A) Equation (17-A) is seen to be Besselts Equation with ikr as the independent variable. The solution to the equation is 0 = B In(kr) + C Kn(kr) (18-A) where In(kr) = Kn(kr) = B and C = Since Kn(O) o, and since [0]r=O # Also, in view of E Bessel's Function of the Bessel's Function of the functions of Q and z, to First Kind of order n, Second Kind of order n, be evaluated. oo then C must be zero, and = q ti n (k A), quation (16-A), (19-A) B = P cos nQ cos kz, and Equation (19-A) becomes 0 = P In(kr) cos nO cos kz. (20-A) (21-A)

-185 P may be evaluated by consideration of the radial velocity at the surface of the jet. The radial velocity of material in the jet results from the Lagrangian point of view in which the surface described in Equation (3-A) is considered to move past a point fixed in space. In this sense, the amplitude, a, can be considered to be a function of time only, and from Equation (3-A), a — = cos nQ cos kz (22-A) Also, from the velocity potential concept, - = -- =- -k 4 (T - P k In(1r)cos n cos kz. (23-A) t an o(7n) Equating (22-A) and (23-A) at the surface, (r = a): _ dS 6 = I'CLt ( )(24-A) A well-known consequence of Greents Theorem is that the Kinetic Energy of motion in a body of liquid can be found from the following surface integral: K.E. _ 2 (25-A) where 0 the velocity potential 5n = element of a vector normal to the surface S, p = liquid density, and S = the surface bounding the liquid system. Since a is considered 0- a (d),n r Ecn (z5-A) is * See for instance, V. L. Streeter, "Fluid Dynamics," p. 34, McGraw-Hill Book Company, New York, 1948.

-186 2wrr K~,= (- i a, /) CLc~t = — d @.: kI (k (k1) C osm cosk, dlt d -o I i(knIa ) I]. (26-A) Disregarding the term sin 2kz/2kz, and substituting the value of P from Equation (24-A) yields the Kinetic Energy per unit length, z, as a function of a:.i - o4-k I'() k2 Jt' If the Kinetic Energy of radial motion is equal to the Potential Energy of the distorted surface, then by equating Equations (27-A) and (lS1-A) the following relationship is found: & - O. (28-A),t/ c+e I(k2) Differentiating with respect to t, ^eo (rkI ke) ((< = 0o (29-A) dAL IJ I^(ka) If a is considered to vary with time according to the periodic function 0o - M cos (ait- e) where M. any constant of proportionality, f = the frequency of the periodic oscillation, and. = some small time lag due to damping,

-187 then: CLtZ 4-r M Co s?-Trrf - = 47rZ (C (30-A) and Equation (29-A) becomes Bn 0 dk I(k'L (31-A) Reduction of the Bessel's Functions proceeds by writing the derivative as follows:* rI k = d[,-)]=am In(km (+ t I\T at (kk) 0 (32-A) then kI' (kC) IT,(ka) -__ +kI~(, (k, ) Z- Im (,<) (33-A) Further, since by definition, when n is a positive integer, 00 ri!&+2i In (a = 2 i! (Y-+j)! 3=0 (34-A) if the quantity ka is very small, only the first term of the Besselas series need be considered, and I,n+ (k ) imA a I+k m+)! (koa) a'/n' z M CM0O 2(m+ I) 3(55-A) so that Equation (33-A) may be approximated by See for instance, W. Ro Marshall, Jr., and R. L. Pigford, "The Application of Differential Equations to Chemical Engineering Problems," p. 541 The University of Delaware, Newark, 1947.

k'(kAo) _ an + - r +-. I, (k ) X (^+1) XL 2- (0+1) 7 (36-A) Rayleigh's approximate expression for the frequency of oscillation is then LL (37-A) or, IL 4___ _ "'+ +.7r(,'aZ, 1 IT+rn-I)[ 2 + UL M (M+l) (58-A) For the case of an elliptically shaped orifice, n 1 2, and Equation (358A) becomes, /__ _3 +3) Z 7r ( O' X F +3 +.1 L 3 A? I (39-A)

APPENDIX B OUTLINE OF BOHR'S MODIFICATIONS OF RAYLEIGHtS EQUATION FOR THE OSCILLATING JET

OUTLINE OF BOHR'S MODIFICATIONS OF RAYLEIGHIS EQUATION FOR OSCILLATING JET Section I: Effect of Viscosity on Frequency of Oscillation Bohr(27) examined the oscillating jet, considering that the frequency of oscillation will be decreased slightly by the damping action of the viscous forces of the liquid. In the following summary, his method of arriving at a correction factor for Rayleigh's equation is shown. The motion in an incompressible, viscous liquid, with no external forces, is governed by the Navier-Stokes equations, /A(oVl - P"DL( = 1/ ^-D t and also by the continuity equation, _ + a__ + *~ + a' = 0 5 (2-B) where V = -a +- + D 4 _j) +, a +, A4. v d ar t i' at he and u, v, and w are the components of the velocity at any point in the jet. Considering the velocity with components u, v, and w to be superimposed upon the axial velocity, c, of the undisturbed jet, the axial -l90

-191 component becomes Uj =- C4 + <t (5-B) Bohr further supposes that u, v, and a will have the periodic form f(x,y)e, where b is then 2t/X and corresponds to Rayleigh's k (see p. 181, Appendix A). Assuming that u, v, and a are so small with respect to c that their products, or terms of the same order of magnitude are negligible, the term D/Dt reduces to Dt = (4-B) or, for example, = (5-B) and the Navier-Stokes equations become (6-B) (v'- Zbg) 2- _e Then by a succession of mathematical manipulations, including conversion to polar coordinates and assuming that the pressure, p, the radial component of the velocity, a, and the tangential component of the inQ+ibz, (27) velocity, P, all have the periodic form f(r)e Bohr ) demonstrates that Equations (2-B) and (6-B) yield the results: 1o = AI,<,h) SL: (7-B)

-192 ^-[-A^^^^^^cV^ I (8-B) *= [ —A e r U ^(b+3 ^^b - C -# I'/.M MO] 46L (9-B) 0JA= c+'4 = c+p-A, An^ E, ai (10-B) where 4t - b /x. It is seen that n is identical with Rayleigh's index of periodicity, n (see p. 180, Appendix A). Bohr next evaluates b in Equations (7-B), (8-B), (9-B) and (10-B) from the general equation for the condition at the surface,* O( _ + a + B )LF = 0, (11-B) 3It TL DE and the equations for the pressure forces at the surface, ( +'I ) + Pr constant PQg O (12-B) Pz = 0 where F = mathematical expression for the surface of the system, R1,R2 = principal radii of curvature of the surface, and Pr,PQ,Pz = radial, tangential, and axial components of the viscous traction per unit area across a surface element normal to the radius vector. See for instance, V. L, Streeter, "Fluid Dynamics," po 17, McGrawHill Book Company, New York, 19486

-193 Since* and I = n +Z(n ) 2 h3,' _ (14-B) P -T — 4 (7~ Bohr shows thiat if the surface is expressed as h-) L+ = _L-+6= (15-B) the surface relationships (58) through (61) can be reduced to (converting to polar coordinates) ~~~~~~~~~~~[ cs sZ cb-L + - ~(16-B) and. (k (17-B) ~m(,,X) -- X P.X JJ+ ( < ~+ =- 0, (18-B) X.- OW Considering that iba will be very small, and that ida will be very large, the Modified Besselts Functions, evaluated at the surface, r = a + r s a, can be represented by the power series for small x: arndt) - ^!+_ _2( am+,.m+ (-B) Im~c)= z*( ( zj* a'-&'.+4! -, (19-B) * See for instance, V. L. Streeter, o. cit., p. 217 ff.

and the assymptotic expansion for large x: i )f" i a.^ #) {[P )]- I- L e' - (20-B) in which P x) 2. — (4t_)(4- 3 ) + (4" -)(LrMk-3')(4'"-5)(4 "7z) Qn(X) = g,,, 3! (S/()3''' Substitution of these expansions in Equations (7-B), (8-B), (9-B) and (10-B), utilizing Equations (16-B), (17-B), and (18-B), yields, neglecting terms with e-i, which are negligible compared with e ix b _ibt e( n)S ~+- ^+r +J(m l) 3) lI -i-L2)= (21-B) a o (m-OJL o-& 2.^^ OkJ.- ecIb)' Since f = c/X = kc/2r, Equation (21-B) is seen to be that of Lord Rayleigh when p.= O (see p. 187, Appendix A), Denoting the solution to Rayleigh's Equation as ko, ~Ko = e (4-+'- $) (22-B) Equation (21-B) becomes approximately imm-')+ 0.+ -2l -.. (23-B) c - L 2m Z-klo ) - o. r^

-195 From the definition of d from Equation (10-B), Bohr makes the following approximation, since b is small, ixLd X; (;ko ) - (I-) k.c - H i and Equation (23-B) now becomes - _. -,(,-_,) (5,_4_) )' ka _reZ_,) _.' ~.J- z,,- (m Lc k -- 4 ] =~' (24-B) If b is now defined as the complex quantity k - is, Equation (24-B) yields k = k[I- - () 34(2,, _ - / 1) (25-B) and A_ 2m(-i) l(5m+,)o5ko][ m-1 ( N21 (26- B)? aLc L a'(^-i) a 2 ck J * -J Equation (22-B) may be written - ) k c' Io (6o (27-B) O (o(bo^(m'- 14 60 /^) This is the expression for oscillation in a non-viscous liquid. Bohr suggests that it may be corrected to apply approximately to oscillation in viscous liquids by substitution of k from Equation (25-B), Th<I~~ Qek.^) IL( c r )to Zi 2s (28-B) Lek a 4.,o?-k2 9 J The correction is of the form -,- k (+2,-3!+ ~ ) +

-196 Taking only the first two terms of the series, since 2~j/pc2ak is small, and letting bo = ko = k in the remaining terms of the equation, Bohr's modification of Rayleigh's equation is'kC AI, (k., ) k __. 3__-.- _ "-ikA) Mk +2K-,k (29-B) Section _II: Effect of Finite Amplitude on Frequency of Oscillation Bohr(27) studied the effect of a finite displacement of the liquid surface of the jet, considering the jet to be an infinite cylinder vibrating in two dimensions only. The liquid is considered, in this analysis, to be non-viscous, so that by the flow-potential concept, radial velocity component o( - -- _ B) 7rL tangential velocity component = 1 (31- B) The continuity equation in polar coordinates for potential flow is a + i = o. (-c An1 ^ 71Z n^ e) (52-B) Solving Equation (52-B), requiring ~ to be a periodic function of the time, t, and under the condition that 0 is finite at r 0, <= A ocos ( - rZ si(c-~. (55-B) Also, the motion must satisfy the general boundary equation'DF =(a E + b a) r 3 F = ~ (-B) If the radius of the surface of the jet is expressed as =_ a A; S- 3( ^) )* (355-B)

-197 Equation (35-B) is Dat +r - - at + (36-B) r'= tD f 1 Bernoulli's equation gives the pressure relations at the surface;' v-2_ + = - (t) (37-B) where v is the absolute magnitude of the velocity at any point, or and since the pressure at the surface is a result of the surface tension forces, p = a/R, where R = radius of curvature of the jet surface. From elementary calculus, __ 12 + 2 2) "L and v2 = a2 + P2 then Equation (37-B) becomes or^ - [t {^}]v 2f n-l:1 S +( x- -F(t)=0 (38-B) Equation (33-B), (36-B) and (38-B) are sufficient to solve for ~. In order to permit successive approximations for 5, r, i, and q, Bohr expands Equations (36-B) and (38-B) by Taylor's Theorem: (9 t) x = Si(I(<I + i-~If: +.411 - ~ + ^ + ( ) ~ I\gj,2 z ~ jY "4.

-198 or ^(n) i < = + ^(a + & }(~ 2) _ (. - G (39-B) Equations (36-B) and (38-B) are functions of (a-~), and may therefore be written as functions of a: I+ + 2 3 +''! -6 lz a (40oB) and _ _ _ _ _ _ _ __6_ _ _ _ _ _ _ _ _ _ _], 0.. ( 41, B ) Utilizing the requirement that the area of the jet cross-section must remain constant 2 D a dTL 19 = - 2 z( the successive values of ~, r, 9, and q can be found from (5533-B), (40-B) and (41..B)o First Approximation and (41-B) become + [3J 0 = 0a (45-B) and =1 [latS - o'- -9- 2ai d' 3 -" Solving (43-B) and (44-B) when F(t) is assumed to be constant, r a + 1 cos (ng — n) cos (qt - ~) =0 a A rn cos n3 sin qt, 5 n an11 A cos ng cos qt q2 5 5 (n3-n) pa3

-199 Second Approximation: Neglecting all terms higher than second order, Equations (40-B) and (41-B) become t ln az n as asJ' (46-B) and p [ +. t - $ - 2o D;t 04'0\r 20, -2 — 71. ~k~ i - a- a a-eI 2?^3G *Ft) =. (47 -B) Using the values for /, ~, and q from (45-B), and setting F()= e (4m +3) ^-2, A2siny t, (48-B) manipulation of Equations (46-B) and (47-B) yields =~-c jA ^'- S q^-Af2y 23 7-2, 2-3, oas cos2 2 +A z 2 2 - /3 cos 2 - AZ _2 2 m- 3 - * Y 2 —3 o= nA sico sn5nft 3(a-cltz) _ t os re n 2 t (49-B) Third a,3 roxi: Third Approximation: Repeating the process, neglecting those terms higher than third order in Equations (40-B) and (41-B), and utilizing the values of [, 0, and q from (49-B),the third approximation yields, setting F'(t) = S sin 2qt,

(where S is a constant), 2= - -_ )E _- ('23-3)(3 "%50m- 5o 8) b-.. - 1+..o. (5o0B):This expression depicts the vibration in two dimensions. According to Bohr, if the wavelength of the vibration is long in comparison with the diameter of the jet, the motion in the 73dimensional jet section will differ little from that in two dimensions, and the solution (50-B) can be extended to three dimensions as 9,, "' 4'~ i=C-3(,\3 3(a) (7 + fl+M1TA)26t(+2 +0 (51B) where Ml 1)(34-33+ 50-) 16 (2-~41)(,- j).. PlI P2'7l etc,, are undetermined constants, By analogy with Rayleigh's equation for oscillations with infinitesimal amplitude, and since q = 2Tc = kc, Equation (51-B) can be written, neglecting the higher order terms, _1= rh^(k) (m-lk)21 (52-B) ~~~c ~~~~I~~~&~~~)~ Since I 2 3 -M( m =X 2 3. 3 I-M, +2 N1.. ^~2 S (53-B) then (5 4-B)

-201Neglecting terms higher than second order in the series, Bohr's corrected equation for finite oscillations in a jet is 6- = C-dL I'6) L (55-B)

APPENDIX C FURTHER REARRANGEENT OF THE OSCILLATING JET EQUATION -202

FURTHER BEARRANGmEINT OF THE OSCILLATING JET EQUATION Bohrts modification of Rayleights equation for the oscillating jet is, for n = 2; ^VC n) rL / ^ TW -^- ir (l-C) 0- 3(1 j+ )(ka) [2 k + n) r 24 o (1- C) To facilitate the computation of large amounts of data it is desirable to expand the Besselts Function terms into a power series in the following manner: (2-C) I (t'2 - Z/) -I I= -A Zi )(,+)! If ka is reasonably small it is possible to approximate the Bessel's series as the sum of the first three or four terms of the series,, \. M m+2 +4- - M +(. zv J I~ (m^l,, 2,2)!2! a^^s)!3' (3-c) 2== ( tl)(mtUr)(m+ 3) 3!X z( )(m+t ) 3!s.( +2 (m2+3)3?< + 3 +x. &+6' (^43)1 3! Similarly, I (x = 2 (+I)(Z)(3)3! 3 m+ z(mt2nif3~3! A-+t 2 2 (m+3(m-4.)3 + (m,,..) (4.c) I 2. 3 -'"'' ~~) _ ~+,),,,-,,(',.,,-0 ~,,,~'"-,. 2 ~',,,,.4(,,+4 0 -203

Dividing (3-C) by (4-C), I +/) 3 + 2-(rn,,,+,) 3a(,~ 3(' -, a 3q4. (m + r>-n+z)(m+3).I r (X im, (W ) (5-c) (1m+)x2 (+4) (4- + 4 (m I) 3Z (+)(+2) (m +e.) ey4 -394 (,A+ ((MZ.)(/11 3) Letting 0-= 4. (M+I) n= I~~~~ 32 Z(,,)(,t+z) (m+S) = 3 4.(,~+.)(,m+z)+(,,3) (.a- I ) and = k~ dc (m+ 2) 4(M. I) the non-bracketed terms in Equation (104) become: 0-_ = kA^c, 4 I + t L 4 64 4 ] c ]1 3 L( +r w)(+^ 4 tX Zt4+ %+ ) (6-c) - __ I + ax 2 4-Cx4.+ c6 3 L m + (c+M )2++ (e+my),I+(+t)8 +yT 8 J 8 Disregarding the term mgx, the fraction enclosed in the brackets in Equation (6-C) can be expanded into the following Maclaurin's Series: S() - = (o) 4s'(o) X 441(o) PZ 4-() Xl 4.. - h e 3n When r /,\ -+,xz + bx 4, c 6 (7-C) /YX - (AL4- n ) +(L t)-4 +(4ce) 7 6

-205 Then f(O) X 1/n f (0), O 2. mn) (13n) n n2(n+l)(n-l) "t'(o) ) O f"It o ( 24( d + Yy cc + n m - e, - a/" c- ynL- y\rm )n M3 3r 4+ 3,o3 4- 5/,- 33,Yi-4 12 3 () (-) (n +z) f(5)(o), O f (6) ( O) 7Zno v Z. + 6mL/zmA- Ga/v< tm abr'-e b Y 4 b-m3 - 6 mC =,., 7+ 74,-~_ 4 I6- o507m4- Z25.,. - %_+ 4._4__ 4_ ( 0 (+.)( +3)(ry- 1)3 When n = 2, as is the case for the elliptical cross-section, the derivatives are f(o) 1/2 f'"' (0) 85/I8 f,(O) O f(5)(o) = o f"(O) = - 5/12 (6)() a -821/48 f"(0o) o and the series, Equation (7-C), beccaes (,) - -( -5 + -. _ S2 +.... ) (8-c) Bohrts Equation, Equation (1,-C)^ can then be expressed as follows -= e^tZ (i- 5k2zS^-417 $5^\)K+^ (^t2] 24 5, -,-37 _ _ _ _ _ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~

Since the term ka is small for most jets, the term to the sixth power is usually negligible, Also, the terms 2Wi/pcka2 and b/a are usually small so that by disregarding the products of these terms, the equation is s r the ea i n576 e (t +2 a3_l (I)24 9c) This of the euation is used by ansen, et al. (78) This form of the equation is used by Hansen, et al.

APPENDIX D DEVELOPKENTAL PROBLEMS WITH THE MIJUTE ORIFICE

DEVELOIEJNTAL PROBLEMS WITH THE MINUTE ORIFICE The orifice employed in this research was very much smaller in diameter than any known. The extremely small dimensions of the orifice led to many operating difficulties not reported. by the investigators using larger orifices, and which by their very nature would necessarily be unique to the operation of minute orifices. Perhaps the complexity of these problems can best be described by presenting a somewhat chronological account of the attempt to calibrate the "micro-orifice"' The oscillating jet apparatus, as initially constructed, consisted. of a barrel and retainer ring of unpolished stainless steel, with a liquid. feed line of Pyrex tubing leading from a Pyrex liquid reservoir. The reservoir was stoppered with a rubber stopper and the air line contained several lengths of rubber tubing. The stopper and the rubber tubing had been well washed to remove any traces of talc before installation. It was necessary to install a sintered stainless steel filter disc (pore size ca. 10 microns) in the barrel to prevent small particles in the double-distilled water from plugging the orifice. Even with this filter in place, large build.-ups of waxeyappearing deposits and colors less "needles" 5 to 30 microns long occurred at the discharge and entrance sides of the orifice, respectively. These deposits were accompanied by decreases in the liquid rate through the orifice. Filtration of the water through a 0,65-micron porcelain filter before use was found to effectively eliminate the needle-like deposits, but the waxey precipitate and its accompanying rate decreases persisted. -208

-209 It was learned that much of the initial liquid rate decrease resulted from gradual displacement of air from the barrel filter(l51?l8l) For this reason it became necessary to operate the orifice without a barrel filter. Since slight rate decreases attributable to the gradual accumulation of waxey deposit was still encountered, all possible sources of the depositing material were eliminated. Rubber air lines and stoppers were replaced with glass tubing and ground joints, and a fritted glass filter was installed in the air line. No decrease in precipitate resulted. When the Pyrex liquid reservoir and feed line were replaced with a polyethylene reservoir bottle and polyethylene tubing, the amount of precipitate decreased markedly, so that it was possible to operate for several hours without appreciable rate changes. After several hours of operation, however, the rate of waxey deposition increased considerably. It was further found that by using Vycor for the reservoir and feed line, the waxey precipitate could be eliminated completely, so that it became possible to run indefinitely with no measurable decrease in liquid rate. It appears probable that the orifice deposit consisted of borates or silicates leached gradually out of the Pyrex, and deposited at the orifice because of the electrical fields created there by electrokinetic effects. Data obtained using the polyethylene system are designed by run numbers 403-493, while those obtained with the Vycor system have run numbers 501-559.

