THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING MULTIPLE EMULSION FORMATION AS A HYDRODYNAMIC PHENOMENON USING CYLINDRICAL JETS David Po Kessler A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Chemical and Metallurgical Engineering 1962 June, 1962 IP-568

ACKNOWLEDGEMENTS The author owes a debt of gratitude to many people for assistance in the course of his doctoral program. Particular thanks should go to the following people: Professor J. Louis York, the chairman of the doctoral committee, for his assistance and encouragement throughout the course of the research, Professors A, G, Hansen, Ro Bo Morrison, M. R. Tek, and Go B. Williams, the other members of the doctoral committee, for assistance in many ways, particularly with respect to interpretation of certain aspects of the data obtained, and to Dr, Keith Ho Coats, who served as a committee member while a staff member of the Chemical and Metallurgical Engineering Department, Mr. Gordon Ringrose, who constructed much of the electronic equipment used in the research. The National Science Foundation, for support for three years of study, and to Consumers Power Company for support during the first year of graduate studyo The Commercial Solvents Corporation, who were very generous in supplying surfactants for use in the course of the research, iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENT............................................... iii LIST OF TABLESo................................................. v LIST OF FIGURES................................................. vii LIST OF APPENDICES..........o........................... xi NOMENCLATURE x.. o.... o.............. xii ABSTRACTo.... o.................................. o... xiv I INTRODUCTIONo o............................................. 1 II LITERATURE REVIEW........................... 6 III PRELIMINARY CONSIDERATIONS............................... 12 III1 Investigations with Microscope and Well Slide,,..... 12 III2 Investigations Using Transient Equipment........... 17 IV ANALYSIS OF SPRAYS................ o.............,.. 23 V EXPERIMENTAL EQUIPMENT..................................o 26 V 1 Liquid Injection System,............................ 26 V, 2 Lights and Time Delay System,,.................... 30 Vo3 Camera, Film, and Darkroom Procedure,,.e o,.......... 33 Vo 4 Interfacial Tension Determination,,,..............,, 34 VI EXPERIMENTAL PROCEDURE,................................. 35 VII DISCUSSION AND RESULTS OF COUNTED DATA o.,,................ 46 VII 1 Ranges of Variables Studied.................. 46 VIIo2 Typical Raw Data Results,. O,.............. o. o o 48 VIIo3 Determination of Probability Density Functions..., 48 VIIo4 Correlation of Multiple Emulsion Parameters........ 67 VIII DETERMINATION OF MECHANISM~o......................85 IX CONCLUSIONSo...............e........ o 103 X RECOMMENDATIONS FOR FUTURE WORKo o,....................o104 iv

LIST OF TABLES Table Page I Diameters of Hypodermic Needles Used as Injection Orifices............................................. 29 II Typical Raw Data Set - Run Number 10.,............ 49 III Experimental Conditions and Derived Data,............ 51 IV Transformations and Integrals for Density Functions,. 54 V Typical Large Drop and Inclusion Distribution Data,.o 54 VI Typical Data Set Fitted by the Rosin-Rammler Function Applied to the Volume Distribution......... 58 VII Typical Data Set Fitted by the Rosin-Rammler Function Applied to the Number Distribution......... 60 VIII Typical Data Set Fitted by the Nukiyama-Tanasawa Function, n = 1/4 and n = 1/2...................... 63 IX Conditional Distribution Parameters of Inclusions for a Typical Run................................... 69 X Number of Inclusions Per Large Drop as a Function of Large Drop Diameter............................... 70 XI Computer Program..................................... 117 XII Input Variables for Computer Program................. 124 XIII Computer Input Data for Run 10.................. 127 XIV Computer Output Data for Run 10................... 129 XV Calculated Calibration Curve for Rotameter,......... 153 XVI Calibration of Tensiometer........................... 155 XVII Calibration of Dial-Type Pressure Gauges............ 157 XVIII Depth of Field Calibrations for 2,6X and 10X Cameras, 158 XIX Raw Data - Run Number............................ 160 XX Raw Data - Run Number 2............................. 160 v

LIST OF TABLES CONTPD Table XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIV wsxxiii6 Raw Raw Raw Raw Raw Raw Raw Raw Raw Raw Raw Raw Raw Data Data Data Data Data Data Data Data Data Data Data Data Data - Run - Run - Run - Run - Run - Run - Run - Run - Run -Run - Run - Run - Run Number Number Number Number Number Number Number Number Number Number Number Number Number 4..... 6...... 70...... 80....o 6000000 80 o e o o 11..... 12..... 13..... 14.... 15..... 16..... 17................ 0 0 000 ~0 0. 00 0b 00 0 0 0 0 0 00~~ Q ~ gg 0 0.... 0 9 a 0 0 0 0 0 0 a 0 6. 6 0 0 0 9a O ~~0 ~~~ ~0~000 0~0 00 ~Q ~ ~ ~~0~ ~ 0 ~ 0 0.............. 0 ~O a ~~~ e~ ~~ 0 e~ ~0 ~ ~ 0~ ~ 0 0~~~ 0. 0 0. 0 0...... 0 Page 162 162 164 164 166 166 169 169 171 171 173 173....... 175 Raw Data - Run Number 18,...o 175 vi