APPENDIX E DEVELOPEENT OF COMPUTING EQUATION FOR "MICRO-ORIFICE" -210

DEVELOPET OF THE EQUATION USED IN COMPUTING SURFACE TENSION FRCM'E MICRO-OSCILLATING JET The shape of the orifice used in this study was an ellipse with an appreciable deviation from circularity. Because of this high degree of ellipicity it was expected, and indeed found to be so, that Rayleigh's theoretical expression would not be valid for jets produced by the microorifice. Bohrts modifications for the effects of viscosity and finite wave amplitudes were similarly ineffective. Attempts at developing an empirical correction for the results calculated using Rayleigh's or Bohrts equations also failed. It was therefore necessary to develop the following equation for use with jets having appreciable wave amplitudes, The development is based upon Rayleigh's original treatment. In his analysis,(128) Rayleigh chooses the following expression for the cross-sectional shape of the jet: rs ro + a cos nQ (l-E) where rs = radius at any Q r = arithmetic mean radius O n = mode of vibration (see po 18c) or for an "elliptical" section, rS = ro + a cos 2Q (2-E) It can be seen, however, that this model is not suited for expressing the section of a jet with large amplitude, a. As an example, the following diagram illustrates the section described by Equation (2-E) when oa = OO 5r0 -211

-212 For large amplitudes, the jet section may be more Suitably expressed by the equation for a true ellipse: X I( 2+ 7 (3-E) where a = major radius b - minor radius Rewriting Equation (3-E) in polar coordinates yields - _____ _______ (4-E) Is6 bcos2 o + a s- WivG If the major and minor axes are considered to vary along the length of the jet according to b r r + a cos k z a, r -a cos k z

-213 where ro = arithmetic mean radius of section a = maximum amplitude at peak of node, then Equation (4-E) becomes rLS, (6,E) a_ (no+o~co+kj?) (f-~coski) _ (,n+oecoske) coste + (.(n,-~ cosks) sin2 0 (5-E) = ______ - o<2 cos'k_ +2 + 2on cos ki (osz. - siL) + E CoS kiC o J If it is assumed that the liquid is ideal, i.e., non-viscous and incompressible, then the time rate of doing work on the boundary of the liquid will be equal to the time rate of change of kinetic energy in the liquid (assuming no change in potential energy). The work performed on the boundary of the liquid can be found by evaluating the increase in surface area of the jet resulting from the deviation of its shape from that of a circular cylinder. From elementary calculus, the area of a surface can be expressed in cylindrical coordinates as follows: -Z /l~ ~f. 2ls\2 2 r Arem I+ ~ —j (-,Rk-, --.^)Z /a), 7l c].O d v Area ~ f j;7MCt 9 o 0 and the change in surface area is i 2 f AArea= I )}+( n4 + -2r r s! 0 0

-214 The work done upon the surface is then the change in surface energy, Aur~aceaft/ fff ~ a e, tlr~ae \'+ t~ z'j 4(7-E) surface {J (s t ^ i(- a} ( E) o o The kinetic energy of radial motion of the liquid in the jet section for an ideal liquid, is found by the surface integral, K.E.= -2 i c dAS (8-E) where 0 the flow potential function, p = liquid density, 65 an element of a vector normal to the surface, S = the surface bounding the liquid. In order to obtain an analytic expression for the flow potential,,, it is necessary to adopt Rayleigh's assumption that = m f(r) cos 20 cos k z (9-E) where f(r) is some function of r yet to be evaluated. The expression, like Equation (l-E) is only valid for small as; however, its mathematical convenience outweighs the small error introduced by its use for moderately large values of c. Rayleigh shows that use of Equation (9-E) in the continuity equation: leads to te solution:Leads to the solution 0 = piI2(kr) cos 20 cos k z. (10-E) p may be evaluated from the velocity potential concept, which requires

-215 that t = - _ = -@ kI2(kn) cos a coS k.S Further, at the surface, ans = ans <ag bt;i'St where represents, in the La Grangian point of view, the velocity with which an element of the fluid moves parallel to the z - axis: c = liquid velocity. Then, at the surface a * * = - 1 k 12 (kn) cos 26 cos ki ^ 2P, rz ^-0s Zo Cos /";sC (ll-E) Q- c \-.-/,,, v k T2 (483) coszQ 2 cos k The velocity potential is therefore approximately expressed as kr k< ^ (k )' (12-E) can be evaluated from the relation a,7L ~_ _: ^ n As shown in Figure l-e, 5 = n sec y 6r/~n - sec 7 /n Figure l-e.

-216 so that a} = sec (13-E) where y is the angle in space separating n and 6r. Sec y can be found as a function of Q, and z by considering the projections of the vector n on the two perpendicular planes, z = constant, and ~ = constant. 1) Consider the plane, z = constant, in which the radius vector r lies. As shown by Figure 2-e, the angle a separating 5r and 5n', the projection of 5n, can be expressed as 1 6rs tan a - -. rs ae r 6S Figure 2-e Figure 5-e 2) Similarly, as shown in Figure 3-e, on the plane G - constant, containing the vector r, tan = as az

-217 then since, from Figure 4-e e2 1 + sec 7s 1 +ta a + tan2 p sec 7 = 1 1 r S,r6 2, r,2 (14-E) ( ) + Figure 4Ie. Substituting (12-E), (13-E) and (14-E) into the surface integral (8-E) yields - CX-': Ia(km) I(kn ") K.E. - a arc)S S [I I (kn - z 2-r\ R2 2 + + al~ Ji~ / 3n~a3~\2 I ds Since the integral is to be evaluated over the surface, I2(kr)' I2(krs) 2 2 eonsz I (kn~ i 2 k I (47, \- N / S z c 5 (15-E) Further, since in cylindrical coordinates d S = Jl 13n5 t+ ) O(2 i ) xtCL dGi the kinetic energy relation becomes o 2o 20JJ0 I (k0, o o +()n W)+n L (l6-E)

-218 Since the kinetic energy of radial motion of the liquid must equal the change in surface energy, equating (16-E) and (7-E) yields: 6- ~XVkt'LiR^l +)((I (17-E).2- Er ]0 2. (1z Equation (17-E) relates the surface tension to c, ca, rg, and the wavelength, X, with no restrictions on a other than that possibly imposed by the use of Equation (9-E) for /. Because of the symmetry involved, Equation (17-E) need only be evaluated over one-fourth of a wavelength and through one quadrant of the angular space, Thus Equation (17-E) becomes L JJ 0 \ ( u == = -----— X —) —--------------- S. (18-E) 0 Equation (l8-E) may then be used to calculate the surface tension from the wavelength and dimension data obtained from the oscillating jet, The terms ar/bz and ar/6a are evaluated from Equation (6-E): Mi, 2o oc cos2(se -cos ( l9-E) 3U2~~n)^~s _n~ -4~~ /C~ oC~(n-i~co~s7~Ct Loski~ 65~in9cosj ~ C (20-E) a9 [ZR + dcaOs2zki + z2ono cos kzn (sine-CoS0 )]

-219 bir C[n~ +ocoSk- ~Z ^ (sinZO-c&so8) cos k| i osk (1 k cZcosok) sIn c <s [aom(sn- - c&s2e) 4 cos kz] [1?Z4 (CoSZ~k + aou- P (s r n O- CosI) cs kt]-// [^4^o5 cos + Z 1 K ((10-COs?) k*] (21C E) Since Equation (18-E) cannot be integrated analytically, calculation of a was performed. by stepwise suiaation on an IBM 704 digital computer. In this method, since d.Q and dz are represented by smiall, finite constant increments AQ and. AZ, Equation (18-E) may be expressed 2? k1\'(kn)) <1 l*(-F c0= o *. (22-E) r t=Y Y /i+2 1. aA LL L V J JlfJnwtJ, J - AJ 0 O Finally, letting c =- L 2 and introducing the conversion constant to r 2 rg permit the use of L in the convenient dimensions, cm3/min, and r and z in inches, the general expression employed for computation is: 6-= a ~ __________________-) —— (-)-( —j-j —-2-. (25-E) "~~' /L /,,,f:~y -] ~'A:Xt 7_ - -N~ L k ) - -V —o O The "Fortran" program for computing Equation (2-E) using the IBM 701 coaputer is given in Appendix F,

APPENDIX F IBM "FORTRAi' COMPUTER PROGRAM -220

IBM "FORTRAN" COMPUTER PROGRAM Calculation of Equation (23-E) N = 14 INCREMENTS J = 6 INCREMENTS 1 FORMAT(19H2 RUN NO. 16//20H LIQUID // X 120H LIQUID RATE LIQUID DENSIT XY LIQUID VISCOSITY ASSUMED SURF. TENSION REYNOLDS NO. X//F36.4,F17.4,F20.4,F23.2,F22. 3///120H NODE WAVELENGTH MAX DIAM X MIN DIAM 2 FACTOR BOHR FACTOR AMPL, RATIO CORRECTN. JET AGE XSURF.TENS. SURF. TENSION //) 2 FORMAT(15,2Fll1 5,F10. 5,2F1. 5,F12. 4,F10, 3,Fll 6,F1O. 6,F14o 4) DIMENSION SINK(20), COSK(20), SINT(20), COST(20) ACCY =.001 STEPN = 14 STEPJ = 6 SECTOR = 1. 570796/STEPN ANGLE = SECTOR/2 N = STEPN 5 DO 35 J =1, N COSK(J) = COS(ANGLE) SINK(J) = SIN(ANGLE) 355 ANGLE ANGLE + SECTOR SECTOR = 1.570796/STEPJ ANGLE = SECTOR/2 M = STEPJ 6 DO 36 I = 1, M COST(I) = COS(ANGLE) SINT(I) = SIN(ANGLE) 36 ANGLE = ANGLE + SECTOR 11 READ INPUT TAPE 7,12,W1,W2,W35,W4,NO 12 FORMAT(F10.4, 3F10.5, I10) FIRST DATA CARD (L, p, p, RUN NO. ) 13 RATE = W1/W2 Gl w1/w3 RE 233.51*G1 RHO = W2 VISC = W5 CALIB = W4 WRITE OUTPUT TAPE6,1,NO,RATE,RHO,W3,W4,RE -221

-222 SIGMA O. ZH2 0. P4 0. TIME2 0. TIMEP = 0. PHIA 0. NODE =0. G5 = 3096~*RHO/VISC READ INPUT TAPE 7,12, Wl, WAVE,DMAX, MIN,NO FIRST NODE CALCULATIONS A = DMAX/2. B = DMIN/2. RG2 A A*B RG SQRT(RG2) P8 ((A-B)/2.)/RG ROO (A+B)/2. 17 PHI WAVE/G1 PHIB = PHIA + PHI CENTER = PHIA + PHI/2. PHIA = PHIB ZH1 = ZH2 + 4.8*PHI ZBM E (ZH1 + ZH2)/2. ZH2: ZH1 TIME1 T TIME2 + G5*PHI*RG2 TIMEM = (TmE1 + TDME2)/2. TIME2 = TIME1 NODAL OUTPUT INSTRUCTIONS 25 NODE = NODE + 1 WRITE OUTPUT TAPE6,2,NODE,WAVEDMAX,DMIN, ZM,P7,P8,CORR, XTIMEM, CALC, SIGMA READ INPUT TAPE 7,12,W1,W2,W3,W4,NO GENERAL CALCULATIONS, ANY NODE 30 IF (W1) 31,31,13 31 WAVE = W2 DMAX ~ W3 DMIN W4 A a DMAX/2. B = DMIN/2. RG2 = A*B RG = SQRT(RG2) ROO (A+B)/2. P8 = ((A-B)/2.)/RG SLK - 0. SUMB B 0. L s STEPN

44 DO 78 J = 1,L vi = (A-B)*COSK(J)/2. V2 = (A-B)*SINK(J)/2. V4 Vl**2. R02 = RG2 + V4 RO SQBRT(R02) SIMS = 0. SUM3 0. M = STEPJ 48 DO 74 r =,M 49 V5 s SINT(I)**2. - COST(I)**2. V8 - RG2 + 2. *RO*V1*V5 + 2.*V4 V10 - V8**3. DRDZ = (((6.283186/WAVE)*( 2*V2*v2 ~05 + V1) + 2.*V8W1*v2))**2. )/V10 DRDT = ((4. *Vl*RO*RG2*Sr(I)*COST(I) )**2, )/V10 R2 - (RG2**2.)/V8 R SQRT(R2) V3 L + DRDZ + (DRDT/R2) RAD2 3 SQRT(V3) RAD1 = SQRT(V3 + DRDZ*DRDT/R2) SUMS = SMS + RAD1*R XR = 6,283186*R/WAVE BESSL2 = BESSEL(XR,2.,ACCY) BESSL3 = BESSEL(XR, 3.,ACCY) 74 SUM3 5 SUM3 + (DRDZ*BESSL2*RRA1*RD2*R2)/(2.*BESSL2 + XR*BESSL3) SUMK = SUMK + SUM3/(RG2)**2. 78 SUMB = SUMB + SUMS SIGMA = (RATE**2.)*RHO*SUMK/( 1164514. 1*(SUMB-(STEPN*STEPJ*RG))) GO TO 25

APPENDIX G CALIBRATION OF EQUIPMENT -224

CALIBRATION OF EQUIPMENT Calibration of Schutte-Koertting 3HCF, 1/2-Inch Rotameter, With J-32 Stainless Steel Float The rotameter was calibrated in the low air-rate range using an American Meter Company bellows-type dry-test meter (C4-34)o At the higher ranges, the air flow rate was determined by measuring the rate at which the air displaced water from a steel drum. This was accomplished by filling the drum completely with water, and then admitting air from the rotameter into the top of the drum, forcing the water through a siphon tube into a container placed on a Fairbanks-Morse platform balance. The balance was set to "trip" at some convenient weight of water, wl, before which time the back pressure had been adjusted on the rotameter, and the flow rate had become essentially constant. After the balance tripped at wl, it was reset to trip at some heavier weight w2, and the time interval between w1 and w2 was measured. The volumetric gas rate was then calculated from the relation: V = _ _ SPaz We_ W PAd AL where V = air rate, ft3/sec PlP2 = pressure of air in drum at beginning and end of timing period, respectively, atm. P - pressure at which V is calculated, atm. t - time interval between wl and w2 eL = density of water in drum, lbs/ft3. -225

.18.16 z 0 w.14 C) I-,..12 Ln.10 on.08 r-.06. 04 - - ~ DRY-TEST METER, WATER DISPLACEMENT'02 0 20 40 60 80 100 120 140 160 180 200 220 240 260 ROTAMETER SCALE READING, MM. Figure 1-g. Calibration of Schutte-Koerting 3HCF 1/2 - Rotameter.

-227 Calibration of Schutte-Koertting 6HCF, 1 l/4-Inch Rotameter, With Modified (Lightened) J-64 Stainless Steel Float The rotameter was calibrated at the lower air.rate range by the water displacement method used for the 3HCF rotaameter. At the higher ranges the air flow rate through the rotameter was determined by the heat dilution technique, using dry air. The discharge from the rotameter was passed through a heating chanber containing two 500-watt G.E, Calrod flat heating elements. The heater and piping were well insulated thermally. The power supplied to the heater was measured with a Weston precision A. C. wattmeter, and the temperature upstream and downstream from the heater were measured with copper-constanten thermocouples. The volumetric air rate was calculated from the relations QRT V C, ATFPM where V = air rate, ft3/sec. Q = power to heater, BTU/sec. R gas constant, atm. ft3/~R Cp =heat capacity of dry air, BTU/~F AT difference between upstream and downstream air temperatures,'F P pressure at which V is calculated M ~ molecular weight of air.

I.' 1.0' t6 I BACK PRESSURE: 10 PSIG. 0.9 0.8 0 0 " 0.7 Iw w' 0.6 Qo 5 c l.2 ____ __ __ 0METHOD.< 0.3 A WATER DISPLACEMENT 0.1 0 20 40 60 80 100 120 140 160 180 200 220 240 260 ROTAMETER SCALE READING, MILLIMETERS Figure 2-g. Calibration of Schutte-Koertting 6HCF 1 1/4-Inch Rotamneter.

Calibration of 40-Gauge Chromel-P vs Copel-X Thermocouple for Oscillating Jet The thermocouple and its cold.-junction were prepared from uninsulated Chromel^P and Copel-X wire from the Hoskins Co., Detroit, Michigan, The thermocouple was calibrated by comparing its EMF with the temperature indicated by a calibrated mercury thermometer in a water bath. The thermometer (Cenco 19245-A) reads in 0.01~C., and agrees within 0.02~C with the NBS-standardized mercury thermometer in the Sohma Precision Laboratory in the Department of Chemical and Metallurgical Engineering.

28 26 - - CHROMEL VS. COPEL- X ___ 24 COLD JUNCTION 0 ~C o 22 20 w 18 Q~- I- ~ ca 14 12 10 0.6 0.8 1.0 1.2 1.4 1.6 1.8 THERMOCOUPLE EMF, MILLIVOLTS Figure 3-g. Calibration Curve for Oscillating Jet Thermocouple.

APPENDIX H FROTHING DATA

-232 TABLE I FROTH DATA FOR DISTILLED WATER SINGLE AIChE BUBBLE CAP DISPERSER Ruh No. Superficial Clear Liquid Froth Air Velocity Depth Height Ft/Sec In. In. Froth Density Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Ft/Sec In. In. 1 0.654 1.196 1.340 1.645 1.957 2.280 2.595 3.49 4.10 4.53 5.19 5.95 8.09 1.34 2 0.654 1.294 1.957 3.49 4.74 5.95 8.09 1.359 3. 630 1.318 2.095 2.84 3.60 4.37 4.37 5.15 6.36 7.17 8.00 1.95 1.95 1.95 1.95 1.95 1.95 1.95 1.75 1.75 1.75 1.75 2.0 2.0 1.55 4.05 4.05 4.05 4.15 4.05 3.80 3.60 3.80 6.0 6.0 6.0 6.0 6.0 5.95 6.0 5.95 5.65 5.65 5.45 2.2 0.872 2.5 0.769 2.7 0.711 2.8 0.685 2.9 0.685 2.95 0.651 3.15 0.604 3.7 0.514 4.0 0.513 4.3 0.512 4.6 0.435 4.9 0.327 5.4 0.287 2.1 0.762 5.0 5.8 6.2 7.35 8.9 10.3 11.8 5.5 7.2 8.8 10.0 10.8 11.5 12.5 13.5 13.6 15.0 15.0 16.5 0.811 0.700 0.654 0.565 0.456 0.370 0.305 0.692 0.834 0.674 0.600 0.555 0.521 0.475 0.455 0.438 0.373 0.373 0.327 13 6.27 5.86 5.65 4.69 3.70 3.08 3.62 3.12 2.57 2.47 1.89 1.54 1.12 0.244 0.988 0.925 0.835 0.779 0.749 o. 650 0.556 0.469 0.382 0.177 0.255 0.0885 0.193 0.302 0.465 26 0.336 0.561 0.771 1.081 1.280 1.905 2.68 3.69 4.72 5.48 3.75 3.16 2.53 1.325 1.250 1.034 0.458 0.759 7.8 7.8 7.8 7.8 7.8 7.8 8.0 7.9 7.8 7.8 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 7.9 3.9 4.05 4.05 4.1 4.0 4.0 4.0 4.0 4.1 4.1 4.0 4.0 4.0 4.0 4.0 4.0 4.05 4.10 18.0 0.433 17.4 0.448 17.5 0.451 16.5 0.479 15.5 0.510 14.2 0.549 15.3 0.522 14.6 0.541 13.8 0.565 14.0 0.557 12.9 0.620 12. k 0.645 11.5 0.695 9.1 0.880 11.3 0.710 10.8 0.741 10.8 0.741 10.6 0.755 10.5 0.763 10.4 0.770 10.1 0.794 9.9 0.810 9.6 0.835 8.8 o.910 9.6 0.835 8.35 0.960 8.85 0.905 9.3 0.860 9.7 0.825 4.9 0.796 5.8 0.698 6.4 0.633 6.8 0.603 7.0 0.571 8.0 0.500 8.7 0.460 9.6 0.417 10.4 0.394 10.8 0.380 8.2 0.488 7.8 0.513 7.0 0.571 5.9 0.678 5.6 0.715 5.5 0.728 5.0 0.810 5.6 0.732

TABLE II FROTH DATA FOR DISTILLED WATER WIRE GAUZE DISPERSER Run No. Superficial Air Velocity Ft/Sec Clear Liquid Depth In. Froth Height Ino Froth Density 7 8 0.372 0.566 0.865 1.22 1.03 1.36 1.55 2.33 3.13 4.22 0.1125 0.148 0.222 0.183 0.288 0.320 0.413 0.373 0.442 0.478 0.581 0.627 0.705 0.914 1.200 0.133 0.911 1.455 2.22 2.0 1.9 1.9 1.9 1.9 1.9 1.8 1.8 2.0 1.8 6.1 6.1 6.1 6,0 6.0 359 5.9 509 5.9 5.9 6.0 6,0 6.0 5.9 5.9 6,2 6,1 5.9 5.5 3.1 3.1 3.1 3,2 301 3o1 3.0 3.2 4.0 4,3 0 645 0,613 0.613 0,594 0o613 0.613 o0600 0,563 0.500 0o419 6.7 6.8 7.5 7.2 7.8 8.3 8.6 8.4 8.8 8.9 10.0 10.2 9,8 9.6 9,8 7.3 9.5 9.3 10.0 0,896 884 800 835 770 724 699 715 683 675 600 589 613 626 613 824 632 646 600 -233

Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Ft/Sec In. In. FROTH DATA FOR DISTILLED WATER PERFORATED PLATE DISPERSER Run No. Superficial Clear Liquid Froth Froth Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Air Velocity Depth Height Density Ft/Sec In. In. Ft/Sec In. In. A-4 0.123 0.264 0.438 0.676 0.874 1.128 1.33 1.737 0.453 1.147 1.458 1.800 2.100 3.97 5.23 6.50 7.78 6.21 5.33 4.13 3.00 2.51 A-6 0.218 0.155 0.614 1.34 1.75 2.75 3.50 4.92 6.75 A-7 0.258 0.675 1.27 1.69 2.18 3.21 5.19 7.21 4.18 i.37 0.734 0.212 A-10 0.138 0.298 0.424 0.217 0.390 0.618 0.860 1.20 1.33 1.63 1.95 2.45 3.09 3.52 4.79 6.00 6.07 7.35 7.76 4.74 4.1 4.1 4.05 4.05 4.0 4.0 4.0 3.95 3.90 4.05 4.05 4.0 4.0 3.95 4.05 4.0 3.9 3.8 4.05 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 3.9 3.9 4.0 4.0 4.0 4.0 4.0 4.0 4.0 3.9 3.8 4.05 4.05 4.0 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.05 4.0 4.1 4.1 4.05 4.0 3.9 3.8 4.1 4.05 4.0 4.0 5.3 0.774 6.8 0.602 9.2 0.440 10.5 0.386 11.2-16.0 0.357-0.250 12.0-18.0 0.333-0.222 13.0 0.304 11.1 0.351 9.0 0.450 12.5-15.0 0.324-0.270 12.0 0.333 10.8 0.370 10.6 0.373 12.6 0.321 13.8 0.290 15.1 0.258 15.5 0.244 15.0 0.270 14.0 0.286 12.8 0.312 11.4 0.351 10.6 0.377 6.4 0.625 5.7 0.703 9.9 0.405 12.3 0.326 11.5 0.348 11.3 0.355 12.0 0.333 12.8 0.305 13.4 0.291 7.1 0.564 11.0 0.364 13.0-15.5 0.308-0.258 11.8 0.339 11.2 0.357 11.7 0.342 13.2 0.303 13.2 0.295 11.8 0.322 11.0 0.368 8.5-11.0 0.478-0.368 6.2 0.646 5.6 0.733 7.6 0.540 8.9 0.462 6.4 0.641 8.4-9.0 O. 490-0.456 9.9-11.5 0.415-0.357 11.6-16.6 0.354-0.247 12.5-17 0.328-0.241 13-15.5 0.312-0.261 12.1 0.330 11.6 0.353 11.4 0.359 11.8 0.343 12.1 0.330 12.5 0.312 13.3 0.285 14.3 0.286 15.1 0.268 15.2 0.263 13.2 0.303 A-14 0.166 0.428 0.690 0.950 1.44 1.94 2.17 2.55 3.31 4.23 4.95 5.41 6.01 4.30 2.13 1.48 0.790 0.459 0.138 A-16 0.191 0.212 0.423 0.580 0.717 0.851 1.08 1.48 1.81 2.40 2.90 4.26 8.63 6.76 2.98 1.85 0.995 0.443 0.321 A-17 0.147 0.275 0.420 0.671 0.819 0.904 1.008 1.151 1.290 1.316 1.42 1.68 1.91 2.44 3.63 4.91 6.60 8.50 3.80 1.73 1.26 0.715 0.505 0.320 0.253 0.118 4.0 5.2 0.77 4.2 7.7 0.55 4.1 9.1 0.45 4.1 12.1 0.340 4.0 12.9 0.310 4.0 9.7 0.412 4.1 9.9 0.414 4.0 9.8 0.407 4.0 10.3 0.403 3.9 10.8 0.360 3.8 10.7 0.355 4.o 11.4 0.351 3.9 11.9 0.327 4.1 11.5 0.356 4.0 10.2 0.392 4.0 11 0.264 4.0 11.2 0.357 4.0 9.6 0.417 4.0 5.2 0.77 8.0 9.7 0.825 8.0 9.9 0.810 8.0 11.7 0.685 8.0 13.1 o.611 8.0 12.5 0.641 8.0 12.6 0.635 8.o 13.1 o.611 7.9 13.8 0.574 7.8 14.6 0.535 8.1 16.1 0.503 8.0 16.9 0.474 7.9 18.6 0.426 7.7 23.0 0.335 7.5 21 0.357 8.1 17 0.476 8.0 14.8 0.540 8.0 13.8 0.580 7.9 12.4 0.637 8.0 11.1 0.720 6.0 7.4 0.811 6.0 9.2 0.653 6.0 11.9 0.505 6.0 12.5 0.480 6.o 13.5 0.445 5.9 14.0 0.422 6.0 13.5 0.445 6.0 13 0.462 5.9 12.7 0.465 5.9 12.5 0.473 6.1 12.7 0.481 6.0 12.7 0.474 5.9 12.8 o.461 6.1 13.2 0.464 6.0 14.5 0.414 5.8 15.5 0.375 6.0 17.2 0.349 5.9 18.4 0.321 5.7 14.2 0.403 6.0 11.9 0.505 6.0 12.4 0.485 6.0 11.5 0.522 6.0 11 0.546 6.0 9.2 0.653 6.1 8.5 0.519 6.1 7.2 0.440 A-18 0.1116 0.258 0.292 0.402 0.519 0.634 0.766 0.862 0.869 1.100 1.205 1.490 1.948 2.442 3.616 4.465 6.198 8.605 A-20 0.146 0.212 0.285 0.510 0.685 0.851 1.058 1.192 1.40 1.66 1.92 2.79 3.42 4.88 6.69 8.54 2.13 1.655 1.175 0.425 A-21 0.156 0.251 0.565 0.84 1.122 1.44 1.95 2.50 3.35 5.35 1.88 0.952 0.188 A-22 0.214 0.382 0.601 0.856 0.942 1.36 1.64 1.93 2.44 3.19 1.845 1.135 0.612 2.1 2.1 2.05 2.05 2.05 2.0 2.0 2.05 2.0 2.0 2.1 2.0 1.95 2.0 1.90 1.95 1.8 1.9 1.0 1.0 1.0 1.0 0.95 1.0 1.0 0.95 1.0 0.95 1.0 1.0 0.95 0.95 0.95 1.0 1.0 1.0 1.0 1.0 18.1 18.0 18.0 17.9 18.1 18.1 18.7 18.1 18.0 18.0 17.5 17.7 17.7 24.5 24.5 24.0 23.8 23.9 23.8 24.0 24.8 24.5 24.6 24.4 24.3 24.0 2.75 0.765 3.75 0.560 3.9 0.525 4.85 O. 423 6.5 0.316 7.8 0.256 9.1 0.220 8.9 0.230 9.7 0.206 11.5 0.174 10.5 0.200 9.4 0.213 7.6 0.256 6.0 0.333 6.0 0.317 6.5 0.300 6.8 0.265 7.5 0.253 1.65 0.605 2.2 0.455 3.1 0.330 7.5 0.133 9.5 0.100 8.0 0.125 9.3 0.107 9.2-10.3 0.103-0.092 7.5-9.0 0.133-0.111 7.5 0.133 6.5 0.154 4.0 0.250 3.5 0.271 3.3 0.288 3.5 0.271 4.7 0.213 5.3 0.189 6.2 0.161 7.8 0.128 4.7 0.212 20.6 0.880 21.6 0.835 24.0 0.750 25.6 0.700 28.3 0.640 30.2 0.600 33.0 0.566 35.5 0.510 39.5 0.455 46.0 0.391 32.0 0.546 27 0.655 21.2 0.833 28.5 0.890 30.0 0.816 32.0 0.748 34.0 0.700 35.0 0.682 37.4 0.635 40.0 0.600 43.5 0.570 47.0 0.520 53.0 o.464 41.5 0.589 38.0 0.639 33.0 0.726 I 4='

TABLE IV FROTH DATA FOR ACETONE - PERFORATED PLATE DISPERSER TABLE V FROTH DATA FOR CYCLOHEXANOL - PERFORATED PLATE DISPERSER Run No. Superficial Clear Liquid Froth Froth A: ir Velocity Depth Height Density Ft/Sec In. In. Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Ft/Sec In. In. AC-1 0.685 1.81 0.440 1.87 0.612 0.122 0.159 0.116 0.630 0.165 1.950 0.751 0.318 0.430 0.483 0.974 3.16 4.22 5.01 AC-2 0.107 0.284 0.397 0.151 0.236 0.488 0.417 0.646 0.740 0.673 1.274 AC-3 0.170 0.200 0.150 0.304 0.140 0.575 0.314 0.187 0.232 0.625 0.700 0.728 0.588 0.412. 463 1.000 1.31 1.35 1.87 0.564 2.68 2.55 5.41 3.78 2.79 5.56 1.22 4.8 4.5 4.1 4.9 4.5 4.4 4.4 4.4 4.1 4.0 4.0 3.1 4.8 4.5 4.3 4.1 4.0 3.8 4.3 1.9 2.2 2.1 2.0 1.9 1.6 2.1 1.7 2.1 2.0 1.85 11.0 10.8 10.7 10.1 10. 9.4 10.6 10.4 9.8 9.5 11.3 9.8 11.0 12.1 9.7 10.1 10.8 10.5 10.0 9.8 12.0 11.8 10.8 10.4 10.2 9.6 9.5 12 0.400 14 0.321 9.0 0.456 14.7 0.334 11.3 0.398 6.0 0.735 6.4 0.689 5.8 0.760 11.5 0.356 5.9 0.680 12.4 0.322 11.6-10.4 0.267-0.298 8.1-8.9 0.593-0.540 9.7 0.465 10.5-10. 410-0.430 11.3 0.363 15.5 0.258 16 0.237 19.0 0.226 8.8 0.216 5.9 0.373 8-10.5 0.262-0.200 3.7 0.540 4.9 0.387 12.6 0.127 9.2-10.5 0.228-0.200 11-13.5 0.155-0.126 9.5-10.5 0.221-0.200 9.5-11.5 0.211-0.174 7.1 0.260 14.4 0.765 14.4 0.751 13.7 0.781 15.6 0.648 12.2 0.820 17.3 0.543 15.5 0.685 13.7 0.760 13.7 0.716 17.2 0.553 20 0.565 19 0.516 18.9 0.582 18.8 0.645 16.8 0.578 21 0.482 23.6 0.458 24.3 0.433 26 3 0.381 18 0.545 34.5 0.348 34 0.347 42 0.257 36 0.289 31 0.329 40 0.240 21.7 0.437 H-1 0.167 0.217 0.295 0.348 0.370 0.486 0.614 0.790 0.925 1.230 1.62 1.98 2.80 3.90 5.25 6.35 2.92 1.30.900.596 H-2 0.148 0.215 0.295 0.428 0.483 0.558 0.641 0.805 1.040 1.24 1.62 2.02 2.39 3.77 5.65 6.45 1.76 1.85 0.845 0.123 H-3 0.131 0.173 0.223 0.321 0.377 0.480 0.581 0.669 0.808 0.930 1.116 1.29 1.42 1.68 2.07 2.60 3.68 5.57 1.55 0.975 0.358 0.151 H-4 0.130 0.239 0.269 0.409 0.531 0.715 0.911 1.240 1.58 2.02 2.84 4.62 6.36 1.07 0.559 0.196 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.1 2.1 2.1 2.0 2.0 2.0 1.9 2.1 2.1 2.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.0 4.0 3.9 3.9 4.0 4.2 4.2 16.2 16.2 16.2 16.2 16.2 16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.0 16.0 16.0 16 15.7 15.4 15.9 15.9 15.9 15.9 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.9 9.8 9.9 9.8 10.0 10.0 10.0 10.0 2.8 0.715 3.0 0.667 3.3 0.605 3.3 0.605 3.5 0.571 3.6 0.555 4.0 0.500 4.1 0.488 4.2 0.476 4.4 0.454 4.9 0.428 5.2 0.404 5.8 0.362 6.3 0.318 7.2 0.278 7.8 0.256 5.1 0.372 4.8 0.437 4.3 0.488 4.1 0.511 5.0 0.820 5.3 0.775 5.8 0.708 6.1 0.674 5.9 0.696 6.4 0.641 6.4 0.641 6.7 0.613 6.9 0.595 7.2 0.570 7.6 0.540 8.0 0.514 8.4 0.489 9.0 0.445 10.0 0.400 11.5 0.339 12.5 0.312 8.2 0.489 7.0 0.600 5.1 0.824 17.8 0.911 18.3 0.886 18.8 0.863 19.8 0.819 20.2 0.803 21 0.768 21.6 0.746 22.4 0.720 22.5-23.1 0.716-0.698 24.1 0.669 24.9 0.647 26.0 0.620 25.5-27.5 0.628-0.581 28.0 0.571 28.7 0.556 33 0.484 35.5 0.442 42 0.366 26.6 0.599 23.8 0.669 19.7 0.809 17.8 0.895 11.2 0.891 11.9 0.840 12.1 0.825 12.9 0.775 13.7 0.730 14.4 0.695 15.3 0.654 16.5 0.606 17.0 0.584 18.4 0.534 20.3 0.489 24.0 0.409 27.5 0.363 15.6 0.641 13.7 0.730 11.7 0.854

TABLE VI FROTH DATA FOR ETHYLENE DIBROMIDE PERFORATED PLATE DISPERSER Run No, Superficial Air Velocity Ft/Sec Clear Liquid Depth In. Froth Height In. Froth Density E-1 0. 609 0.375 1.31 0. 464 1. 070 1. 052 0.333 35 42 5.44 4.23 3.5 4.2 4.2 4.3 3.9 4. 4 4. o 4.5 4.1 3.9 4.2 4.0 4.4 348 4.5 3.9 3.8 4.5 5.9 8.0 10. 5 8.3 8.5 10.1 7.0 16.0 19.0 14.5 7.0 6. 4 9.2 9.0 9, 0 8, 2 5 8 12.3 0.594 0.526 o. 4oo 0.519 0. 460 o.436 0.571 0.281 0.216 0.269 o, 601 0.625 o. 479 o. 423 0.500 o. 476 0. 656 0. 366 E-2 0.230 0.225. 661 o. 820 0.535 0.515 0. 196 0.198 -236

-237 TABLE VII FROTH DATA FOR CARBON TETRACHLORIDE PERFORATED PLATE DISPERSER Run No. Superficial Clear Liquid Air Velocity Depth Ft/Sec In. Froth Froth Run No. Superficial Clear Liquid Froth Froth Height Density Air Velocity Depth Height Density In. Ft/Sec In. In. C-1 4.58 4.33 4.77 6.36 5.10 4.42 4.10 4.24 3.62 2.35 3.76 1.80 1.83 1.88 1.163 0.500 0.200 0.611 0.403 1.43 0.529 0.769 0.254 0.213 0.526 C-2 o0.653 2.01 1.31 0.965 0.583 0.890 0.624 0.304 0.263 0.589 0.301 0.240 3.37 4.29 6.14 4.78 3.29 5.47 5.53 2.26 3.01 3.7 4.4 4.9 4.3 3.8 3.2 3.6 4.0 4.0 3.9 3.8 4.8 4.4 4.1 4.1 4.0 3.8 3.7 3.7 4.0 3.0 4.6 4.1 4.0 3.9 2.4 2.2 2.0 3.0 3.5 1.9 2.2 2.0 1.7 1.7 2.5 1.8 3.7 2.8 2.2 1.9 1.9 2.5 2.2 1.7 1.9 15.0 16.2 18.8 21.0 15.3 12.4 13.0 14.5 15.0 11.0 13.8 12.0 11.4 10.5 8.5 6.6 5.0 7.0 6.0 9.4 5.8 8.5 5.8 5.7 6.7 5.0 6.4 5.1 6.5 5.4 4.7 4.7 3.6 3.1 4.0 3.0 3.0 12.4 10.5 11.3 8.8 6.9 11.5 10.6 2.7 3.4 0.246 C-3 0.272 0.261 0.205 0.248 0.258 0.277 0.275 0.266 0.354 0.275 0.400 0.385 0.390 0.483 0.606 0.760 0.530 0.618 0.426 0.519 0.542 0.709 0.703 0.583 0.480 0.343 0.392 0.461 0.649 0.404 0.468 0.555 0.548 0.425 0.834 0.600 0.298 0.266 0.195 0.216 0.275 0.218 0.190 0.629 0.559 5.35 3.74 2.76 1.65 1.28 1.245. 800 0.443 0.215 4.06 2.66 1.85 1.54 1.28 0.95 0.63 0.443 0.298 0.172 0.209 0.209 10.2 10.7 10.2 10.0 9.7 10.0 9.8 10.0 10.0 10.5 10.3 10.1 9.9 9.9 9.7 10.0 10.1 9.9 9.6 10.5 10.0 29.0 26.5 20.5 18.0 16.0 19.0 16.2 13.6 12.0 34.0 26.3 21.5 20.0 18.0 16.6 15.3 14.1 12.5 11.4 13.1 12.4 0.352 0.404 0.497 0.555 0.606 0.526 0.606 0.735 0.833 0.309 0.392 0.470 0.495 0.550 0.584 0.654 0.719 0.794 0.842 0.804 0.806