LIST OF FIGURES Figure Page 1 Simple Emulsion..........................2...... 2 2 Double-Multiple Emulsion.......................... 2 3 Quinque-Multiple Emulsion............................2 4 Schematic Drop with Inclusions "Packed in".......... 13 5 Coalescence of Inclusion Containing Drop with Flat Interface....................................... 16 6 Apparatus for Transient Injectiono................... 18 7 Photo of Transient Injection Process - 2o6Xoo,..... 20 8 Photo of Transient Injection Process - 206Xo,....... 20 9 Photo of Transient Injection Process - 2o6Xo........ 21 10 Photo of Transient Injection Process - 2o6X......... 21 11 Photo of Transient Injection Process - 206Xo........o 22 12 Photo of Transient Injection Process - 2o6X....,... 22 13 Schematic Diagram of Experimental Equipment......... 27 14 Time Delay Unite................5,.......1o......... 31 15 Power Supply for Time Delay Unit................ 32 16 Print from Typical Single Flash Photo............... 36 17 Typical Single Flash Negative - lOXo.o............. 36 18 Print from Typical Double Flash PhotOo............. 37 19 Typical Double Flash Negative - lOXo.............. 37 20 Schematic Diagram of Drop Appearance During Counting 39 21 Reflected Light Method for Examination of Negativeso 41 22 Typical Drop Travel Data - Run Number 4,........ 42 23 Schematic Diagram of Counted Data............44 vii

LIST OF FIGURES CONT'D Figure Page 24 Typical Fit of Log-Normal Function to Large Drop and Inclusion Distributions - Run Number 13......... 56 25 Fit of Rosin-Rammler Function to Run 13 Volume Distribution....................................... 59 26 Fit of Rosin-Rammler Function to Run 13 Number Distribution.................................6...... 61 27 Fit of Nukiyama-Tanasawa Function to Run 13 Data, n = 1/4.......................................... 64 28 Fit of Nukiyama-Tanasawa Function to Run 13 Data, n = 1/2............................................ 65 29 Log-Normal Function Fitted to Distribution Data From Varicose Breakup............................. 66 30 Typical Data for Conditional Distribution of Inclusions,...................................... 68 31 Number of Inclusions Per Drop as a Function of Large Drop Diameter.......................... 71 32 Typical Data for Weighted Drop Distributions,........ 74 33 d32 versus d.................................... 76 34 D32 versus D10 o.................... 77 35 Percent Included Volume as a Function of Re x We.... 81 36 Percent Included Area as a Function of Re x We,...... 82 37 Percent Included Area as a Function of Percent Included Volume.................................... 83 38 Varicose Breakup.................................... 86 39 Sinuous Breakup.................................. 86 40 Ligament-Type Breakup................................ 86 41 Typical Photograph of Jet Breakup in Low Viscosity System - 26X....................................... 87 viii

LIST OF FIGURES CONT'D Figure Page 42 Carbon Tetrachloride into Glycerine - No, 19 Hypodermic Needle, 5-1/2 cm, From Orifice - O1X - Re = 7,4..................................... 89 43 Carbon Tetrachloride into Glycerine - No, 19 Hypodermic Needle, 5-1/2 cmo From Orifice - 10X - Re = 35o,9............................... 89 44 Carbon Tetrachloride into Glycerine - No, 19 Hypodermic Needle, 5-1/2 cmo From Orifice - 10X - Re = 48o,6.......................... 90 45 Carbon Tetrachloride into Glycerine - No, 19 Hypodermic Needle, 5-1/2 cmo From Orifice - O1X - Re = 63,4,.................................... 90 46 Carbon Tetrachloride into Glycerine - No, 19 Hypodermic Needle, at Orifice - 10X - Re = 39,60, o.o 91 47 Carbon Tetrachloride into Glycerine - No, 19 Hypodermic Needle, 2,5 cmo From Orifice - O1X - Re = 47,5..................................... 91 48 Schematic Depiction of Mechanism.................... 92 49 Carbon Tetrachloride into Glycerine - No, 22 Hypodermic Needle - 10X - Re = 80 88................. 93 50 Carbon Tetrachloride into Glycerine - No, 22 Hypodermic Needle - 10X - Re = 30o6,................ 93 51 Carbon Tetrachloride into Glycerine - No, 22 Hypodermic Needle - 10X - Re = 420............... 94 52 Carbon Tetrachloride into Glycerine - No, 17 Hypodermic Needle - 10X - 4 cmo From Orifice - Re = 24o,6.......................... 95 53 Carbon Tetrachloride into Glycerine - Noo 17 Hypodermic Needle - 1OX - 4 cm. From Orifice - Re = 335 8................................... 95 54 Carbon Tetrachloride into Glycerine - No, 17 Hypodermic Needle - 10X - 4 cmo From Orifice - Re = 603o................................. 96 ix