-238TABLE VIII FROTH DATA FOR BENZENE SOLUTION - PERFORATED PLATE DISPERSER Run No. Superficial Air Velocity Ft/Sec Clear Liquid Depth In. Froth Froth Height Density In. Run No. Superficial Clear Liquid Froth Air Velocity Depth Height Ft/Sec In. In. Froth Density B-l 0.13 (0.01 vol%) 0.16 0.20 0.28 0.31 0.38 0.14 0.29 0.38 0.50 0.57 0.62 0.24 0.175 0.45 0.67 0.84 o.90 0.73 0.97 1.10 0.76 0.99 1.27 1.47 1.66 1.84 2.56 3.20 4.70 B-2 0.105 (0.001 vol%) 0.175 0.21 0.29 0.41 0.49 0.60 0.65 0.15 0.36 0.56 0.66 o.65 0.74 0.90 0.93 1.12 0.33 0.43 0.66 0.79 1.06 1.27 1.46 1.64 1.85 3.33 4.0 5.2 4.0 5.7 4.0 6.5 4.0 8.2 4.0 8.8 4.0 9.4-12.0 4.0 5.4 4.0 8.3-9.0 4.0 10.0-11.5 4.0 11.0-14.5 4.o 12.0-17.5 4.0 12.0-18.0 3.9 7.6 3.9 6.0 4.0 10.2-12.0 4.0 13.0-18.0 4.0 15.0-24.0 3.9 14.0-20.0 3.8 13.0-22.0 3.8 13.0-17.0 3.7 12.0-14.0 4.0 13.0-19.0 4.0 13.0-14.5 4.0 12.3 4.0 11.8 3.9 11.5 3.9 11.2 4.0 12.0 4.0 13.0 4.0 14.0 4.0 5.4 4.0 6.5 4.0 7.7 4.0 9.6 4.0 10.0-12.5 4.0 11.0-13.5 4.0 12.5-17.5 4.0 13.0-19.0 4.0 6.2 4.0 10.5 4.0 12.0-317.0 3.9 14.0-18.0 3.9 14.0-21.0 3.9 13.0-19.0 3.8 16.0-21.0 3.8 16.0-27.0 3.8 12.0-14.5 4.0 8.3 4.0 9.5-13.0 4.0 11.5-16.0 4.0 13.0-17.0 4.0 12.5-14.5 3.9 11.0-12.0 3.9 10.7 3.9 11.0 3.8 11.0 3.8 12.3 0.771 0.703 0.616 0.503 0.455 0.426-0.333 0.742 0.482-0.445 0.400-0.348 0.364-0.276 0.333-0.228 0.333-0.222 0.514 0.650 0.392-0.333 0.308-0.222 0.266-0.167 0.278-0.195 0.292-0.172 0.292-0.223 0.308-0.264 0.307-0.210 0.307-0.276 0.325 0.339 0.339 0.348 0.333 0.308 0.286 0.742 0.616 0.520 0.417 0.400-0.321 O.364-0.296 0.320-0.228 0.307-0.210 0.646 0.381 0.333-0.235 0.278-0.217 0.278-0.186 0.300-0.205 0.237-0.181 0.237-0.141 0.316-0.262 0.483 0.380-0.308 0.348-0.250 0.308-0.235 0.320-0.276 0.354-0.325 0.364 0.355 0.346 0.309 B-3 0.13 (0.045 vol%) 0.20 0.24 0.31 0.40 0.55 0.67 0.79 0.87 0.38 0.58 0.79 0.78 0.93 0.81 0.87 0.76 1.00 1.16 1.41 1.76 1.90 4.0 5.2 4.0 6.4 4.0 7.8 4.0 9.2-10.0 4.0 10.0-12.0 3.9 11.0-15.0 3.9 13.0-22.0 3.8 21.0-29.0 3.8 13.0-1Y.O 4.0 9.2-10.2 4.0 12.0-16.0 3.9 13.0-18.0 3.9 13.0-20.0 3.8 14.0-21.0 3.8 13.0-17.0 4.0 14.5-18.5 4.0 13.0-19.0 3.9 13.6 3.9 11.9 3.9 11.0 3.8 10.7 3.8 10.5 0.770 0.625 0.513 0.435-0.400 0.400-0.333 0.354-0.260 0.300-0.177 0.181-0.131 0.292-0.224 0.435-0.392 0.333-0.250 0.300-0.216 o.300o-o.195 0.271-0.181 0.292-0.223 0.276-0.216 0.308-0.210 0.287 0.328 0.354 0.355 0.362

-259TABLE IX FROTH DATA FOR GLYCEROL SOLUTION PERFORATED PLATE DISPERSER Run No. Superficial Clear Liquid Froth Froth Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Air Velocity Depth Height Density Ft/Sec In. In. Ft/Sec In. In. G-16 0.385 (1.0 vol%) 0.494 0.650 0.265 0.193 0.325 0.533 0.458 0.685 0.590 0.806 1.07 0.710 1.14 1.52 1.94 2.49 3.44 4.88 G-17 0.541 (10.0 vol%) 0.313 0.240 0.421 0.541 0.650 0.493 0.361 0.722 0.505 0.674 0.600 4.0 12.0 0.333 0.577 4.0 14.0-17.0 0.286-0.235 0.746 4.0 13.0-17.0 0.308-0.235 0.697 4.0 8.6 0.476 0.842 4.0 6.5 0.616 1.02 4.0 10.8 0.370 1.25 4.0 15.0-22.0 0.266-0.182 1.48 4.0 15.0-17.5 0.266-0.228 1.87 4.0 16.0-21.0 0.250-0.190 2.65 4.0 16.0-20.0 0.250-0.200 3.42 3.9 19.0-25.0 0.205-0.156 4.43 3.9 14.0-16.0 0.278-0.244 4.93 4.0 16.0-20.0 0.250-0.200 4.0 14.5 0.276 G-18 0.325 4.0 12.5 0.320 (20.0 vol%) 0.458 3.9 11.6 0.336 0.615 4.0 11.8 0.338 0.820 4.0 12.6 0.317 0.542 3.9 13.4 0.291 0.615 0.362 4.0 20.0-25.0 0.200-0.160 0.518 4.0 9.0 0.445 0.205 4.0 7.5 0.533 0.422 4.0 12.0-14.0 0.333-0.285 0.711 3.9 22.0-29.0 0.177-0.134 0.760 3.9 24.0-33.0 0.162-0.118 1.31 3.9 13.0-16.0 0.300-0.244 1.77 3.9 11.0 0.354 1.52 4.1 18.0 0.228 2.66 4.0 17.0-21.0 0.235-0.190 3.89 4.0 17.0-24.0 0.235-0.167 4.90 4.0 20.0-27.0 0.200-0.148 3.9 26.0-32.0 0.150-0.122 3.9 17.0-20.0 0.230-0.195 4.0 17.0-21.0 0.235-0.190 4.0 15.0-18.0 0.266-0.222 4.0 14.4 0.277 3.9 13.0 0.300 3.9 12.5 0.312 3.9 11.5 0.339 4.0 11.8 0.331 4.0 12.5 0.312 4.0 13.0 0.300 4.0 13.0 0.300 4.0 11.0 0.363 4.0 16.0-19.0 0.250-0.210 4.0 22.0-26.0 0.182-0.154 4.0 16.0 0.250 4.0 22.0-32.0 0.182-0.125 4.0 19.0-25.0 0.210-0.160 4.0 14.o 0.285 3.9 13.6-16.5 0.300 4.0 6.5 0.615 4.0 12.5 0.320 4.0 15.0 0.266 4.0 16.0 0.250 3.9 12.7 0.307 3.9 11.7 0.333 3.9 11.6 0.336 4.0 12.3 0.325 4.0 13.5 0.296 4.0 13.6 0.294

TABLE X FROTH DATA FOR POTASSIUM CARBONATE SOLUTION PERFORATED PLATE DISPERSER Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Ft/Sec In. In. Run No. Superficial Clear Liquid Froth Froth Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Air Velocity Depth Height Density Ft/Sec In. In. Ft/Sec In. In. K-18 0.115 (O.O15M) 0.145 0.162 0.197 0.248 0.292 0.397 0.373 o.440 0.505 0.590 0.672 0.742 0.857 0.646 0.738 0.866 0.981 1.31 1.59 1.99 2.36 2.97 4.19 5.00 K-17 0.134 (0.075M) 0.165 0.178 0.214 0.250 0.297 0.378 0.402 0.475 0.552 0.625 0.660 0.750 O.810 0.880 1.01 1.23 1.51 1.97 1.98 2.41 3.88 5.05 K-16 0.109 (0.150M) 0.129 0.150 0.207 0.248 0.306 0.407 0.517 0.612 0.680 0.760 0.684 0.803 0.890 0.984 1.293 1.69 1.89 1.95 2.26 2.85 3.75 4.85 4.1 5.4 0.760 4.1 6.1 0.671 4.05 6.5 0.623 4.0 8.o 0.500 4.0 11.0-12.3 0.363-0.325 5.9 15 0.260 3.8 17.0-22.0 0.223-0.173 4.1 15.5-19.0 0.264-0.215 4.0 31.0 0.129 5.9 31.0-35.0 0.126-0.111 3.8 27.0-38.0 0.140-0.100 5.7 28.0-42.o 0.152-0.0880 5.6 29.0-41.0 0.124-0.0876.35 14.5 0.242 4.1 25.0-33.0 0.164-0.124 4.0 26.0-34.0 0.154-0.108 5.9 15.0-17.0 0.260-0.250 3.9 14.5 0.269 3.8 12.3 0.308 3.7 11.O 0.557 5.6 11.0 0.527 4.1 12.0 0.341 4.0 12.4 0.322 4.0 13.2 0.503 5.9 14.0 o.278 4.15 6.7 0.619 4.10 8.3 0.495 4.10 10.4 o.395 4.10 14.3 0.286 4.10 20.7 0.198 4.0 24.0-26.0 0.166-0.154 4.0 57.0 o.lo8 4.0 38.o-40.o 0.105-0.100 4.o 40.0-42.5 0.100-0.094 4.0 41.o-44.5 0.0975-0.090 4.o 35.0-46.0 o.ll4-o.087 4.00 56.0-45.0 0.111-0.089 5.9 36.0-46.0o o.108-0.085 5.9 16.5-20.5 0.256-0.191 3.8 17.4 0.218 3.8 14.0-17.0 0.272-0.224 5.7 15.0 0.287 3.7 12.4 0.298 3.7 11.5 0.321 4.1 12.5 0.555 4.1 12.7 0.523 4.1 13.7 0.299 4.1 14.3 0.296 4.1 6.0 0.682 4.1 6.4 0.640 4.1 7.2 0.569 4.1 11.o 0.572 4.1 19.1 0.214 4.1 23.0 0.178 4.0 52.6 0.122 4.0 35.0-39.0 0.114-0.102 3.9 32.0-42.0 0.122-0.093 3.8 33.0-42.0 0.115-0.086 3.7 39.0-45.0 0.095-0.082 4.1 39.0-45.5 0.105-0.0o9 4.1 18.0-24.0 0.227-0.171 4.1 18.0 0.227 4.0 16.3 0.246 4.0 14.5 0.276 3.9 13.0 0.300 3.9 12.4 0.314 4.1 12.8 0.320 4.0 13.1 0.304 4.0o 1.3 0.301 3.9 13.5 0.289 3.9 14.1 0.276 K-15 O.109 (0.375M) 0.151 0.206 0.261 0.316 0.378 0.435 0.546 0.630 0.700 0.814 0.939 0.714 0.800 0.909 1.00 1.24 1.41 1.85 1.88 3.73 5.00 K-14 0.120 (0.750M) 0.151 0.206 0.264 0.356 0.417 0.460 0.503 0.610 0.700 0.923 0.348 0.238 0.176 0.574 0.703 0.890 1.095 1.29 1.32 1.79 1.98 2.49 3.29 4.48 5.45 K-13 0.094 (1.50M) 0.145 0.168 0.231 0.301 0,336 0.410 0.508 0.517 0.598 0.734 0.795 0.863 1.01 1.13 1.35 1.54 1.89 2.25 2.48 2.88 3.74 5.22 4.1 5.4 0.760 K-12 4.0 6.9 0.580 (3.0M) 4.0 10.4 0.384 4.0 18.0 0.222 4.0 24.0-25.8 0.167-0.155 3.9 31.0 0.126 4.0 32.0-34.5 0.125-0.116 4.0 34.0-37.4 0.118-0.107 4.0 36.0-39.5 0.111-0.101 4.1 33.0-40.0 0.124-0.103 4.0 35.0-41.0 0.114-0.098 4.1 17.5-22.0 0.234-0.186 4.0 35.0-41.0 0.114-0.098 4.0 23.0-32.0 0.174-0.125 4.0 19.0-23.0 0.210-0.174 3.9 17.0-20.5 0.229-0.190 3.9 15.5 0.251 4.1 15.0 0.273 4.0 14.0 0.286 4.0 14.0 0.286 4.0 14.4 0.278 4.0 15.0 0.266 4.1 5.6 0.731 4.1 6.4 0.640 4.0 9.2 0.435 3.9 16.0 0.244 3.9 21.3 0.183 4.1 27.8 0.147 4.0 31.5 0.127 3.9 31.0-34.0 0.126-0.112 3.8 32.0-35.0 0.119-0.108 3.9 32.0-36.0 0.122-0.108 4.1 16.0-18.0 0.256-0.228 4.1 14.6 0.281 4.1 11.7 0.350 4.0 7.1 0.563 3.9 24.0-30.8 0.163-0.27 3.8 24.0-32.5 0.158-0.117 3.8 14.0-17.0 0.273-0.223 3.7 12.8-14.0 0.289-0.264 3.7 11.5 0.321 4.1 11.8 0.347 4.1 11.3 0.362 4.1 11.0 0.373 4.1 11.2 0.366 4.1 11.6 0.353 4.1 12.7 0.298 4.1 13.8 0.284 4.0 5.2 0.770 4.0 6.3 0.635 4.0 7.3 0.548 4.0 11.1 0.360 4.0 17.0 0.235 4.0 19.0 0.210 4.1 21.8 0.188 4.1 22.0-26.4 0.186-0.155 4.2 22.5-28.o 0.190-0.150 4.2 25.5-29.5 0.164-0.142 4.2 26.5-36.5 0.158-0.133 4.2 23.0-30.5 0.182-0.138 4.2 21.0-28.0 0.200-0.150 4.2 20.5-23.5 0.205-0.178 4.1 17.0 0.241 4.1 15.1 0.291 4.0 13.0 0.307 4.0 12.8 0.312 4.0 11.1 0.360 4.0 11.5 0.348 4.0 11.9 0.336 4.0 13.2 0.303 4.0 14.7 0.272 0.109 0.145 0.225 0.312 0.340 0.371 0.420 0.526 0.670 0.795 0.880 1.08 1.26 1.49 1.70 1.85 2.51 3.00 5.15 4.0 4.6 0.870 4.0 4.8 0.833 4.0 5.3 0.755 3.9 5.7 0.682 3.8 5.9 0.644 4.2 6.6 0.636 4.2 6.8 0.617 4.2 7.1 0.591 4.1 7.5 0.546 4.1 7.9 0.519 4.1 8.1 0.505 4.0 8.2 0.487 4.0 8.6 o.465 4.0 9.0 0.444 4.0 9.5 0.421 4.0 9.7 0.412 4.2 10.7 0.392 4.1 11.5 0.356 4.0 13.6 0.294 I I!

TABLE XI FROTH DATA FOR ACETIC ACID SOLUTIONS PERFORATED PLATE DISPERSER Run No. Superficial Clear Liquid Froth Froth Run No. Superficial Clear Liquid Froth Froth Air Velocity Depth Height Density Air Velocity Depth Height Density Ft/Sec In. In. Ft/Sec In. In. HA-1 0.293 (O.01 vol%) 0.440 0.550 0.708 0.854 0.634 o.854 0.989 1.13 1.39 1.62 1.97 2.75 3.56 4.51 5.25 1.77 0.854 0.940 0.671 0.329 0.244 HA-2 0.144 (0.1 vol%) 0.240 0.228 0.276 0.432 0.528 0.564 o.696 0.840 0.600 0.744 0.912 1.40 1.56 1.69 1.92 2.68 3.72 5.11 1.23 0.745 0.576 0.276 0.180 HA-3 0.157 (1.0 vol%) 0.241 0.350 0.386 0.640 0.724 0.651 0.507 0.856 1.12 1.39 1.62 2.00 2.34 3.12 4.03 5.32 4.0 8.8 0.455 HA-4 0.205 4.0 10.0-12.0 0.400-0.333 (10.0 vol%) 0.307 4.0 11.5-13.5 0.348-0.296 0.380 4.1 12.5-15.5 0.328-0.258 0.290 4.0 11.5-13.0 0.348-0.308 0.398 3.9 10.5-12.5 0.371-0.312 0.470 4.0 11.0-12.0 0.364-0.333 0.626 3.9 10.5-12.0 0.371-0.325 0.325 3.8 10.3 0.369 0.626 4.0 10.1 0.396 0.772 4.0 10.3 0.388 0.978 4.0 10.5 0.381 0.990 3.9 11.3 0.345 1.33 3.9 12.2 0.320 1.57 3.9 13.7 0.284 1.95 3.8 14.2 0.268 4.0 10.5 0.381 HA-5 0.400 4.0 10.6-12.2 0.377-0.328 (10.0 vol%) 0.253 4.0 10.0-11.2 0.400-0.357 0.434 4.0 9.5-11.3 0.422-0.352 0.590 3.9 7.7 0.507 0.386 3.8 6.7 0.567 0.750 0.494 4.1 6.1 0.672 1.160 4.1 10.2 0.402 0.905 4.0 9.1 0.440 0.265 4.0 11.2-12.0 0.357-0.333 1.65 4.0 15.5-19.3 0.258-0.207 1.90 4.0 16.0-24.0 0.250-0.166 4.0 20.0-25.0 0.200-0.160 HA-6 0.722 3.9 16.5-23.0 0.269-0.169 (20.0 vol%) 0.506 3.9 15.5-19.0 0.252-0.205 0.349 4.1 18.0-25.0 0.228-0.164 0.976 4.1 16.0-19.5 0.256-0.210 0.722 4.0 14.5-17.0 0.276-0.235 0.470 4.0 12.4 0.322 0.410 3.9 11.0 0.354 1.34 3.9 10.9 0.348 1.14 4.0 10.8 0.370 0.482 4.0 11.4 0.351 0.241 4.0 12.6 0.317 1.69 4.0 13.5 0.296 1.29 4.0 9.2 0.435 2.85 4.0 8.5-10.5 0.470-0.381 3.9 8.0-10.3 0.488-0.379 HA-7 0.58 3.8 7.2 0.529 (5.0 vol%) 0.795 3.8 5.7 0.667 0.493 0.325 4.o 6.5 0.616 0.35 3.9 14.7 0.265 0.613 3.9 23.5 0.166 0.975 3.8 24.5-25.5 0.155-0.149 0.457 3.6 25.0-31.0 0.144-0.116 0.192 3.9 19.0-25.0 0.205-0.156 0.638 4.1 19.0-25.0 0.216-0.164 0.782 4.0 20.0-23.0 0.200-0.174 0.493 4.0 20.0-26.0 0.200-0.154 0.806 4.0 22.0-17.0 o.182-0.236 0.962 4.0 15.2 0.263 0.385 3.9 14.7 0.265 1.42 3.9 13.6 0.286 1.79 3.9 12.7 0.307 4.82 3.9 12.4 0.314 4.98 3.8 13.4 0.284 3.8 14.5 0.262 HA-8 0.325 (15.0 vol%) 0.397 0.710 0.866 0.782 0.914 0.394 0.493 0.301 0.794 0.986 0.577 0.530 o.686 0.553 1.336 1.85 2.49 3.49 4.85 4.0 16.0 0.250 4.0 30.0 0.133 4.0 25.0 0.160 4.0 26.0 0.154 4.1 28.0 0.146 4.0 38.5 0.104 4.0 40.0 0.100 4.1 24.0 0.171 4.0 40.0 0.100 4.0 41.0-32.0 0.098-0.125 3.9 38.0-25.0 0.102-0.156 4.0 41.0-29.0 0.098-0.138 4.0 19.0-24.0 0.210-0.166 4.1 20.5 0.200 4.1 19.0 0.215 3.8 33.5 0.114 4.2 25.8 0.163 4.0 33.0 0.121 4.0 44.0 0.091 4.0 28.5 0.140 4.2 56.o 0.075 4.2 38.5 0.109 4.2 25.0-30.0 0.168-0.140 4.2 46.0-36.0 0.091-0.117 4.0 24.0 0.167 4.2 20.0 0.210 4.4 20.7 0.212 4.2 20.5 0.205 4.3 11.0 0.391 4.1 9.0 0.455 4.0 14.0 0.286 3.9 14.0 0.279 4.0 14.0 0.286 3.9 12.0 0.325 3.9 15.0 0.260 3.9 13.5 0.289 4.1 10.0 0.410 4.1 7.0 0.587 4.1 14.0 0.293 4.0 12.7 0.315 4.2 15.0 0.280 3.9 33.0 0.118 3.8 38.0-32.0 0.100-0.119 4.1 28.0 0.146 4.2 20.0 0.210 4.0 24.5 0.163 4.0 34.0 0.117 4.0 35.0-27.0 0.114-0.148 4.1 28.0 0.146 4.2 7.3 0.575 4.0 29.0-31.0 0.138-0.129 3.9 27.0-34.0 0.145-0.115 3.9 28.5 0.137 4.0 40.0-34.0. 100-0.118 3.9 44.0-34.0 0.089-0.115 3.8 24.0 0.157 4.1 24.5 0.167 4.o 20.5 0.195 4.5 25.0 0.180 4.0 21.0 0.191 4.0 16.0 0.250 4.1 27.0 0.152 4.1 38.0 0.108 4.1 33.0-38.0 0.124-0.108 4.0 34.0-39.0 0.118-0.103 3.9 29.0-38.0 0.135-0.103 4.0 21.0 0.190 4.2 33.5 0.125 4.2 16.0 0.262 4.0 33.0-40.0 0.121-0.100 3.9 24.0-21.0 0.162-0.186 3.9 28.0 0.139 4.0 32.0 0.125 4.1 35.0-38.0 0.117-0.080 4.2 30.5 0.138 3.9 - 21.0 0.186 3.9 18.5 0.210 4.0 17.5 0.229 4.0 18.5 0.216 4.1 20.0 0.205

APPENDIX I OSCILLATING JET DATA

TABLE I CALBUATION DATA FOR TRIPIX-DIBTILIXD WKTR Surface Major Minor Geometric Amplitude Z Tension Iaperimental Radius Hansen' s Liquid Jet Water Water Equilibrium Reynolds Jet Nodal Diameter Diameter Mean Radius Ratio Computed Correction Correction Correction Run Rate Temperature Density, Viscosity, turface Tension No. Thru Node Wavelength, At Node, At Node, At Node, a F rol Eq (23-E) Factor, Factor, Factor, No. ML/MIN C0 g/cc. Centipoises Dynes/cm Orifice No. inches inches inches inches ng pL Dynes/c K Kr K Corrected Correction Calc'd Facts C&le'd Surface From Eqn (19) Tension, x - KK K Dynes/cm 404 0.8012 22.5 0.9977 0.9468 72.36 197.2 1 2 3 4 5 6 7 405 0.8812 21.8 0.9978 0.9625 72.47 213.3 1 2 3 4 406 0.8821 23.2 0.9975 0.9315 72.25 220.6 1 2 3 4 5 6 7 407 0.8800 23.0 0.9975 0.9358 72.28 219.0 1 2 3 4 5 6 408 0.724 23.2 0.9975 0.9535 72.25 180.7 1 2 3 4 5 6 7 409 0.7703 23.2 0.9975 0.9335 72.25 192.2 1 2 3 4 5 6 7 410 0.8188 24.2 0.9972 0.9101 72.10 209.5 1 2 5 4 5 6 7 411 0.8554 24.1 0.9972 0.9121 72.11 218.4 1 2 5 4 5 6 7 412 0.8965 24.7 0.9971 0.8999 72.02 232.0 1 2 5 4 5 6 7 413 0.6260 24.6 0.9971 0.9019 72.03 161.6 1 2 4 5 6 414 0.6664 24.6 0.9971 0.9019 72.03 172.0 1 2 3 4 5 6 7 0.00379 0.01023 0.01029 0.01030 0.01030 0.01029 0.01028 0.00413 0.01167 0.01165 0.01165 0.00412 0.01167 0.01163 0.01159 0.01153 0.01149 0.01146 o.00408 0.01162 o.o1164 0.01159 0.01151 0.01146 0.00352 0.00888 0.00905 0.00909 0.009o9 o.oo9o8 0.00909 0.00362 o.o0962 0.00978 0.00978 0.00981 o.oo984 0.00979 0.00380 0.01051 0.01051 0.01059 0.01058 0.01055 0.01056 0.00398 0.01121 0.01117 0.01118 0.01111 0.01107 0.01108 0.00443 0.01211 0.01200 0.01192 0.01180 0.01175 0.01169 0.00270 0.00720 0.00735 0.00744 0.00750 0.00755 0.00313 0.00801 o.oo8o09 0.00816 0.00818 o.00820 o.oo819.00246.00224.00210.00202.00197 o00192.00190.00250.00230.00220.00216.00248.00228.00215.00209.00208.00205.00202.00246.00223.00210.00204.00197.00192.00251.00235.00220.00211.00207.00206.00203.00254.00240.00227.00oo218.00211.00208.00205.00257.00245.00230.00225.00217.00209.00206.00252.00235.00222.00213.00206.0o0198.00202.00255.00244.00230.oo219.00212.00206.00202.00247.00222.00208.00201.00198.00197 0.00247 0.00226 0.00213 0.00205 0.00201 0o.00oo199 o.oo00196.00166.00137 0.000876.00142 0.000863.00149 0.000867.00157 0.000879.00162 0.o00882.00168 o0.000893.00170.o00151 o0.000868.00143 0.000887.00155 0.000915.00148.00128 0.000854.00140 0.000863.00148 0.000879.0016 o0.000912.00168 o.000928.00173 0.000935.00146.00129 0.000848.00139 o.ooo854.00147 0.000866.00153 0.000868.00156 0.000865.oo169.00149 o.ooo936.00158 0.000932.00165 0.000933.00173 o.o000946.00178 0.000957.00181 o0.000958.0017 ---.00147 0.000959.00157 o.ooo944.00165 0.000949.00170 0.000947.00174 0.000951.00183 o.ooo968.00171.00148 0.000952.00157 o0.000950.oo169 0.000975.00170 o.oo00096.oo176 0.000959.00179 o.ooo096.00156.00138 0.000900.00146 0.000900.00154 o0.000906.00158 0.000902.00169 0.000915.00167 0.000918.00150 ----.00136 0.000911.00148 0.000922.00155 0.000921.00157 0.000912.00164 0.000919.00172 0.000932.00200.00oo161 0.000945.00165 0.000926.00170 o.000924.00176 0.000933.00180 0.000942 0.00195 ---- 0.00156 0.000939 0.00161 0.000926 0.00166 0.000922 0.00173 0.000932 0.00178 0.0ooo41 0.00180 o.000939 0.198 0.0108 0.248.0506 74.15 0.197.1090 73.18 0.153.1675 71.69 0.114.2260 69.90 0.085.2846 69.45 0.062.3430 68.27 0.194 0.0108 0.284 0.0534 72.64 0.217 0.1136 68.98 0.167 0o1748 65.42 0.260 0.0105 0.291 0.0506 74.40 o.211 O.1098 71.37 0.173 0.1688 69.44 0.131 0.2275 66.42 0.100 0.2860 65.09 0.077 o0.3443 64.62 0.263 0.0104 0.276 0.0506 74.68 0.207 0.1101 71.71 0.164 0.1696 70.20 0.127 0.2287 70.24 0.104 0.2874 "".76 0.199 0.0109 --- 0.229 0.0494 70.74 0.166 0.1050 67.27 0.123 0.1613 65.96 0.090 o0.2177 64.34 0.073 0.2740 63.31 0.057 0.3304 62.99 O.19o 0.0106 0.247 0.0492 70.03 0.185 0.1057 66.00 o.140 0.1627 64.76 0.108 0.2199 64.09 0.089 0.2772 63.19 0.057 o0.3344 62.04 0.205 0.0102 0.254 0.0485 66.9C 0.192 0.1047 65.50 0.143 0.1611 61.50 0.122 0.2178 62.60 0.086 0.2743 62.60 0.070 0.3308 62.15 0.241 0.0102 0.268 o.o492 69.97 0.211 0.1066 68.75 0.163 0.1640 67.11 0.133 0.2212 67.69 0.079 0.2781 66.37 0.095 0.3350 66.09 0.268:0.0107 0.295 0.0507 66.75 0.222 0.1089 64.66 0.173 0.1667 64.50 0.151 0.2240 66.05 0.114 0.2809 65.45 o.o8o 0.3376 64.62 0.106 0.0094 0.161 0.0437 71.40 0.116 o0.0942 70.27 0.084 0.145 68.80 0.059 o0.197 66.65 0.045 0.249 65.05 0.118 0.0102 0.186 0.0465 69.58 0.140 o0.0989 68.80 0.106 0.1519 67.65 0.075 0.2051 66.06 0.056 0.2584 64.82 0.043 0.3118 65.04 1.025 1.011 0.991 0.968 o.960 1.003 0.954 0.904 1.030 0.988 0.961 0.920 0.900 0.896 1.030 0.991 0.972 0.972 0.979 0.979 o.531 0.913 0.891 0.876 0,872 0.969 0.915 o.8%6 0.887 0.875 0.859 0.927 0.909 0.853 0.868 0.868 0O862 0.970 0.952 0.930 O.938 0.921 0.917 0.928 0.900 0.898 0.920 0.910 0.900 0.991 0.976 0.955 0.926 0.904 0.966 0.955 0.939 0.917 0.900 0.903 0.953 0.963 0.960 0.950 0.948 0.938 0.926 0.919 0.886 0.948 0.940 0.927 0.887 0.887 0.881 0.963 0.958 0.948 0.946 0.946 0.897 0.901 0.900 0.888 0.879 0.878 0.887 0.8o5 0.880 0.879 0.877 o.865 0.850 0.852 0.831 0.843 0.844 0.843 0.915 0.914 0.909 0.912 0.901 0.898 0.887 0.878 0.879 0.886 0.880 0.870 0.928 0.945 0.946 0.939 0.932 0.924 0.935 0.938 0.929 0.924 0.923 1.058 1.036 1.023 1.015 1.010 1.005 1.069 1.045 1.027 1.072 1.046 1.030 1.012 1.012 1.008 1.065 1.041 1.027 1.017 1.011 1.099 1.064 1.042 1.027 1.018 1.012 1.072 1.047 1.030 1.020 1.015 1.008 1.022 1.014 1.009 1.001 1.001 1.000 1.038 1.025 1.016 1.011 1.005 1.002 1.037 1.024 1.016 1.011 1.005 1.001 1.100 1.067 1.045 1.031 1.021 1.090 1.06o 1.040 1.027 1.018 1.012 1.008 0.996 0.982 0.964 0.957 o.942 0.99O 0.96o 0.91o 1.018 0.983 0.955 0.917 0.898 0.888 1.028 0.998 0.974 0.962 0.956 0.986 0.959 0.939 0.911 0.895 0.889 0.951 0.924 0.9o6 0.897 0.890 0.970 0.870 0.865 0.838 0.845 0.846 o.845 0.950 o.940 0.926 0.924 0.908 0.902 0.920 0.990 0.893 0.896 0.885 0.871 1.021 1.010 0.989 0.969 o. 952 1.008 0.991 0.975 0.954 o0.940 0.935 73.5 73.5 73.0 72.6 72.6 72.5 73.4 71.9 71.9 73.0 72.6 72.7 72.5 72.5 72.9 72.6 71.9 72.1 73.0 73.9 77.1 70.5 70.3 70.6 70.7 70.9 73.6 71.5 72.9 71.6 71.0 71.5 76.9 75.8 73.4 74.2 74.0 73.9 73.6 73.2 72.5 73.3 73.1 73.3 72.6 71.9 72.5 75.7 75.9 74.2 69.9 69.6 69.6 68.9 68.4 69.0 69.4 69.4 69.3 69.0 69.6 I 4k I

TABLE I. CALIBRATION DATA FOR TRIPLE-DISTILTL WATER (Cont'd) Surface Major Minor Geometric Amplitude Z Tension Experimental Radius Hansen's Liquid Jet Water Water Equilibrium Reynolds Jet Nodal Diameter Diameter Mean Radius Ratio Computed Correction Correction Correction Run Rate Temperature Density Viscosity, Surface Tension No. Thru Node Wavelength, At Node, At Node, At Node, a 9z From Eqn (23-E) Factor, Factor, Factor, No. ML/MIN *C g/cc. Centipoises Dynes/cm Orifice No. inches inches inches inches rg pL Dynes/ca K K, K H Corrected Correction Calc'd Factor Calc'd Surface From Eqn (19) Tension, K - KHK Dynes/cm 415 0.6986 24.8 416 0.7476 23.6 417 0.7913 23.8 418 0.6426 23.5 419 0.7039 24.0 501 0.7106 25.4 502 0.6782 24.6 503 0.8047 25.3 504 0.7365 24.5 505 0.7801 24.5 0.9971 0.8978 72.00 181.2 1 2 3 4 5 6 7 8 0.9974 0.9228 72.19 188.7 1 2 3 4 5 6 0.9973 0.9185 0.9974 0.9250 0.9973 0.9147 0.9969 0.8857 0.9971 0.9019 0.9969 o.8877 0.9971 0.9037 0.9971 0.9037 72.16 200.6 1 2 3 4 5 6 72.20 161.8 1 2 3 4 5 6 7 72.13 179.2 1 2 3 4 5 6 71.91 186.8 1 2 3 4 5 6 7 72.03 175.1 1 2 3 4 5 6 7 71.92 211.0 1 2 3 4 5 6 72.05 189.8 1 2 3 4 5 6 7 72.05 201.0 1 2 3 4 5 6 0.00320 0.00249 0.00180 - o.00855 0.00230 0.00153 o.000938 0.00860 0.00217 0.00161 0.000935 0.00862 0.00209 0.00166 0.000931 0.00862 0.00204 0.00174 0.000942 0.00863 0.00201 0.00176 0.000940 0.00863 0.00198 0.00178 0.000939 0.00865 0.00194 0.00182 0.000940 0.00360 0.00251 0.00171 - 0.00939 0.00233 0.00151 0.000938 0.00940 0.00220 0.00158 0.000932 0.00942 0.0.00212.00165 0.000935 0.00939 0.00202 0.00168 0.000921 0.00943 0.00194 0.00170 0.000908 0.00370 0.00248 0.00161 - 0.01021 0.00229 0.00143 0.000905 0.01020 0.00216 0.00151 0.000903 0.01014 0.00208 0.00160 0.000912 0.01015 0.00202 0.00162 0.000904 0.01005 0.00197 0100167 0.000907 0.00280 0.00246 0.00194 - 0.00761 0.00223 0.00159 0.000942 0.00769 0.0021 0.00165 0.000931 0.00776 0o.o00204 0.00169 0.000928 0.00782 0.00199 0.00176 0.000ooo936 0.00785 0.00197 0.00179 0.000939 o.0Q785 0.00196 0.00180 0.000939 0.00322 0.00248 0.00185 ---- 0.00870 0.00227 0.00153 0.000932 0.00869 0.00215 0.00161 0.000930 0.00874 0.00208 0.00170 0.000940 0.00874 0.00202 0.00171 0.000929 0.00874 0.00197 0.00176 0.000931 0.00321 0.00239 0.00221 - 0.00857 0.o00221 0.00147 0.000901 0.00874 o.oo211 0.00156 0.000907 0.00869 0.00208 0.00165 0.000926 0.00871 0.00205 0.00170 0.000933 0.00873 0.00201 0.00174 o.ooo000935 0.00673 0.00199 0.00181 0.000949 0.00304 0.00260 0.00211 - 0.00774 0.00219 0.00144 0.000888.oo8oo 0.00206 0.00153.ooo000887 0.00812 0.00201 0.00161 o.000899 0.00813 0.00199 0.00168 0.000914 0.00815 0.00198 0.00171 0.000920 0.00820 0.00198 0.00181 o.000946 0.00578 0.00260 0.00173 --- 0.01013 0.00246 0.00142 0.000935 0.01022 0.00234 0.00157 0.000958 0.01025 0.00225 0.00164 0.000960 0.01025 0.00216 0.00164 0.000941 0.01025 0.00208 0.00173 0.000948 0.00336 0.00260 0.00214 - 0.0090ooo8 0.00251 0.00156 0.000990 0.00920 0.00236 0.00166 0.000990 0.00917 0.00229 0.00175 0.001001 0.00919 0.00226 0.00184 0.001020 0.00922 0.00222 0.00189 0.001024 0.00920 0.00218 0.00190 0.001018 0.00367 0.00260 0.00181 - o.oo986 0.00237 0.00140 0.000911 0.00995 0.00224 0.00151 0.000920 0.00992 0.00219 0.00163 o.000944 0.00986 0.00216 0.00168 0.000952 0.0oo987 0.00209 0.00173 0.000950 0.163 0.00o99 0.205 0.0462 69.25 0.962 0.150 0.0993 67.67 0.940 0.115 0.1526 67.16 0.933 0.080 0.2059 65.73 0.913 0.066 0.2592 65.63 0.912 0.053 0.3126 65.70 0.913 0.032 0.3661 65.26 0.907 0.193 0.0107 - 0.218 0.0493 68.05 0.943 0.166 0.1051 67.23 0.931 0.126 0.1610 66.01 0.914 0.092 0.2168 67.25 0.932 0.066 0.2727 67.75 0.958 0.217 0.0103 --- 0.237 0.0492 69.41 0.961 0.180 0.1062 68.25 0.946 0.131 0.1630 67.23 0.930 0.110 0.2197 67.53 0.935 0.083 0.2761 68.17 0.944 o.119 0.0097 --- 0.170 0.0458 69.58 0.121 0.0988 68.61 0.094 0.1523 67.49 0.061 0.2062 65.62 0.048 0.2605 64.81 0.043 0.3149 64.75 0.147 0.0101 --- 0.198 0.0473 68.72 0.145 0.1017 67.85 0.101 0.1562 65.62 0.083 0.2109 66.45 0.056 0.2656 66.05 0.039 0.0096 - 0.204 o.o45o 75.22 0.151 0.0969 70.89 0.116 0.1492 69.04 o.094 0.2014 67.80 0.072 0.2538 67.16 0.047 0.3062 65.67 0.104 0.0097 --- 0.210 0.0442 83.01 0.149 0.0946 77.02 o0.11 0.1462 73-15 0.085 0.1982 71.08 0.073 0.2504 70.07 0.045 0,3027 66.50 0.204.0100 --- 0.275 0.0470 71.25 0.200 0.1010 65.75 0.158 0.1554 64.38 0.138 0.2098 65.69 0.092 0.2643 64.46 0.964 0.950 0.935 0.909 0.898 0.897 0.953 0.941 0.910 0.921 0.916 1.050 0.988 0.960 0.942 0.935 0.912 1.153 1.070 1.017 0.987 0.973 0.924 0.991 0.911 0.898 o.912 o.899 0.910 0.913 0.916 0.907 0.908 0.910 o.909 o.9o6 0.911 0.909 0.922 0.931 0.926 0.928 0.920 0.927 0.924 0.923 0.935 0.936 0.929 0.926 0.926 o.917 0.918 0.909 0.920 0.918 0.938 0.933 0.917 0.910 0.909 0.898 0.965 0.966 0.955 0.943 0.938 0.913 0.889 0.869 0.867 0.884 0.878 0.804 0.804 0.795 0.779 0.776 0.781 0.917 0.910 0.888 0.882 0.883 1.088 1.058 1.039 1.026 1.017 1.012 1.008 1.047 1.031 1.020 1.013 1.009 1.056 1.037 1.024 1.016 1.010 1.104 1.068 1.045 1.030 1.020 1.014 1.082 1.054 1.035 1.023 1.016 1.111 1.073 1.049 1.033 1.022 1.016 1.187 1.120 1.080 1.053 1.036 1.024 1.069 1.049 1.033 1.022 1.014 1.060 1.040 1.027 1.018 1.012 1.008 1.104 1.067 1.044 1.029 1.019 0.990 0.965 0,955 0.930 0.923 0.921 0.915 0.949 0.940 0.927 o.g34 0.934 0.940 0.978 o.961 0.943 0.941 0.933 1.020 0.998 0.979 0.956 0.945 0.940 0.992 0.968 0.940 0.941 0.932 1.043 1.002 0.961 0.940 0.929 0.912 1.148 1.084 1.032 0.995 0.972 0.935 0.950 0.911 0.896 0.9o4 0.890 0.851 0.836 0.816 0.793 0.786 0.787 1.013 o.971 0.928 0.907 0.899 70.0 70.1 70,4 70.7 71.2 71.3 71.5 71.8 71.6 71.2 72.0 72.1 70.9 71.1 71.3 71.8 73.1 68.3 68.8 68.9 68.7 68.5 68.9 69.4 70.1 69.9 70.6 70.9 72.1 70.7 71.8 72.2 72.3 72.0 72.4 71.0 70.9 71.4 72.1 71.2 75.0 72.2 71.8 72.7 72.4 77.3 75.2 75.3 74.8 74.3 75.0 71.1 70.2 70.3 71.4 71.8 i -4;I 0.097 0.0099 g 0.238 0.0467 65.79 0.915 0.176 0.1007 62.78 0.873 0.135 0.1549 61.43 0.854 0.103 0.2091 59.30 0.824 0.081 0.2635 58.40 0.811 0.069 0.3179 59.03 0.820 0.181 0.0102 - - 0.263 0.0480 72.08 1.000 0.197 0.1032 68.14 0.945 0.148 0.1586 65.22 0.910 0.126 0.2138 64.86 0.900 o.095 0.2688 64.52 o.890