LIST OF FIGURES CONT'D Figure 55 Carbon Tetrachloride into Glycerine - No. 17 Hypodermic Needle - 10X - 4 cm, From Orifice - Re = 71 4.........................................0 56 Schematic Diagram of Inclusion Coalescence,......... 57 D10 versus d10............................... 58 dlo versus Re x We....................... Page 96 98 100 101 59 Calibration of 1043B Rotameter 60 Calibration of 1043B Rotameter 61 Calibration Curve for Tensiome at 34,7 Psia........ at 49,9" Hg Absolute,, ter.................... 151 152 156 62 Distribution Plot 63 Distribution Plot 64 Distribution Plot 65 Distribution Plot 66 Distribution Plot 67 Distribution Plot 68 Distribution Plot 69 Distribution Plot 70 Distribution Plot 71 Distribution Plot 72 Distribution Plot 73 Distribution Plot 74 Distribution Plot 75 Distribution Plot 76 Distribution Plot for for for for for for for for for for for for for for for Run 1.. Run 2,. Run 4. Run 6,. Run 7. Run 8.. Run 9.. Run 10o e e e e e e.............. 161 0 0.... 0. 0 -. - 0 a 0 - 0 161 163 165 165 167 167 168 170 170 172 174 174 176 176 Run Run Run Run Run Run Run 11......................... 12......................... 14......................... 15......................... 16........................ 17......................... 18......................... x

LIST OF APPENDICES Appendix A BIBLIOGRAPHY........................ B COMPUTER PROGRAM.................... C EQUIPMENT CALIBRATIONS............. Co 1 Rotameter..................... Co 2 Tensiometer................... C. 3 Pressure Gauges............... C, 4 Camera,........................ D RAW DATA AND DISTRIBUTION PLOTS.. 0. 0 0 0. 0 a 0 a0 0 0 0 0. 0 0 0 0 0 0 4 9 0 0 0 0 0 * a 4 0 0 0 0 - -. 0 0. 0 0 0 0 0 - - 0 0... 0 0 0. a 0 0 0 0 0 0 a.. 0 0 0 0 0 0 0 Page 107 115 149 150 150 155 157 159 xi

NOMENCLATURE D. Large drop diameter Dn Nozzle diameter d Inclusion diameter oo00 E(z) = f z f(z)dz 00 f(z) Probability density function, Section VIIo3 F(z) Probability distribution function, Section VIIo3 f(z) Probability density function estimated from sample, Section VIIo4 F(z) Probability distribution function estimated from sample, Section VII, 4 G(z) = 1/[1 - F(z)] 6i distance from double exposure photograph of travel of large drop of diameter Di M Maximum number of large drop size classes N Number of drops, see VIIo3; maximum number of inclusion size classes elsewhere Pr(a) Probability of the event a Re Reynolds number, Section VIIo 4 T Temperature v Nozzle velocity V Volume We Weber number, Section VIIo 4 xij Number of inclusions of diameter dj in large drops of diameter D. yi Number of large drops of diameter Di E(zP) 1/p-q z = [E( —)]; see Section VIIo 4 p = E(zg) xii

Greek 7 r' (e) rc Interfacial tension = t - e dt; see Section VIIo5 o Viscosity, mean of distribution Standard deviation Subscripts r Refers to receiving phase s Refers to sprayed phase xiii * * Xlll

ABSTRACT The classical emulsion is made up of drops of one liquid dispersed in a containing liquid. Under certain circumstances, however, some of the containing phase may form drops within the drops of the dispersed liquid, giving rise to a structure known as a double-multiple emulsion, The purpose of this study was the investigation of the formation of these structures as a hydrodynamic phenomenon. Double-multiple emulsions were produced using both transient and steady-state liquid injection, with a cylindrical jet configurationo Analysis of the spray was by means of high-speed photographyo The distribution of the large drops and that of the included drops were both found to be satisfactorily represented by a log-normal probability functiono The percent of volume and interfacial area represented by the included drops were found to be most strongly dependent on inertial forces. A simplified model based on the use of nozzle parameters was found to correlate satisfactorily percent included area and volume as a function of Reynolds number and Weber number. Large size classes of the dispersed phase drops contained proportionally many more inclusions than did the smaller size classes, The mechanism of inclusion formation was found to involve the drawing out of a ligament or sheet from the flowing jet, followed by the re-coalescence of the free end of this ligament or sheet with the xiv

main jet body, entraining in the process a portion of the containing phase. Thus, the inclusions pre-date the formation of the drops of the dispersed phase from the jet disruption. xv