TABLE II. CALIBRATION DATA FOR METHANOL Major Minor- Geometric Amplitude Z Surface Tension Experimental Liquid Jet Liquidp04) Liquid (04) Equilibrium Reynold's Jet Nodal Diameter Diameter Mean Radius Ratio, Computed From Correction Run Rate, Temperature Density, Viscosity, Surface Tension, No. Thru Node Wavelength, At Node, At Node, At Node, q z Eqn. (25-E) Factor, No. ML/MIN C g/ml Centipoises Dynes/cm Orifice No. Inches Inches hes Inches Ir pL Dynes/cm K 420 0.6871 18.0 421 0.7545 18.0 422 0.4908 21.4 423 0.5523 21.4 424 0.4552 21.0 0.7909 0.5840 22.51 217.5 1 0.00547 2 0.01546 3 0.01514 4 0.01495 5 0.01477 6 0.01465 7 0.01460 0.7909 0.5340 22.51 238.6 1 o.00605 2 0.01740 3 0.01678 4 0.01663 5 0.01265 6 0.01613 7 o.o16o9 0.7905 0.5800 22.47 156.2 1 0.00350 2 0.01000 3 0.01002 4 0.01002 5 0.00996 6 o.oo996 0.7905 0.5800 22.47 175.8 1 0.00418 2 0.01172 3 0.01170 4 0.01161 5 0.01150 6 0.01148 0.7909 0.5840 22.51 145.9 1 0.00330 2 0.00893 3 0.00910 4 0.00910 5 0.00912 6 0.00906 0.00260 0.00147 --- 0.00248 0.00131 0.000901 0.00230 0.00145 0.000913 0.00224 0.00154 0.000928 0.00211 0.00162 0.000924 0.00205 0.00170 0.000933 0.00201 0.00176 0.000940 0.00261 0.00146 0.00251 0.00123 0.000878 0.00231 0.00157 0.000890 0.00217 0.00147 o.ooo893 0.00209 0.00158 o.ooo9o8 0.0020o 0.00168 0.000923 o.00197 0.00167 0.000907 o.00253 0.00178 -- 0.00235 0.00154 0.000951 0.00219 0.00162 0.000942 o.00211 0.00171 0.000949 o.00206 o.00177 0.000955 0.00200 0.00181 0.000951 0.00255 0.00164 --- 0.00241 0.00163 0.000928 0.00226 0.00155 0.000956.00216 0.00166 0.000947 0.00209 0.00174 0.000953 0.002053.00179 0.000953 0.00251 0.00195 — 3 0.00232 0.00159 0.000960 0.00217 0.00168 0.000954 0.00209 0.00175 0.000956 o.00204 0.00180 0.000958 0.00201 0.00183 0.000959 0.286 0.0141 0.320 0.0681 0.231 0.1470 0.188 0.2246 0.152 0.3012 0.094 0.3770 0.066 o.4524 0.291 0.0142 0.357 o.o693 o.262 0.1496 0.195 0.2281 0.140 0.5053 0.095 0.3814 0.0853 0.4570 0.176 0.0126 0.211 0.0610 0.151 0.1328 0.105 0.2047 0.076 o.2764 0.050 0.5479 0.221 0.0133 0.261 0.0640 0.189 0.1387 0.132 0.2130 0.092 0.2867 0.063 o.3600 0.151 0.0129 0.189 0.0605 0.128 0.1307 0.089 0.2015 o.063 0.2725 0.047 0.3432 20.2 o.899 19.8 0.882 19.7 0.875 19.9 0.885 19.9 0.885 19.8 0.878 20.5 0.911 20.5 0.912 20.2 0.900 20.4 0.909 20.2 0.898 20.7 0.919 20.4 0.909 20.2 0.899 19.8 0.881 19.8 o.880 19.8 0.882 20.5 o.913 19.8 0.881 19.5 o.868 19.5 0.868 19.5 0.868 20.9 0.928 20.0 o.890 19.9 0.882 19.7 o.873 19.8 0.880 I ro 4\J1 I TABLE III. CALIBRATION DATA FOR NITROBENZENE Major Minor Geometric Amplitude Z Surface Tension Experimental Liquid Jet Liquid(D04) Liquid (10) Equilibrium Reynold's Jet Nodal Diameter Diameter Mean Radius Ratio, Computed From Correction Run Rate, Temperature Density, Viscosity, Surface Tension, No. Thru Node Wavelength, At Node, At Node, At Node, Oa iz Eqn. (23-E) Factor, No. ML/MIN C g/ml Centipoises Dynes/cm'Orifice No. he Inches Inch es Inches p DyInches/cm K 425 0.5991 426 0.7018 427 0.7467 470 0.6363 471 0.7027 472 0.6659 473 0.5911 1.1975 1.825 42.96 91.8 1 0.00363 2 0.01070 3 0.01080 4 0.01060 1.1973 1.820 42.96 107.8 1 0.00442 2 0.01322 3 0.01309 4 0.01297 1.1973 1.820 42.96 114.7 1 0.00485 2 0.01454 3 0.01417 4 0.01406 5 0.01401 1 1960 1.792 42.70 99.2 1 0.00417 2 0.0.330 3 0.01165 4 0.01165 1.2043 2.040 43.60 96.9 1 0.00441 2 0.01330 3 0.01318 4 0.01315 1.2043 2.040 43.60 91.8 1 0.00424 2 0.01259 3 0.01230 4 0.01225 1.1999 1.880 45.03 88.1 1 0.00350 2 0.01058 3 0.01074 4 0.01061 0.00251 0.00179 --- 0.00251 0.00157 0.000952 0.00212 0.00172 0.000955 0.00202 0.00178 0.000948 0.00258 0.00158 ---.24 150 0.000241 0500. 95 o.oo00220 0.00166 0.000955 0.00207 0.00179 0.000962 0.00261 0.00176 --- 0.00248 0.00147 o.000955 0.00224 o.00166 0.000964 0.00209 0.00176 0.000959 0.00200 0.00180 0.000949 0.00260 o.00170 --- o.00254 o.00139 o.000902 0.00211 0.00159 0.000916 0.00200 0.00171 0.000925 0.00260 0.00162 --- 0.00234 0.00139 0.000902 0.00212 0.00162 o.000926 0.00203 0.00171 0.000951 0.00260 0.00167 - 0.00227 0.00147 0.000914 0.00205 0.0015 o0.ooo8c6 0.00196 0.00163 0.000893 0.00246 o.00200 --- o.00216 0.00157 0.000921 0.00202 0.00165 0.000913 0.00200 0.00177 o.0009ooo40 0.170 0.0222 -- 0.194 0.1097 40.6 0.105 0.2409 39.0 0.063 0.3716 40.4 0.247 0.020 --- 0.239 0.1147 38.5 0.141 0.2514 38.0 0.086 0.5947 37.8 0.198 0.0257 --- 0.264 0.1175 37.9 0.150 0.2567 36.8 0.086 0.3947 37.2 0.053 0.5318 37.7 0.213 0.0236 -- 0.261 0.1280 41.5 0.142 0.2443 40.6 0.078 0.3759 39.7 0.237 0.0255 --- 0.261 0.1280 41.5 0.135 0.0255 59.1 0.086 0.4337 58.7 0.222 0.0259 -- 0.217 0.1274 41.0 0.146 0.2781 42.2 01092 0.4280 41.6 0.104 0.0225 --- 0.160 0.1118 41.7 0.101 0.2475 40.5 0.061 0.3833 39.7 o.945 0.906 o.959 0.901 0.884 0.881 0.882 0.858 0.865 0.878 0.967 0.953 0.929 0.951 0.898 0.888 0.942 0.968 0.955 0.968 0.941 0.921

TABLE IV CALIBRATION DATA FOR ISOPROPANOL Major Minor Geometric Amplitude Z Surface Tension Experimental Liquid Jet Liquid(l0o) Liquid (10q) Equilibrium Reynold's Jet Nodal Diameter Diameter Mean Radius Ratio, Computed From Correction Run Rate, Temperature Density, Viscosity Surface Tension, No. thru Node Wavelength, At Node, At Node, At Node, a Iz Eqn. (25E), Factor, No. ML/MIN S C g/ml Centipoises Dynes/cm Orifice No. Inches Inches Inches Inches rg pL Dynes/cm K 483 o.6356 20.1 484 0.4642 20.9 485 0.5471 19.1 510 0.5663 21.8 511 0.4644 21.6 512 0.5537 21.6 0.7888 2.3500 21.70 0.7881 2.3000 21.68 0.7898 2.4300 21.80 0.7871 2.2600 21.53 0.7873 2.2700 21.57 0.7873 2.2700 21.57 49.8 1 0.00462 0.00260 0.00165 --- 2 0.01425 0.00220 0.00159 0.000935 3 0.01415 0.00202 0.00177 0.000945 37.1 1 0.00303 0.00260 0.00219 -- 2 0.00955 0.00226 0.00181 0.001011 3 0.00996 0.00205 0.00188 0.000981 41.5 1 0.00382 0.00260 0.00181 2 0.01201 0.00230 0.00176 0.001001 3 o.o1226 0.00206 0.00183 0.000971 46.1 1 o0083 0.00oo260 0.00171 -- 2 0.01267 0.00227 0.00165 o.o00968 3 0.01258 0.00205 0.00180 0.000956 4 0.01226 0.00195 0.00184 0.000948 37.6 1 0.00284 0.00260 0.00210 -- 2 0.00980 0.00224 0.00177 0.000995 3 0.00981 0.00205 0.00187 o.000979 44.8 1 0.00341 0.00260 0.00170 --- 2 0.01215 0.0223 0.00165 0.000959 3 0.01210 0.00200 0.00177 0.000940 0.228 0.0520 0.162 0.2642 0.066 0.5837 o.o86 0.0457 O.-l 0.2356 0.043 o.5500 0.182 0.0516 0.134 0.2652 0.059 0.5928 0.210 0.0466 0.160 0.2474 o.o60 0.5547 0.029 0.8570 0.213 o0.0426 0.118 0.2307 0.046 0.5229 0.213 0.0426 0.151 0.2571 0.061 0.5402 18.1 o.833 17.8 0.819 17.7 0.816 17.0 0.782 16.7 0.767 16.6 0.762 17.1 0.793 17.2 o.8o0 18.2 0.846 17.5 0.802 17.5 0.810 17.8 0.824 18.0 o.836 TABLE V CALIBRATION DATA FOR DIETHYLANILINE Major Minor Geometric Amplitude Z Surface Tension Experimental Liquid Jet LiquidCLO4) Liquid C4) Equilibrium Reynold's Jet Nodal Diameter Diameter MeanRadi Radius tio, Computed From Correction Run Rate, Temperature Density, Viscosity Surface Tension, No. Thru Node Wavelength, At Node, At Node, At Node, a A Eqn. (25-E) Factor, No. ML/MIN C g/ml Centipoises Dynes/cm Orifice No. Inches Inches Inches Inches rg pL Dynes/cm K 533 o.6058 25-3 0.9327 1.9300 35.66 68.4 1 0.0062 o.oo0026 0.00188 --- 0.162 0.0297 2 0.01084 0.00241 0.00171 0.001015 0.172 0.1482 29.0 0.861 3 0.01105 0.00222 0.00195 0.001040 0.065 0.3277 26.6 0.790 4 0.01105 0.00217 0.00205 0.001055 0.028 0.5089 26.0 0.774 534 o.6478 25.3 o.9327 1.9500 33.66 73.1 1 0.00400 0.00260 0.0017 ----.24 0.0307 2 0.01176 0.00231 0.00156 0.000949 0.196 0.1515 31.4 0.933 3 0.01194 0.00211 0.00172 0.000953 0.102 0.3352 29.7 0.882 4 0.01194 0.00203 0.00182 0.000961 0.055 0.5165 29.2 0.867 TABLE VI CALIBRATION DATA FOR ACETONE I ro 4zr 536 0.4868 21.5 537 0.5241 21.0 0.7900 0.3260 23.46 0.7910 0.3270 23.56 275.5 1 0.00388 0.00260 0.00193 -- 2 0.01041 0.00241 0.00140 0.000919 3 0.01037 0.00229 0.00145 0.000911 4 0.01035 0.00220 0.00154 0.000921 5 0.01026 0.00217 0.00161 0.000935 6 0.01021 0.00214 0.00169 0.000951 7 0.01017 0.00211 0.00171 0.000950 296.1 1 0.00407 0.00260 0.00178 - 2 0.01130 0.00243 0.00136 0.000909ogog 3 0.01125 0.00231.00143 0.000909 4 0.01121 0.00225 0.00153 0.000928 5 0.01108 0.00216 0.00155 0.000915 6 0.01096 0.00210 0.00162 0.000922 7 0.01092 0.00206 0.00165 0.000922 0.149 0.0079 0.272 0.0370 0.229 0.0792 0.178 o0.12i4 0.149 0.1633 0.118 0.2050 0.105 0.2464 0.190 0.0077 0.291 0.0368 0.240 0.0795 0.193 0.1220 0.166 o.1642 0.130 0.2059 0.111 0.2473 20.1 20.0 19.5 19.2 18.9 19.0 20.5 20.2 19.5 20.1 20.1 21.0 o.856 0.853 0.830 0.820 0.804 0.808 0.873 0.859 0.828 0.855 0.853 0.856

TABLE VII CALIBRATION DATA FOR CARBON TETRACHLORIDE Major Minor Geometric Liquid Jet Liquid Liquid Equilibrium Reynolds Jet Nodal Diameter Diameter Mean Radius Run Rate Temperature Density, Viscosity, Surface Tension No. Thru Node Wavelength At Node, At' Node, At Node, No. ML/MIN *C g/cc Centipoises Dynes/cm Orifice No. Inches Inches Inches Inches 428 0.4085 18.0 1.5987 0.9960 27.00 153.1 1 0.00397 2 0.01146 3 0.01144 429 0.4268 1.6 1.5976 0.9880 26.92 161.1 1 0.00435 2 0.01205 3 0.01201 4 0.01191 5 0.01186 6 0.01179 7 0.01180 430 0.4987 19.5 1.5960 0.9760 26.62 190.4 1 0.00540 2 0.01488 3 0.01463 4 0.01442 431 0.5498 24.0 1.5876 0.9200 26.40 221.5 1 0.00587 2 0.01691 3 0.01628 4 0.01606 5 0.01593 6 0.01585 7 0.01580 8 0.01574 432 0.5307 23.6 1.5884 0.9240 26.32 213.0 1 0.00572 2 0.01643 3 0.01573 4 0.01548 5 0.01531 464 0.5933 19.0 1.5968 0.9820 26.88 225.3 1 0.00650 2 0.01876 3 0.01774 4 0.01740 465 0.4507 18.5 1.5978 0.9900 26.95 169.9 1 0.00460 2 0.01271 3 0.01268 466 0.4427 17.0 1.6050 1.0100 27.11 164.3 1 0.00427 2 0.01241 3 0.01230 4 0.01220 5 0.01212 467 0.4293 17.0 1.6050 1.0100 27.11 159.3 1 0.00426 2 0.01215 3 0.01203 4 0.01199 5 0.01193 6 0.01191 468 0.4370 24.0 1.5874 0.0200 26.30 176.1 1 0.00437 2 0.01255 3 0.01249 469 0.4286 24.0 1.5874 0.9200 26.30 172.7 1 0.00445 2 0.01232 3 0.01214 4 0.01213 5 0.01206 506 0.4357 18.7 1.5977 0.9860 26.90 26.90 1 0.00430 2 0.01264 3 0.01248 4 o.01236 5 0.01234 6 0.01235 507 0.4662 17.8 1.5990 0.9980 27.00 174.4 1 o.00470 2 0.01369 3 0.01345 4 0.01335 5 0.01321 508 0.3472 17.9 1.5990 0.9980 27.00 129.9 1 0.00235 2 0.00924 3 0.00930 4 o.oo00935 5 0.00936 6 o.00940 509 0.3754 17.9 1.5990 0.9980 27.00 140.5 1 0.00352 2 0.01020 3 0.01032 4 0.01029 5 0.01025 6 0.01026 0.00252 0.00160 --- 0.00234 0.00140 0.000905 0.00220 0.00158 0.000932 0.00254 0.00172 --- 0.00236 0.00134 0.000889 0.00218 0.00145 0.000889 0.00204 0.00155 0.000889 0.00197 0.00160 0.000888 0.00193 0.00170 0.000906 0.00190 0.00172 0.000904 o.00255 0.00144 --- o.00239 0.00126 0.000868 0.00222 0.00141 0.000885 0.00210 0.00150 0.000887 0.0Q252 0.00136 --- 0.00236 0.00122 o.000848 0.00221 0.00135 0.000864 0.00210 0.00148 0.000381 0.00200 0.00152 0.000872 0.00193 0.00160 0.000878 0.00190 0.00163 o.000880 0.00186 0.00165 0.000876 0.00240 0.00138 -- 0.00222 0.00117 0.000806 0.00206 0'.00125 0.000802 0.oo093. 36 0.0060.000810 0.00184 0.00144 0.000814 0.00260 0.00137 -- 0.00254 0.00126 0.000895 0.00231 0.00132 0.000873 0.00216 0.00153 0.000909 0.00260 0.00158 --- 0.00251 0.00139 0.000934 0.00235 0.00152 0.000945 0.00260 0.00151 --- 0.00234 0.00134 0.000880 0.00214 o.00140 0.000865 0.00205 0.00160 0.000905 0.00199 0.00164 0.000903 0.00260 0.00156 --- 0.00233 0.00143 0.000912 0.00219 0.00151 0.000909 0.00209 0.00160 0.000915 0.00202 0.00165 0.000913 0.00196 0.00167 0.000905 0.00260 0.00148 --- 0.00248 0.00137 o.000921 0.00233 0.00150 0.000935 0.00260 0.00152 --- 0.00241 0.00134 0.000898 0.00224 0.00142 0.000891 0.00214 0.00157 0.000916 0.00207 0.00166 0.000927 0.00260 0.00159 ---- 0.00250 0.00137 0.000925 0.00231 0.00150 0.000930 0.00219 0.00162 0.000942 0.00210 0.00167 0.000938 o.oo206 0.00173 0.000944 0.00260 0.00160 -- 0.00247 0.00135 0.ooo913 0.00229 0.00149 0.000924 0.00214 0.00151 0.000899 0.00205 0.00158 0.000900 0.00260 0.00210 --- 0.00235 0.00153 0.000948 0.00222 0.00164 0.000954 0.00213 0.00176 0.000968 0.00205 0.00179 0.000958 0.00201 0.00185 0.000964 0.00260 0.00183 -- 0.00239 0.00148 0.000940 0.00223 0.00160 0.000945 0.00215 0.00169 0.000953 0.00206 0.00168 0.000950 0.00200 0.00175 0.000936 Amplitude Ratio, 0.227 0.257 0.166 0.195 0.283 0.204 0.137 0.104 0.063 0.050 0.286 0.321 0.227 0.168 0.309 0.331 0.247 0.175 0.137 0.094 0.077 o.o60 0.277 0.321 0.250 0.175 0.123 0,234 0.256 0.282 0.173 0.251 0.299 0.219 0.274 0.281 0.213 0.124 0.097 0.257 0.246 0.187 0.134 0.101 o.o80 0,284 0.300 0.221 0.271 o.296 0.229 0.155 0.111 0.246 0.301 0.216 o.151 0.117 0.087 0.243 0.303 0.215 0.174 o.130 0.107 0.215 0.152 o.095 0.068 0.042 0.176 0.240 0.166 0.120 0.102 0.067 Surface Tension Experimental Computed From Correction Eqn. (25-E) Factor, Dynes/cm K 24.4 0.901 22.8 0.843 25.1 0.930 24.4 0.904 24.3 0.898 24.3 0.902 23.9 0.886 23.9 0.886 24.2 0.900 23.3 0.869 23.4 0.872 23.6 0.895 23.9 0.904 23.4 0.885 23.8 0.901 23.6 0.895 23.7 0.897 23.9 0.906 24.4 0.926 25.7 0.976 25.5 0.970 25.6 0.973 21.6 0.804 23.7 0.882 22.6 0.841 24.0 0.893 22.9 0.853 25.7 0.948 26.0 0.961 24.4 0.902 24.7 0.911 23.8 0.880 23.8 0.830 23.5 01368 23.6 0.872 23.9 0.881 23.6 0.889 22.4 0.851 23.9 0.910 24.0 0.914 22.8 0.865 22.5 0.855 23.0 0.856 22.5 0.836 22.1 0.823 22.1 0,822 21.8 o.811 23.1 0.856 22.7 o.859 23.4 0.865 23.5 0.872 23.8 0.882 22.9 0.847 22.0 0.813 22.1 0.820 21.7 o.805 24.0 0.888 22.7 0.842 22.3 0.827 23.1 0.855 22.8 0.844

OSCILLATING JET MEASUREMENTS FOR AQUEOUS SOLUTIONS Major Minor Apparent Uncorrected Correction Corrected Liquid Jet Liquid Liquid Reynolds Jet Nodal Diameter Diameter Jet Age Surface Tension Factor Surface Run Rate Temperature Density Viscosity No.'Thru Node Wavelength at Node at Node at Node Tension No. Liquid ML/Min *C g/cc Centipoises Orifice No. Inches Inches Inches Microseconds Dynes/cm K.KH Dynes/cm 443 0.003 M K2CO3 0.8537 20.0 0.9982 1.005 198.0 1 0.00402 0.00249 0.00150 7. -- 2 0.01105 0.00228 0.00132 29. 75.11 1.036 72.6 3 0.01101 0.00214 0.00138 58. 74.63 1.012 73.7 4 0.01095 0.00202 0.00151 88. 72.24 0.984 73.4 5 0.01093 0.00194 0.00157 119. 71.94 0.969 74.2 6 0.01089 0.00193 0.00159 149. 71.98 0.965 74.6 7 0.01092 0.00189 0.00160 179. 72.11 0.965 74.8 442 0.003 K2C3 M 0.7721 26.4 0.9967 0.8660 207.5 1 0.00370 0.00247 0.00159 7. - - 2 0.00985 0.00227 0.00140 30. 71.89 1.068 67.3 3 0.00980 0.00214 0.00147 61. 71.47 1.042 68.4 4 0.00980 0.00204 0.00156 92. 69.89 1.019 68.6 5 0.00982 0.00197 0.00158 123. 70.25 1.011 69.5 6 0.00978 0.00194 0.00162 154. 70.09.999 70.1 7 0.00978 0.00193 0.00170 186. 67.99.975 69.7 538 0.003 M KI20C3 0.6409 23.0 0.9975 0.9358 159.5 1 0.00283 0.00260 0.00263 12. - 2 0.00744 0.00222 0.00162 40. 70.74 1.057 67.0 3 0.00755 0.00208 0.00166 71. 70.33 1.047 67.2 4 0.00764 0.00202 0.00173 103. 68.00 1.028 66.2 5 0.00771 0.00200 0.00179 136. 65.71 1.010 65.1 6 0.00770 0.00199 0.00181 169. 65.50.999 65.6 539 0.003 M K2CO3 0.7616 24.0 0.9973 0.9142 194.0 1 0.00347 0.00260 0.00212 10. 2 0.00958 0.00236 0.00152 37. 67.45.988 68.3 3 0.00961 0.00223 0.00161 72. 65.72.982 66.9 4 0.00961 0.00216 0.00165 107. 65.53.976 67.2 5 0.00957 0.00209 0.00169 141. 65.98.973 67.9 6 0.00958 0.00203 0.00174 176. 65.56.970 67.6 7 0.00956 o0.00198 0.00175 210. 66.49.977 68.0 433 0.010 M K2CO3 0.6913 20.8 0.9982 1.0000 161.1 1 0.00388 0.00251 0.00189 10. - - 2 0.00830 0.00232 0.00154 37. 70.61 1.176 60.1 3 0.00844 0.00218 0.00162 70. 67.93 1.102 61.6 4 0.00850 0.00209 0.00173 104. 65.28 1.046 62.4 5 0.00851 0.00204 0.00177 139. 64.98 1.019 63.7 6 0.00852 0.00202 0.00178 173. 64.98 1.006 64.6 7 0.00854 0.00200 0.00181 208. 64.35 0.991 64.9 434 0.01 M K2C03 0.7757 21.5 0.9978 0.9625 187.8 1 0.00335 0.00252 0.00177 7. - - 2 0.00985 0.00235 0.00146 32. 69.15 1.046 66.1 3 0.00983 0.00221 0.00154 65. 68.23 1.002 68.1 4 0.00980 0.00212 0.00163 99. 67.02 0.980 68.4 5 0.00981 0.00205 0.00168 133. 66.61 0.969 68.8 6 0.00980 0.00200 0.00172 166. 66.53 0.966 68.9 7 0.00979 0.00196 0.00175 200. 66.63 0.957 69.7 435 0.010 M K2C03 0.9003 21.6 0.9978 0.9625 217.9 1 0.00422 0.00253 0.00157 7. 2 0.01195 0.00239 0.00132 31. 71.26 1.028 69.3 3 0.01185 0.00226 0.00146 64. 67.95 0.984 69.1 4 0.01174 0.00217 0.00156 98. 66.87 0.956 69.9 5 0.01170 0.00210 0.00163 132. 66.22 0.943 70.3 6 0.01161 0.00203 0.00169 166. 66.63 0.936 71.2 541 0.010 M K2C03 0.7706 23.2 0.9975 0.9315 192.7 1 0.00350 0.00260 0.00200 9. 2 0.00976 0.00233 0.00146 35. 69-57 1.041 66.8 3 0.00972 0.00220 0.00154 68. 68.79 1.014 67.8 4 0.00978 0.00213 0.00163 102. 66.19 0.990 66.9 5 0.00970 0.00206 0.00169 136. 66.55 0.980 67.9 6 o0.0oo0967 0.00200 0.00172 169. 67.18 0.976 68.8 540 0.01 M kcO03 0.6579 22.6 0.9976 0.9446 162.2 1 0.00293 0.00260 0.00249 11. 2 0.00779 0.00227 0.00157 39. 70.40 1.082 65.1 3 0.00785 0.00210 0.00161 71. 71.00 1.060 67.0 4 0.00793 0.00203 0.00169 102. 68.55 1.039 66.0 5 0.00798 0.00199 0.00172 134. 67.77 1.025 66.1 6 0.00799 0.00195 0.00176 166. 67.34 1.015 66.3 7 0.00799 0.00193 0.00174 198. 68.36 1.033 66.1 436 0.03 M K2CO3 0.7592 27.2 0.9965 0.8508 207.6 1 0.00350 0.00244 0.00168 7. - 2 0.00948 0.00219 0.00136 29. 77.25 1.123 68.7 3 0.00955 0.00208 0.00144 58. 74.42 1.076 69.1 4 0.00953 0.00203 0.00153 88. 72.14 1.034 69.7 5 0.00949 0.00196 0.00158 118. 72.28 1.017 71.1 6 0.00948 0.00193 0.00165 148. 70.82 1.000 70.8 7 0.00951 0.00191 0.00170 179. 69.41 0.980 70.8 8 0.00951 0.00187 0.00172 211. 69.73 0.976 71.4 437 0.03 M K2CO3 0.8580 26.5 0.9966 0.8641 231.1 1 0.00407 0.00252 0.00158 7. - - 2 0.01125 0.00236 0.00136 31. 70.67 1.011 69.9 3 0.01122 0.00224 0.00141 63. 70.23 0.997 70.4 4 0.01111 0.00216 0.00152 96. 68.48 0.969 70.7 5 0.01111 0.00208 0.00161 129. 66.84 0.954 70.1 6 0.01108 0.00203 0.00162 162. 67.69 0.955 70.9 7 0.01106 0.00199 0.00165 195. 67.75 0.951 71.3 542 0.03 M a2C03 0.6705 21.9 0.9978 0.9602 162.7 1 0.00310 0.00260 0.00240 11. 2 0.00785 0.00224 0.00158 38. 72.35 1.020 70.9 3 0.00801 0.00210 0.00161 70. 71.38 1.023 69.7 4 0.00816 0.00205 0.00169 102. 67.58 1.004 67.3 5 0.00821 0.00202 0.00174 135. 66.02.993 66.5 6 0.00816 0.00199 0.00180 168. 65.63 1.010 65.0 543 0.03 M K2C03 0.7750 23.3 0.9974 0.9293 194.2 1 0.00358 0.00260 0.00190 9. 2 0.00973 0.00231 0.00147 34. 70.58 1.010 69.9 3 0.00981 0.00216 o.oo00149 66. 70.86 1.010 70.1 4 0.00981 0.00207 0.00159 98. 68.84 0.990 69.6 5 0.00978 0.00202 0.00164 131. 68.53 0.982 69.9 6 0.00977 0.00198 0.00168 163. 68.24 0.975 70.0 438 0.10 M 82103 0.7860 27.9 1.0081 0.8608 215.0 1 0.00358 0.00245 0.00154 7. - - - 2 0.01008 0.00226 0.00134 28. 75.18 1.082 69.4 3 0.01014 0.00219 0.00142 59. 71.77 1.037 69.2 4 0.01011 0.00211 0.00150 90. 70.25 1.010 69.6 5 0.01010 0.00205 0.00157 122. 68.97 0.989 69.8 6 0.01006 0.00202 0.00163 154. 68.11 0.971 70.2 7 0.01009 0.00199 0.00167 187. 67.15 0.960 69.9 4393 0.85.6 1.0081 0.856 237.5 1 00402 0.00246 0.00152 7. - - - 2 0.011o46 0.04232 0.00137 30. 69.25 0.997 69.4 3 0.01146 0.00223 0.00146 63. 66.79 0.975 68.5 4 0.01138 0.00203 0.00155 96. 67.46 0.980 68.8 5 0.01123 0.00194 0.00151 127. 71.93 1.002 71.6 6 0.01121 0.00194 0.00165 158. 67.96 0.965 70.4 7 0.01121 0.00191 0.00168 190. 67.72 0.963 70.3 544 0.10 M KC03 0.6704 22.7.9624 164. 1 0.00808 0.00263 0.00244 11. 2 0.00776 0.00231 0.00160 39. 72.44 1.058 68.4 3 0.00812 0.00220 0.00167 73. 66.69 1.030 64.7 4 0.00820 0.00214 0.00175 108. 64.23 1.003 64.0 5 0.00818 0.00208 0.00176 143. 65.32 1.000 65.3 6 0.00820 0.00204 0.00183 178. 63.94 0.978 65.4 7 0.00820 0.00202 0.00187 213. 63.33 0.975 65.0

249TABLE vmI (cm'D) Major Minor Apparent Uncorrected Correction Corrected Liquid Jet Liquid Liquid Reynolds Jet Nodal Diameter Diameter Jet Age Surface Tension Factor Surface Run Rate Temperature Density Viscosity No. Thru Node Wavelength at Node at Node at Node Tension No. Liquid ML/Min C g/cc Centipoises Orifice No. Inches Inches Inches Microseconds Dynescm KrKH Dynes/cm 545 0.10 M K2C03 0.7880 22.7 440 0.24 M K2C03 0.7669 27.0 441 0.24 M K2C03 0.8614 25.8 547 0.30 M K2C03 0.7617 22.7 546 0.30 M K2C03 0.6274 22.3 554 0.01 Vol. % 0.6606 21.3 Benzene 555 0.01% Benzene 0.7805 22.4 556 0.001% Benzene 0.6542 21.8 557 0.001% Benzene 0.7669 22.2 558 0.045% Benzene 0.6108 22.6 559 0.049% Benzene 0.7534 22.7 548 1 Vol.% Glycerol 0.6380 23.3 1549 1% Glycerol 0.7571 23.3 458 1% Glycerol 0.7646 27.1 459 1% Glycerol 0.8526 27.8 550 10% Glycerol 0.6194 23.4 551 10% Glycerol 0.7560 26.0 1.0080 0.9624 192.7 1.0217 0.8740 209.3 1.0221 0.8972 229.1 1.0311 1.0204 179.7 1.0312 1.0273 147.1 0.9979 0.9741 158.0 0.9977 0.9491 191.6 0.9978 0.9625 158.4 0.9977 0.9535 187.4 0.9976 o.9446 150.6 0.9976 0.9424 186.2 1.003 0.9393 158.7 1.0003 0.9393 188.3 0.9995 0.8584 207.9 0.9993 0.8640 230.3 1.0244 1.2322 120.2 1.0238 1.1787 153.3 1 0.00377 0.00260 0.00146 2 0.00987 0.00237 0.00146 3 0.01006 0.00223 0.00154 4 0.01005 0.00213 0.00162 5 0.01004 0.00207 0.00169 6 0.01003 0.00203 0.00173 7 0.00997 0.00201 0.00176 1 0.00355 0.00244 0.00166 2 0.00967 0.00220 0.00134 3 0.00970 0.00207 0.00145 4 0.00974 0.00200 0.00153 5 0.00977 0.00193 0.00157 6 0.00978 0.00187 0.00161 7 0.00977 0.00184 0.00163 1 0.00400 0.00249 0.00150 2 0.01138 0.00228 0.00132 3 0.01135 0.00214 0.00138 4 0.01125 0.00202 0.00151 5 0.01118 0.00194 0.00157 6 0.01124 0.00193 0.00159 7 0.01123 0.00189 0.00160 1 0.00347 0.00260 0.00206 2 0.00971 0.00236 o.00148 3 0.00968 0.00224 0.00157 4 0.00969 0.00216 0.00166 5 0.00967 0.00211 0.00170 6 0.00965 0.00206 0.00180 1 0.00287 0.00260 0.00299 2 0.00724 0.00224 0.00162 3 0.00738 0.00210 0.00168 4 0.00752 0.00202 0.00173 5 0.00756 0.00197 0.00178 6 0.00760 0.00195 0.00179 7 0.00762 0.00193 0.00179 1 0.00311 0.00260 0.00224 2 0.00776 0.00218 0.00154 3 0.00795 0.00205 0.00161 4 0.00805 0.00199 0.00168 5 0.008o6 0.00198 0.00171 6 0.00808 0.00196 0.00177 1 0.00370 0.00260 0.00191 2 0.00984 0.00239 0.00148 3 0.00999 0.00222 0.00154 4 0.00992 0.00214 0.00163 5 0.00991 0.00208 0.00167 6 0.00985 0.00200 0.00170 1 0.00313 0.00260 0.00210 2 0.00771 0.00219 0.00152 3 0.00788 0.00206 0.00159 4 0.00799 0.00199 0.00167 5 0.00801 0.00196 0.00172 6 0.00803 0.00195 0.00177 7 0.00803 0.00193 0.00177 1 0.00383 0.00260 0.00181 2 0.00963 0.00235 0.00140 3 0.00975 0.00225 0.00155 4 0.00975 0.00218 0.00165 5 0.00971 0.00213 0.00172 6 0.00972 0.00210 0.00178 1 0.00277 0.00260 0.00229 2 0.00710 0.00222 0.00162 3 0.00720 0.00209 0.00169 4 0.00729 0.00202 0.00174 5 0.00734 0.00199 0.00177 6 0.00735 0.00198 0.00184 1 0.00347 0.00260 0.00185 2 0.00954 0.00235 0.00147 3 0.00959 0.00222 0.00153 4 0.00959 0.00213 0.00161 5 0.00955 0.00206 0.00165 6 0.00948 0.00202 0.00172 1 0.00281 0.00260 0.00264 2 0.00743 0.00227 0.00165 3 0.00760 0.00216 0.00171 4 0.00767 0.00210 0.00178 5 0.00774 0.00206 0.00183 6 0.00777 0.00204 0.00188 7 0.00779 0.00202 0.00187 1 0.00354 0.00260 0.00199 2 0.00957 0.00229 0.00145 3 0.00968 0.00217 0.00155 4 0.00963 0.00209 0.00164 5 0.00957 0.00203 0.00167 6 0.00951 0.00200 0.00173 1 0.00360 0.00260 0.00166 2 0.00980 0.00233 0.00138 3 0.00980 0.00216 0.00144 4 0.00982 0.00206 0.00152 5 0.00980 0.00198 0.00150 6 0.00975 0.00191 0.00158 1 0.00405 0.00260 0.00143 2 0.01140 0.00225 0.00124 3 0.01136 0.00212 0.00136 4 0.01127 0.00203 0.00143 5 0.01119 0.00197 0.00149 6 0.01116 0.00196 0.00158 1 0.00280 0.00260o 0.00268 2 0.00703 0.00221 0.00168 3 0.00736 0.00207 0.00175 4 0.00752 0.00201 0.00182 5 0.00755 0.00199 0.00184 6 0.00758 0.00197 0.00186 1 0.00348 0.00260 0.00200 2 0.00957 0.00233 0.00150 3 0.00971 0.00216 0.00163 4 0.00973 0.00208 0.00166 5 0.00972 0.00206 0.00176 10. 37. 71.59 70. 68.02 104. 67.01 139. 66.06 173. 65.80 208. 66.07 7. 29. 78.87 58. 75.51 88. 73.19 118. 72.78 147. 72.63 177. 72.82 7. 29. 74.19 59. 73.59 90. 71.70 120. 71.98 151. 70.86 182. 71.45 9. 36. 69.71 71. 68.33 106. 66.52 141. 66.40 177. 64.82 14. 44. 72.75 76. 71.09 108. 69.07 141. 68.11 174. 67.71 206. 67.90 11. 36. 74.20 67. 71.12 98. 68.60 130. 67.75 162. 66.20 9. 35. 68.34 70. 67.00 104. 66.10 138. 66.02 172. 67.31 10. 35. 74.20 66. 71.28 97. 68.42 129. 67.26 161. 65.80 193. 66.24 9. 34. 72.88 67. 66.72 102. 64.53 138. 63.78 174. 62.60 10. 37. 69.07 69. 67.57 102. 66.16 134. 65.23 168. 63.38 9. 34. 68.55 68. 67.38 101. 66.o8 135. 66.50 169. 66.08 12. - 40. 68.45 74. 65.98 109. 64.06 144. 62.57 179. 61.30 215. 61.73 9. 35. 70.59 68. 67.16 102. 66.16 135. 67.04 168. 66.64 8. 32. 72.35 63. 72.05 94. 71.65 124. 72.25 154. 73.55 7. - 28. 74.96 57. 71.57 87. 71.46 117. 71.00 147. 71.67 12. - 41. 71.86 74. 67.44 107. 64.49 142. 63.98 177. 63.51 9. 36. 69.51 70. 65.73 105. 65.90 140. 63.63 1.025 1.011 0.996 0.982 0.976 0.970 1.151 1.090 1.048 1.030 1.021 1.010 1.061 1.044 1.019 1.008 0.997 0.997 1.110 1.045 1.018 0.996 0.971 1.019 1.019 1.014 1.007 1.007 1.010 1.119 1.080 1.048 1.023 1.005 0.980 0.984 0.970 0.966 0.972 1.156 1.107 1.064 1.038 1.011 1.008 1.160 1.065 1.015 0.984 0.962 1.178 1.118 1.078 1.050 1.021 1.021 1.010 0.994 0.989 0.976 1.030 1.019 1.002 0.990 0.979 0.980 1.075 1.037 1.007 0.997 0.980 1.089 1.061 1.033 1.039 1.020 1.108 1.050 1.020 0.996 0.965 1.084 1.055 1.026 1.010 1.002 1.066 1.020 1.007 0.973 70.0 67.3 67.3 67.3 67.4 68.1 68.4 69.3 69.9 70.7 71.1 72.0 69.9 70.5 70.4 71.4 71.1 71.6 62.8 65.3 65.4 66.7 66.8 71.4 69.8 68.0 67.6 67.3 67.3 66.4 65.9 65.5 66.2 65.9 70.2 68.1 68.2 68.3 69.3 64.2 64.4 64.3 64.8 65.0 65.7 62.8 62.6 63.6 64.9 65.1 58.7 60.5 61.4 62.1 67.1 66.6 66.5 67.3 67.8 66.4 64.8 63.9 63.2 62.7 63.0 65.6 64.8 65.8 67.3 68.0 66.4 68.0 69.4 69.5 72.1 67.6 68.1 70.0 71.3 74.3 66.3 63.9 62.8 63.3 63.4 65.2 64.5 65.5 65.5