I. INTRODUCTION Before attempting a detailed discussion of the work covered in this dissertation, it is necessary to devote a little time to defining just what is meant by a "double-multiple" emulsion. Multiple emulsions are encountered seldom enough in the literature that it is well to clear up at the outset some possible sources of confusion in terminology. The classical emulsion is made up of a number of minute drops of one liquid within a containing phase of another liquid. The two liquids are commonly referred to as the dispersed phase and the continuous phase respectively, In the simplest case we have the situation depicted in Figure 1, where there is a single dispersed phase and the containing phase is truly continuous in the sense that any two points in the containing phase can be joined by a line lying entirely within that phase. Under some circumstances, however, it is possible to get some of the containing phase within the drops of the other phase, as shown in Figure 2, making the containing phase no longer continuouso Here the terms "continuous phase" and "dispersed phase" lose any meaning as applied to the resultant emulsion0 (They will, of course, have some relevance in the sense that one normally creates an emulsion by adding what can be termed the "dispersed" phase to the "continuous" phase. ) Emulsion structures which lack a continuous phase are normally referred to as multiple emulsions. -1

-2 CONTINUOUS PHASE'.; f 0 FIG. I SIMPLE EMULSION FIG. 2 LARGE DROP INCLUSIONS DOUBLE - MULTIPLE EMULSION.1 ~~~~~~~~~~~~~~~. ii~~~~~~ i i i ol ~ 4,~. ~''~~Z~~~~~~ i ~i i FIG. 3 QUINQUE -MULTIPLE EMULSION

-3 Multiple emulsions structures can be created in surprising complexity - for example, Clayton(19) cites an example of a quinquemultiple emulsion, shown schematically in Figure 35 The level of the multiple emulsion might be defined as the maximum of the minimum number of phase boundaries it is necessary to cross in going from any point (xl,yl,zl) in the outermost phase to any other point (x2,y2,z2) of the system. Thus in Figure 5 we can see that it is necessary to cross five phase boundaries in going from point 1 to point 2. In the present study we are concerned with multiple emulsions of the "doublemultiple" type shown in Figure 2. To avoid confusion, it should be pointed out that there is often reference in the literature to "dual" emulsions. This usage usually refers to pairs of liquids which, through the use of different emulsifying agents, will form emulsions of both the O/W and W/O types, and will frequently invert from one type to the other upon addition of a suitable reagent. These are conjugate systems, but not co-existing systems; that is, at any given time only a W/O or only an O/W emulsion is present. Obviously a pair of liquids must have the "dual" property in order to form stable "double-multiple" emulsions, As is noted in the literature review, multiple emulsions as a class are not new, The early literature is primarily concerned with their production as an inversion phenomenon, i,e,, through the addition of the disperse phase or a suitable reagent to a simple emulsion, causing the structure to invert from O/W to W/O or vice versa, in the process trapping some of the original structure in the inverted emulsion, Later studies noted that there seemed to be some hydrodynamic

-4 factors involved as well - for example, the same effect could sometimes be produced by shaking or stirring. These later studies were purely observational in nature, with no quantitative work being done on mechanism or prediction of effects. The present study was motivated by an observation by Ro H. Boll during his doctoral work at the University of Michigan, Boll was concerned with determining specific surface in liquidliquid sprays using a light transmittance method. The sprays were produced using transient high-pressure injection through a conical spray nozzle. Certain pairs of liquids were found to give dispersions which were double-multiple emulsions. The increased surface area that is available in a multiple emulsion offers certain obvious advantages for mass transfer operations, Boll's work suggested that one might be able to produce multiple emulsions conveniently through liquid-liquid injection, as opposed to the cumbersome inversion method. If one could only define the major variables and predict their effects, it might be possible to upgrade the efficiency of many operations involving mass transfer, At the outset there are a number of obvious questions: 1) Can this be done in pure systems? (All the reported data are for heterogeneous systems ) 2) Is this strictly a transient phenomenon? (If so, it will be considerably more unwieldy to adapt to commercial use ) 3) What is the mechanism?