-250 TABLE vm (coT'oD) Major Minor Apparent Uncorrected Correction Corrected Liquid Jet Liquid Liquid Reynolds Jet Nodal Diameter Diameter Jet Age Surface Tension Factor Surface Run Rate Temperature Density Viscosity No. Thru Node Wavelength at Node at Node at Node Tension No. Liquid ML/Min *C g/cc Centipoises Orifice No. Inches Inches Inches Microseconds Dynes/cm KrKH Dynes/c _ r H Dnsc 460 10% Glycerol 0.7698 26.1 461 10% Glycerol 0.8553 28.5 462 18% Glycerol 0.7550 27.3 463 18% Glycerol 0.8525 29.3 552 20% Glycerol 0.6480 24.2 553 20% Glycerol 0.7554 24.6 513 0.01 Vol. % 0.6751 24.0 Acetic Acid 514 0.01% Acetic 0.7555 24.0 Acid 515 0.01% Acetic 0.8157 24.1 Acid 516 0.1% Acetic 0.6952 23.1 Acid 517 0.1% Acetic 0.8022 23.1 Acid 518 1.0% Acetic 0.7240 21.9 Acid 1.0231 1.1641 158.0 1.0225 1.0193 200.3 1.0508 1.6097 115.1 1.0502 1.5741 132.8 1.0511 1.7083 93.1 1.0510 1.7165 108.0 0.9973 0.9142 172.0 0.9973 0.9142 192.5 0.9973 0.9122 208.2 0.9975 0.9336 173.5 0.9975 0.9336 200.1 0.9978 0.9602 175.7 1 0.00350 0.00260 0.00184 2 0.00991 0.00244 0.00155 3 0.00994 0.00230 0.00167 4 0.00991 0.00224 0.00175 5 0.00992 0.00218 0.00178 6 0.00995 0.00213 0.00185 1 0.00400 0.00260 0.00148 2 0.01142 0.00220 0.00121 3 0.01134 0.00207 0.00135 4 0.01133 0.00200 0.00148 5 0.01125 0.00193 0.00150 6 0.01126 0.00186 0.00157 1 0.00353 0.00260 0.00178 2 0.00990 0.00222 0.00144 3 0.00985 0.00208 0.00155 4 0.00984 0.00199 0.00166 5 0.00989 0.00193 0.00169 6 0.00992 0.00189 0.00175 1 0.00395 0.00260 0.00162 2 0.01156 0.00235 0.00145 3 0.01150 0.00220 0.00158 4 0.01152 0.00211 0.00167 1 0.00283 0.00260 0.00227 2 0.00765 0.00223 0.00174 3 0.00796 0.00210 0.00182 4 0.00804 0.00206 0.00188 5 0.00810 0.00201 0.00189 1 0.00341 0.00260 0.00213 2 0.00956 0.00236 0.00162 3 0.00976 0.00219 0.00175 4 0.00981 0.00209 0.00182 5 0.00979 0.00204 0.00184 1 0.00326 0.00260 0.00272 2 0.00808 0.00233 0.00154 3 0.00816 0.00219 0.00162 4 0.00821 0.00210 0.00170 5 0.00829 0.00203 0.00170 6 0.00825 0.00197 0.00177 1 0.00331 0.00260 0.00228 2 0.00950 0.00235 0.00143 3 0.00951 0.00221 0.00154 4 0.00953 0.00215 0.00160 5 0.00952 0.00209 0.00166 6 0.00956 0.00204 0.00172 7 0.00950 0.00200 0.00171 1 0.00366 0.00260 0.00186 2 0.01047 0.00240 0.00142 3 0.01055 0.00228 0.00152 4 0.01053 0.00217 0.00156 5 0.01046 0.00208 0.00161 6 0.01043 0.00203 0.00170 1 0.00325 0.00260 0.00220 2 0.00842 0.00230 0.00152 3 0.00856 0.00216 0.00161 4 0.00857 0.00210 0.00166 5 0.00862 0.00204 0.00170 6 0.00865 0.00200 0.00175 7 0.00866 0.00199 0.00176 1 0.00368 0.00260 0.00190 2 0.01028 0.00238 0.00144 3 0.01035 0.00224 0.00150 4 0.01034 0.00215 0.00160 5 0.01032 0.00209 0.00163 1 0.00365 0.00260 0.00238 2 0.00909 0.00231 0.00148 3 0.00930 0.00218 0.00155 4 0.00932 0.00208 0.00167 5 0.00931 0.00201 0.00168 6 0.00932 0.00198 0.00171 1 0.00376 0.00260 0.00190 2 0.01035 0.00245 0.00149 3 0.01036 0.00229 0.00155 4 0.01047 0.00220 0.00167 5 0.01047 0.00214 0.00170 6 0.01044 0.00209 0.00170 1 0.00447 0.00260 0.00143 2 0.01269 0.00243 0.00125 3 0.01264 0.00227 0.00137 4 0.01255 0.00215 0.00153 5 0.01245 0.00206 0.00155 6 0.01247 0.00200 0.00159 1 0.00395 0.00260 0.00153 2 0.01082 0.00236 0.00138 3 0.01087 0.00220 0.00147 4 0.01090 0.00211 0.00156 5 0.01086 0.00205 0.00165 6 0.01086 0.00200 0.00173 7 0.01086 0.00195 0.00173 1 0.00305 0.00260 0.00207 2 0.o00864 0.00230 0.00159 3 0.00882 0.00216 0.00170 4 0.00891 0.00208 0.00178 5 0.00894 0.00203 0.00180 6 0.00894 0.00201 0.00186 1 0.00369 0.00260 0.00180 2 0.01036 0.00236 0.00147 3 0.01047 0.00223 0.00157 4 0.01044 0.00211 0.00165 5 0.01041 0.00201 0.00171 6 0.01038 0.00197 0.00174 1 0.00307 0.00260 0.00205 2 o.00811 0.00223 0.00156 3 0.00831 0.00211 0.00167 4 0.00839 0.00204 0.00175 5 0.00845 0.00202 0.00179 8. 36. 74. 112. 151. 190. 7. 28. 56. 85. 115. 145. 8. 33. 65. 98. 132. 165. 8. 33. 69. 106. 10. 38. 74. 110. 147. 10. 38. 76. 114. 152. 13. 43. 76. 110. 143. 176. 10. 36. 69. 103. 136. 171. 204. 8. 34. 68. 102. 136. 169. 10. 37. 70. 103. 137. 170. 204. 9. 35. 68. 102. 136. 12. 41. 74. 108. 142. 176. 9. 36. 73. 109. 146. 183. 7. 32. 67. 103. 139. 175. 8. 34. 69. 105. 141. 179. 216. 10. 40. 80. 120. 161. 202. 9. 38. 78. 118. 157. 196. 11. 40. 77. 116. 155. 64.67 62.20 61.14 61.17 59.97 79.13 74.92 71.14 72.60 71.59 70.81 69.49 67.77 67.49 66.37 66.45 64.50 63.04 68.43 64.36 62.58 62.62 66.56 62.83 62.16 62.80 70.16 68.23 66.54 66.83 66.57 71.09 68.52 67.15 66.41 65.11 66.85 69.70 66.35 66.71 67.32 65.94 70.78 67.73 67.01 66.26 65.25 65.05 69.04 67.61 65.68 65.94 68.91 65.51 63.15 64.20 63.82 64.77 64.37 60.81 60.88 61.96 61.80 58.80 55.97 57.37 57.00 60.37 58.44 56.65 55.56 54.50 55.27 53.16 50.30 48.81 48.86 48.03 53.33 50.88 50.62 50.90 51.14 55.05 51.54 49.92 48.82.990 65.4.970 64.2.951 64.3.950 64.4.941 63.7 1.120 70.6 1.049 71.4.997 71.4.986 73.7.974 73.6 1.069 66.3 1.022 67.9 0.991 68.4 0.986 68.4 0.977 67.9 0.979 67.9 0.956 67.4 0.941 67.0 0.966 70.8 0.972 66.2 0.968 64.7 0.975 64.3 0.970 68.7 0.958 65.6 0.955 65.2 0.959 65.6 1.116 62.9 1.075 63.5 1.040 64.0 1.033 64.6 1.017 65.5 1.091 65.1 1.046 64.9 1.012 66.3 0.996 66.7 0.980 66.5 0.982 68.0 1.021 68.3 0.996 66.5 0.989 67.4 0.981 68.6 0.969 68.1 1.058 66,9 1.045 64.8 1.022 65.5 1.010 65.6 0.998 65.4 0.992 65.6 0.992 69.6 0.986 68.6 0.967 67.9 0.969 68.1 1.069 64.4 1.038 63.1 1.007 62.7 1.009 63.6 o. 996 64.0 0.979 66.2 0.961 66.9 0.955 63.7 0.952 64.0 0.958 64.1 1.076 57.4 1.023 57.4 0.978 57.3 0.975 58.9 0.969 58.9 1.098 54.9 1.050 55.6 1.016 55.7.987 56.3.970 56.3.973 56.9 1.211 43.9 1.103 45.6 1.050 46.4 1.025 47.6 1.000 48.0 1.115 47.8 1.050 48.5 1.020 49.6 1.008 50.5 1.000 51.1 1.348 40.9 1.175 43.8 1.095 45.6 1.050 46.5 519 1% Acetic Acid 455 5% Acetic Acid 0.7974 22.4 0.9977 0.9491 195.7 0.8650 27.1 1.0036 0.9546 212.4 454 5% Acetic Acid 0.7678 28.2 520 10% Acetic Acid 0.6234 20.3 521 10% Acetic Acid 0.7102 20.8 522 10*Acetic Acid 0.5929 23.4 1.0033 0.9340 192.6 1.0109 1.1415 128.9 1.0108 1.1295 148.4 1.0102 1.0709 130.6

-251aBU Tvm (COT'D) Major Minor Apparent Uncorrected Correction Corrected Liquid Jet Liquid Liquid Reynolds Jet Nodal Diameter Diameter Jet Age Surface Tension Factor Surface Run Rate TemDerature Density Viso-ea ty NXo- Th-u No&. W.vliengh + No.&e - Noe. -o t Noc. Tenslon No. Liquid ML/Min C g/cc Centipoises Orifice No. Inches Inches Inches Microseconds Dynes/cm KrKH Dynes/cm 488 10% Acetic Acid 0.7054 21.7 + 0.005 M FeC13 489 10% Acetic Acid 0,7813 22.7 + 0.005 M FeC13 490 10% Acetic Acid 0.7808 22.0 + 0.02 M FeC13 491 10% Acetic Acid 0.7210 22.0 + 0.02 M FeC13 456 14.5% Acetic 0.7598 26.5 Acid 457 14.5% Acetic 0.8355 27.1 Acid 476 10% Acetic Acid 0.6599 21.6 477 10% Acetic Acid 0.7856 21.6 478 10% Acetic Acid 0.8585 19.8 486 10% Acetic Acid 0.7036 21.9 487 10% Acetic Acid 0.7815 22.4 492 10% Acetic Acid 0.7057 23.9 493 10% Acetic Acid 0.8126 23.9 453 18% Acetic Acid 0.8408 27.3 452 18% Acetic Acid 0.7581 27.9 474 25.3% Acetic 0.7298 19.3 Acid 475 25.3% Acetic 0.7917 19.3 Acid 481 24% Acetic Acid 0.6586 21.8'82 24% Acetic Acid 0.7200 22.4 1.0107 1.1085 150.2 1.0104 1.0861 169.7 1.0106 1.1016 167.3 1.0106 1.1016 154.4 1.0156 1.1069 162.8 1.0155 1.0955 180.9 1.0107 1.1108 140.2 1.0107 1.1108 166.9 1.0110 1.1537 175.7 1.0106 1.1039 150.4 1.0106 1.0929 167.1 1.0101 1.0601 157.0 1.0101 1.0601 180.8 1.0195 1.1472 174.5 1.0194 1.1361 158.8 1.0309 1.5326 114.6 1.0309 1.5326 124.4 1.0287 1.4138 111.9 1.0286 1.4004 123.5 1 0.00362 0.00260 0.00179 2 0.01030 0.00233 0.00152 3 0.01039 0.00217 0.00157 4 0.01045 0.00207 0.00163 5 0.01043 0.00198 0.00163 6 0.01041 0.00193 0.00169 1 0.00424 0.00260 0.00158 2 0.01171 0.00240 0.00142 3 0.01169 0.00226 0.00154 4 0.01173 0.00214 0.00165 5 0.01170 0.00207 0.00171 6 0.01171 0.00202 0.00178 1 0.00411 0.00260 0.00166 2.01168 0.00256 0.00149 3 0.01166 0.00231 0.00156 4 0.01168 0.00219 0.00165 5 0.01166 0.00211 0.00169 6 0.01163 0.00207 0.00180 1 0.00383 0.00260 0.00200 2 0.01044 0.00235 0.00142 3 0.01056 0.00220 0.00157 4 0.01063 0.00209 0.00163 5 0.01060 0.00200 0.00163 1 0.00412 0.00260 0.00150 2 0.01195 0.00241 0.00138 3 0.01198 0.00224 0.00150 4 0.01191 0.00210 0.00164 5 0.01191 0.00202 0.00167 6 0.01194 0.00198 0.00174 7 0.01189 0.00194 0.00179 1 0.00475 0.00260 0.00141 2 0.01355 0.00242 0.00130 3 0.01337 0.00224 0.00143 4 0.01336 0.00211 0.00155 5 0.01321 0.00205 0.00165 6 0.01322 0.00201 0.00175 1 0.00345 0.00260 0.00203 2 0.00940 0.00231 0.00147 3 0.00960 0.00212 0.00151 4 0.00954 0.00198 0.00163 5 0.00954 0.00195 0.00169' 6 0.00955 0.00192 0.00169 1 0.00440 0.00260 0.00154 2 0.01183 0.00245 0.00140 3 0.01185 0.00225 0.00153 4 0.01185 0.00212 0.00160 5 0.01178 0.00205 0.00166 6 0.01179 0.00200 0.00170 1 0.00480 0.00260 0.00146 2 0.01323 0.00240 0.00127 3 0.01319 0.00222 0.00145 4 0.01306 0.00208 0.00158 5 0.01303 0.00199 0.00157 1 0.00385 0.00260 0.00168 2 0.01023 0.00236 0.00142 3 0.01035 0.00218 0.00155 4 0.01030 0.00209 0.00166 5 0.01039 0.00203 0.00169 6 0.01037 0.00200 0.00181 1 0.00424 0.00260 0.00160 2 0.01181 0.00244 0.00139 3 0.01176 0.00225 0.00147 4 0.01174 0.00212 0.00162 5 0.01164 0.00197 0.00162 1 0.00379 0.00260 0.00202 2 0.01036 0.00232 0.00147 3 0.01044 0.00218 0.00157 4 0.01046 0.00209 0.00169 5 0.01044 0.00200 0.00167 1 0.00454 0.00260 0.00164 2 0.01244 0.00241 0.00140 3 0.01244 0.00223 0.00151 4 0.01237 0.00211 0.00159 5 0.03231 0.00204 0.00166 1 0.00490 0.00259 0.00140 2 0.01402 0.00248 0.00130 3 0.01390 0.00229 0.00143 4 0.01380 0.00214 0.00162 5 0.01363 0.00206 0.00168 6 0.01363 0.00203 0.00175 1 0.00428 0.00253 0.00142 2 0.01221 0.00236 0.00130 3 0.01220 0.00217 0.00145 4 0.01221 0.00204 0.00155 5 0.01217 0.00198 0.00164 6 0.01220 0.00194 0.00171 1 0.00420 0.00260 0.00170 2 0.01217 0.00235 0.00145 3 0.01215 0.00213 0.00154 4 0.01210 0.00202 0.00167 5 0.01211 0.00195 0.00167 1 0.00475 0.00260 0.00152 2 0.01350 0.00242 0.00142 3 0.01342 0.00216 0.00149 4 0.01331 0.00201 0.00165 1 0.00376 0.00260 0.00167 2 0.01043 0.00232 0.00148 3 0.01060 0.00214 0.00160 4 0.01070 0.00204 0.00172 5 0.01074 0.00197 0.00174 1 o.oo42o 0.00260 o.oo061 2 0.01181 0.00238 0.00139 3 6.01188 0.00217 0.00149 4 0.01187 0.00205 0.00167 5 0.01182 0.00198 0.00173 9. 38. 51.97 78. 51.51 117. 50.77 155. 52.14 192. 51.76 9. 37. 52.65 78. 50.97 118. 49.38 159. 49.21 201. 48.47 9. 40. 49.91 83. 50.19 124. 49.16 166. 49.38 208. 48.02 11. 40. 55.89 78. 51.95 117. 51.20 155. 52.64 8. 37. 49.62 77. 47.47 119. 46.29 160. 46.62 202. 45.65 243. 45.68 8. 36. 49.93 75. 48.60 116. 47.02 156. 46.64 199. 45.28 11. 40. 55.05 77. 53.97 13. 53.37 149. 52.48 186. 52.85 9. 37. 52.84 77. 50.65 117. 50.34 157. 50.42 196. 50.18 8. 35. 56.12 72. 52.02 110. 51.20 148. 52.72 9. 37. 55.11 75. 52.00 114. 50.89 154. 50.26 194. 48.53 9. 37. 52.83 76. 52.40 116. 50.21 154. 52.89 11. - 41. 52.98 80. 50.98 120. 49.16 159. 50.93 9. 38. 51.80 78. 50.23 118. 50.09 158. 49.88 8. 37. 47.31 79. 45.57 122. 43.38 166. 44.11 210. 43.28 8. 35. 50.45 74. 47.68 113. 46.60 153. 45.79 194. 44.83 10. 42. 43.53 85. 43.42 128. 42.42 170. 43.13 9. 41. 42.58 85. 43.28 128. 42.33 10. 40. 46.18 83. 43.79 126. 41.93 170. 42.13 9. 40. 46.02 82. 44.64 124. 42.34 168. 42.44 1.037 1.020 1.009 1.020 1.009 1.077 1.023 0.990 0.974 0.960 1.008 0.996 0.976 0.972 0.949 1.183 1.080 1.038 1.031 1.119 1.046 1.000 0.994 0.974 0.966 1.080 1.009 0.983 0.955 0.934 1.148 1.095 1.053 1.025 1.020 1.083 1.025 1,001 0.987 0.979 1.105 1.018 0.980 0.980 1.194 1.090 1.032 1.015 0.979 1.058 1.023 0.986 1.002 1.123 1.059 1.016 1.020 1.048 1.008 0.989 0.974 1.077 1.010 0o963. 0.951 0.933 1.180 1.075 1.030 0.999 0.979 1.061 1.012 0.990 0.994 1.009 o.996 0.972 1.078 1.031 1.004 1.001 1.123 1.050.1.020 0.980 50.1 50.5 50.3 51.1 51.3 48.9 49.8 49.9 50.6 50.4 49.5 50.4 50.4 50.8 50.6 47.2 48.1 49.3 51.1 44.4 45.4 46.3 46.9 46.9 47.3 46.2 48.2 47.9 48.8 48.5 47.9 49.3 50.6 51.1 51.9 48.7 49.4 50.3 51.1 51.3 50.8 51.1 52.3 53.8 46.1 47.7 49.3 49.5 49.6 49.9 51.2 51.0 52.8 47.1 48.1 48.4 49.9 49.5 49.9 50.7 51.3 43.9 45.1 45.1 46.3 46.4 46.1 44,4 45.2 45.9 45.8 41.0 42.9 42.9 43.4 42.2 43.4 43.6 42.9 42.4 41.7 42.1 41.0 42.6 41.5 43.3

APPENDIX J EXPERf4ENTAL ERRORS -252

EXPERIMENTAL ERRORS The maximum possible error introduced into the calculation of surface tensions from the oscillating jet due to errors in measurement can be most readily estimated by considering that Equation. (9C) is almost the equivalent of Equation (23-E): ~k2r2c2 2r2 [. 1 +1 k2 +..] (96 12 Setting k = 2/kX, c = L/rr2, and assuming that the value of the terms inside the brackets can be approximated by unity, 2 pL2 3 X2z P' from which it is seen that da dL dX dr 2 —' + 2- + 2dr (1J) a L X r The error in determining the liquid rate, as indicated by differences between the initial and final weighings, seldom exceeded 0o 0016 gram; dL 0.06 0016 0 --' - 11 - i' - = 0o 4 L o 8000 The wavelength was measured within an accuracy of + O 00005 inchj dX Ov 0.00010 0010 X 0. 01000

IIl rlYIIo lll 3 15 0!524 5110 It was possible to determine the jet radius with an accuracy of + 0 000005 inchj dr o0000OOOO1 r 00100 Then from Equation (-1J), d w 2(0.002) + 2(0.010) + 2(0.010) w 0.044 + 2.2 percent, This accuracy permits a maximum possible error due to measurement, for the surface tension of water, of da 0 0.022(72) = + 1.6 dyne per cm.