-5 4) What are the important independent variables, and, once found, what are the dependent variables which will exhibit a correlation with these independent variables? 5) What form, if any, of probability distribution function is followed by the drops? (If the probability distribution can be defined, sampling can be reduced and systematic definition of sampling error is possible. ) The consideration of these questions and several others which arose in the course of the research is the essence of the work described in this dissertation. There is one more matter of terminology that must be raised at this point. In the double-multiple emulsion, one has essentially two classes of drops (see Figure 2), The drops contained within the large drops, i.eo, the drops of the same composition as the external phase, will be referred to throughout as the inclusions; the larger drops which are of composition opposite that of the external phase will be referred to as the large drops. This is an important point, as it is necessary to make this distinction many times in the course of the work presented hereo

IIo LITERATURE REVIEW One of the earlier observations with regard to multiple emulsions is made by C. V. Boys in his classic treatise Soap Bubbles - Their Colours and the Forces -Which Mould Them. Boys notes that the liquid pairs "petroleum" and water, and orthotoluidine and water will produce multiple emulsions, Boys' work was one of the earliest found which makes reference to liquid-liquid multiple emulsions (circa 1900). If, however, we do not restrict the term "multiple emulsion" to liquid-liquid systems, the history of observation of multiple emulsions reaches back perhaps to the first individual who discovered the joy of blowing ordinary soap bubbles. Boys indicates that written reference to bubbles has been made as early as Ovid and Martial, Here we must restrict our attention to liquid-liquid systemsO There is seldom any mention of multiple emulsions in the published literature from 1900 to the present day. The few instances in which some note is made are usually in conjunction with another matter entirely - for example, as when Boll(8) encountered multiple emulsions in the course of his work on specific surface in liquid(63) liquid sprays, or Pavloshenko and Yanishevskii ) in their work on interfacial area of mechanically stirred liquid mixtures, Occasionally, pictures are published in the literature which show what might be multiple emulsion structures but have been given no cognizance by the authors. Ranz(67) shows a picture of a carbon tetrachloride-into-water spray (the same system as used in much of -6

-7 this research) which seems to show a well defined multiple emulsion; however, no mention of the phenomenon is made in the accompanying articles Similarly, Scott, Hayes, and Holland81) show a picture of a kerosene-water dispersion - another system which will support multiple emulsion behavior - that appears to show multiple emulsions, but with no comment made in the accompanying article. It should be noted that in the dense dispersions shown in each of these articles, camera depth of field might give a false indication of multiple emulsion structure by picturing drops behind or in front of a large drop as inclusions. Even what is perhaps the best known reference on emulsions, Clayton's The Theory of Emulsions and Their Technical Treatment,(l9) has only two paragraphs on multiple emulsions. This is a reference work which has been through five editions from 1923 to 1954, including German and Russian translations. Such a situation tends to make literature surveying in the multiple emulsion field frequently more fortuitous than systematic. In the 1920's and 1930's, several papers were published treating the subject of dual emulsions, which, as was pointed out in the introduction, is closely related to that of multiple emulsions, A good summary of most of this work can be found in Clayton, The most useful of these articles with respect to the work considered here are probably the ones by Woodman,(9l,92) and the one by Cheesman and King (16) Cheesman and King made an extensive study of the stability of dual emulsions using some 16-20 different emulsifying agents, For

-8 future work on the double-multiple emulsion systems studied here it may be possible to find stabilizing surfactants from this listo Two other remarks of interest are made. A paper by Cassel (Act_Physiochemica UR.S. So, 6, p. 289 (1937)) is cited which makes the observation that stabilization of dual emulsions is impossible on thermodynamic grounds, and also cited is a work by Sugden (JoACoSo, p. 174 (1926)) which notes that in some dual emulsion systems the more easily formed system - that is, O/W or W/O - is less stable and vice versa, The interesting thing with regard to Woodman's work is that he was able to preferentially create either O/W or W/O emulsions with a given pair of liquids by varying his method of shaking the container, This indicated that hydrodynamic considerations could be controlling in the dual emulsion case, and gave encouragement to a possible hydrodynamic mechanism for the double-multiple emulsion case, Most of the work on dual emulsions is useful in only the most general sort of way for double-multiple emulsion work, Although the dual property is necessary for the stable double-multiple case, the mechanism presented here indicates that this is truly a stability relationship, and not a requisite for formation of double-multiple emulsions. Dual emulsion systems can indicate liquid pairs and surfactants which will probably have good success in the creation of double-multiple emulsions, but any more specific conclusions are hardly justified,

-9 In recent years, there have been two articles which make some useful observations with regard to multiple emulsions, and, in particular, with regard to multiple emulsions that apparently have been produced as a hydrodynamic phenomenon. The first of these is the article by Pavloshenko and Yanishevskii (63 on interfacial area of mechanically stirred liquids. This periodical is available in English translation as the Journal of Applied Chemistry of the UoS.SSRo Pavloshenko and Yanishevskii were concerned with the correlation of interfacial surface area created by agitation of two liquid phases in a container using a mechanical stirrer, They observed multiple emulsions in the system machine oil into water, and show a photograph similar to some of the ones taken in conjunction with this dissertation, They also note observation of multiple emulsions in the medicinal petrolatum into water system. The conclusion reached in this article is that the multiple emulsions seemed to be favored by dispersing a high viscosity liquid in a low viscosity medium. This is somewhat at odds with the results presented here, and is also at odds with some of the data in the article, which notes that some multiple emulsion structures were produced in the machine oil into glycerol system - obviously a viscous into viscous, rather than a viscous into non-viscous system, This point will be discussed later; at the moment it will suffice to say that this appears to be a stability phenomenon. Two other remarks are made which are of interest. First, a decrease in surface area with increase in interfacial tension was detected, a result in agreement with the results obtained here. Second,

-10 they remark that the two interfaces (in their double-multiple emulsion) differ greatly from a hydrodynamic standpoint, No quantitative work was done on the multiple emulsions as they were an observation incidental to the main purpose of the research, One comment that might be in order is that the observations of the multiple emulsion structures were made after the agitator was turned off rather than in the dynamic system. This, of course, tends to make stability toward coalescence of far greater effect in the results obtained, The second publication in recent years that is worthy of more than passing discussion is the one by Ro H. Bo1l,(8) which, as was already mentioned, furnished the impetus for the research presented here. Boll, like Pavloshenko and Yanishevskii, was studying interfacial area of liquid-liquid dispersions, but rather than creating the dispersion by mechanical agitation, was using a conical spray nozzle and transient injection. The multiple emulsion formation was an extremely undesirable factor here, since the analysis was by light transmittance methods which were hardly compatible with the abnormal drop structure obtained. Boll observed multiple emulsions in the SAE 10 motor oil and water, and kerosene and water systems. As in the article by Pavloshenko and Yanishevskii, these systems both involved viscous liquids, Also, in both articles, the systems which exhibited multiple emulsion behavior were highly heterogeneous. Boll studied no highly viscous pure systems, but did study the carbon tetrachloride-water system, and observed no multiple emulsions. This is a system which the present research has

-11 shown will support multiple emulsion behavior, although coalescence is rapid. Again, later discussion will show why this stability consideration rectifies the apparent contradiction~ The bibliography shown in the Appendix is not intended to be exhaustive. In general, the field of sprays is very well covered in the bibliography by De Juhasz(25) listed. Rather, the listing here is intended to bring together some of the articles with observations and techniques which suggest possible application to the study of multiple emulsion formation in a dynamic system, References are listed for the general spray considerations, the various aspects of drop mechanics, the surface chemistry considerations, the statistical and experimental design questions, and the photographic problems.

III. PRELIMINARY CONSIDERATIONS Prior to the construction of the equipment which was used for the majority of the data obtained in this study, it was necessary to do some qualitative work to determine approximate ranges for operating variables and to define an appropriate method of analysis~ It is also necessary at this point to consider some general aspects of the spray process with regard to interpretation of data presented latero II111 Investigations with Microscope and Well Slide The first experimental effort was an attempt to create multiple emulsions using a simpler flow geometry than a conical sprayo Toward this end a well slide was constructed of acrylic resin and a hypodermic needle and syringe used to inject the sprayed phase into the stagnant receiving phase. Examination was by means of a Bausch and Lomb binocular microscope. First the system water into kerosene was tried to see if this system (which produced multiple emulsions for Boll(8) with a conical spray nozzle) would produce multiple emulsions with simple cylindrical jet. Multiple emulsions were produced and, as Boll remarked, the emulsions were "packed in." In other words. the included drops had the appearance of filling the parent drop, as shown in Figure 4, very much as one might fill a cellophane bag with marbles, This indicated that whatever mechanism was active with respect to producing the multiple emulsions from a conical spray nozzle was active in the breakup of the simple cylindrical jet. Since the cylindrical jet represents a much -12

-13 Figure 4. Schematic Drop with Inclusions "Packed In."

simpler type of flow geometry than the breakup of a conical sheet, the investigations were carried on in this simpler system for the remainder of the research. The next effort was toward producing multiple emulsions in a homogeneous system, Two of the systems where Boll had failed to produce multiple emulsions were the benzene-water system and the carbon tetrachloride-water system, Investigation using the well slide showed no multiple emulsions formed. The resistance of mutually insoluble liquids to interpenetration across the dividing interface is strongly dependent on interfacial tension, so the next step was an attempt at reducing interfacial tension to reduce interpenetration resistance, Both powdered and liquid commercial detergents were used for the benzene-water system, Some multiple emulsions were produced and, with this encouragement, a search was made for a system with a sufficiently low interfacial tension that it would not require the use of a surfactant to promote multiple emulsion formation, Such a system was found in the isobutanol-water system, Interfacial tension in this system at room temperatures is about 2 dynes per centimeter (as opposed to 30-60 dynes per centimeter for most common liquid pairs), The isobutanol-water system yielded multiple emulsions without surfactant addition, and represented the first verification experimentally of the possibility of multiple emulsion formation in homogeneous systems, that is, systems without some sort of third component added to promote multiple emulsion formation,

-15 Following this discovery, further work was done on the carbon tetrachloride-water system and multiple emulsions were produced with common household detergents, and with sodium lauryl sulfate. In all the work done under the microscope, there were several common factors with regard to coalescence of the emulsions produced. First, the more highly heterogeneous the system, the more slowly coalescence proceeded. Very pure phases yielded emulsions with coalescence times of the order of seconds or fractions of a second, Second, the order of stability of the inclusions was higher than that of the large drops - for example, it was possible to observe large drops containing inclusions migrate to an interface and coalesce, with no effect on the inclusions. This is shown schematically in Figure 5. As the large drop coalesces with the essentially infinite body of fluid, the surface forces snap the interface back to a straight line, and impart a not inconsiderable acceleration to the inclusions, but without causing them to coalesce with one another. Third, it was observed that the order of stability of a small drop with respect to another small drop is higher than with respect to an interface of larger curvature; all inclusions produced seemed to coalesce out through the phase boundary of the parent drop rather than coalescing with other inclusions in the same drop. It was also found that it was possible to produce multiple emulsions in pure systems through the use of Dow Chemical Company "Methocel," This is a water soluble cellulose gum which does not have an extremely pronounced effect on the interfacial tension in the amounts required - this tended to indicate perhaps a stabilizing effect rather

Figure 5. Coalescence of Inclusion Containing Drop with Flat Interface.

-17 than a true effect on the promotion of multiple emulsions, If so, it was felt that study at shorter times after formation of the emulsion might reveal multiple emulsions which coalesce too rapidly to observe using the long time delays associated with a sample cell and microscope. IIIo,2 Investigations Using Transient Equipment Accordingly, the next experimental investigation was carried out using the apparatus shown in Figure 6, an arrangement very similar to that used by Boll(8) in his work. The apparatus consists of a freefloating shaft which rests on a piston, The shaft can be loaded with lead weights, and is held in place with a pino The piston fits in a stainless steel cylinder with a capacity of approximately 1 cmo, the end of which is threaded to accept various spray nozzles, The nozzle is immersed in a transparent sample cell containing the receiving fluido To spray the liquid, the pin is pulled from the shaft and the gravity force on the weights provides pressures up to about 1500 psio The process is essentially a transient one, since spray times are very short (maximum time of the order of one second). The nozzle used was a conical spray nozzle with the internal components removed, so that a simple cylindrical jet was obtained, The spray was observed by means of high-speed photography using the lights and camera described in the section on experimental equipment. A trigger incorporating a microswitch was designed and built to fire the lights at any desired stage of the spray process.

PIN LEAD WEIGHTS CELL Figure 6. Apparatus for Transient Injection.

-19 A series of photographs obtained with this equipment are shown in Figures 7 through 12. These are not photographs of a single spray, but are a series of photographs taken at successively later times on the same system but on different runs, Work with this equipment resulted in two conclusions: first, that it is possible to produce multiple emulsions from a cylindrical jet using the carbon tetrachloride-water system without surfactant addition - this conclusion was possible because multiple emulsion drops could be detected at the edges of the spray zone; and second, that it was necessary to go to lower pressures to decrease spray density to the point that more of the drops could be photographically resolved~ It was not possible to use this transient type of equipment for the lower pressures required, as the friction between the piston and cylinder became important enough that pressures could not be determined accurately. Spray times were also too low to permit more than one photograph per run, Consequently, it was necessary to build completely new equipment for the taking of quantitative data, Before discussing the experimental equipment used for the quantitative data, we will first discuss some of the general considerations involved in a suitable system of analysis,

-20 H 0) 91 CO, E-4 rt. H 0 0 AO aQ 4*, C) 00) E-PC 0(0 a qI OQ CO 0 C) O < h> a~ PU(

I H Figure 9. Photo of Transient Injection Process - 2.6X. Figure 10. Photo of Transient Injection Process - 2.6Xo

-22 H 3* O 0) O 0 0) 00 C4 a) 0 a -i 0Ua O +) 00) O 0 *H 0 0) <Dhi b04

IV. ANALYSIS OF SPRAYS A number of techniques have been described in the literature for general spray analysis. All have their particular advantages and disadvantages; however, not all are readily adapted to analysis of multiple emulsions, where one must not only be concerned with the main drop distribution, but with the distribution of the included drops as well, A good summary of the various methods can be found in the report by Putnam(65) et al, Some methods depend on the physical collection of the drops, either on a specially coated slide or screen, or in a bath of a particular receiving fluido These methods are frequently adequate for liquid-into-gas sprays, but suffer from certain disadvantages, such as distortion of the drop under its own weight and unequal evaporation rates of drops in the various size classes, Even without these disadvantages, the difficulty of introducing a collector into a liquid-liquid spray is sizeable, Ranz(67) sampled some liquid-liquid sprays using a collector which was essentially a box with sliding, rubber-band-loaded top and bottom. With this apparatus it is possible to effectively cut a transverse slice from the spray. It does, however, introduce perturbation into the flow field, and furthermore gives a space-wise rather than the desired time-wise distribution because of varying drop velocities, Other methods of spray analysis require the impaction of the spray upon a coated slide or suitable surface, The traces left -23

by the droplets are then measured to determine the spray distribution, This system obviously will not adapt to multiple emulsion study, Another technique involves the spraying of an artificial fluid - eg., paraffin or wax - which can be solidified and the resultant particles screened or counted. Again, this method is not adaptable to multiple emulsions because of the opacity of the fluids and the difficulty in controlling the physical properties of the sprayed fluid over the desired range. Certain electronic methods use the insertion of a probe into the spray with automatic analysis based on drop impacts. This system introduces a perturbation in the flow field and, which is more serious, cannot discriminate between ordinary drops and drops with included phases. There are in addition certain optical techniques which have been applied to spray analysis, McDonough(55) and Scott(81) have used a light transmittance method for the analysis of interfacial areas in orifice mixing of immiscible liquids. This method has the advantage of extreme rapidity, but gives only the total interfacial area and does not permit discrimination between drops and- inclusions, It is also necessary to calibrate the equipment using the photographic technique which we will discuss next (and which is the method of analysis used in this research). If some way can be found to discriminate using a light transmittance technique between external drop area and area contributed by inclusions, this would be a most desirable method of analysis because of the speed and lack of expense for film, etc.

-25 The photographic technique used in the course of this research has been known for some time, but was brought to its full application by York in 1949 (93) The method consists of taking an actual photograph of the spray droplets with high-speed still-picture photographic equipment. Double-exposure pictures are taken as well as single exposures. A known, very short time delay is used between the two exposures of the double-exposure shots. The single-exposure photographs are then counted - i.e,, the number of drops in each of the selected series of size classes are determined. This gives an instantaneous, or space-wise drop distribution. The double-exposure photographs are then measured to determine the distance between successive images, and thus the velocity, of each size class of drops. By weighting the space-wise distribution with the drop velocities, one can obtain the desired time-wise spray distribution, This process has certain disadvantages. There is a human factor of judgement involved in the counting process, and all the developing, counting, transcribing, etc., tends to grow somewhat tedious. It is, however, the only method which is applicable to multiple emulsion work at this time, since only by direct visual observation is it possible to discriminate between the large drops and the inclusions, A more detailed discussion of certain of the factors in analysis will be made in the following sections,

V. EXPERIMENTAL EQUIPMENT The experimental equipment used for the majority of this investigation can be divided into four categories: 1) Liquid injection system. 2) Photolights and electronic time delay system. 3) Camera, film, and darkroom equipment. 4) Interfacial tension determination. V.1 Liquid Injection System Figure 13 shows the physical relationship of the camera, injection equipment, and photolights while taking data. Valves 2, 35 and 4 are 1/8" needle valves, while valves 1 and 5 are petcocks. The injection system consists of a charging funnel, a reservoir, a nitrogen supply to pressurize the reservoir, a metering system on the nitrogen stream, and a method for attaching a nozzle to the outlet stream from the reservoir. The injected fluid passes into the stagnant receiving fluid which is contained in the sample cello All lines shown in Figure 13 are 1/4" copper tubing. The reservoir is fabricated of stainless steel pipe, The funnel is a standard pyrex lab funnel about 3" in diameter, and is attached to the system by a short length of clear plastic tubing, This tubing serves as a sight glass for the liquid level in the reservoir while charging the system. Pressure is supplied by a standard nitrogen cylinder, and is regulated with an ordinary nitrogen pressure regulator. A ballast -26

-27 ROTAMETER PRESSURE REGULATOR Figure 13. Schematic Diagram of Experimental Equipment.

-28 tank fabricated of steel pipe coupled with a throttling valve (4) damps out pressure fluctuations caused by the pressure regulator. Valve 5 is a petcock used to shut off the nitrogen cylinder while charging the reservoir to avoid the slowness of using the cylinder valve. The nitrogen stream was metered at a known pressure by a rotameter. The pressure gauge is indicated as dial-type, however, both dial-type gauges and manometers were used, Calibrations for the pressure gauges are given in the Appendix. The rotameter used was a dual-float type manufactured by the Manostat Corporation, New York, New York, catalog number FM1043To The flowmeter had spherical floats, one of stainless steel and one of sapphire. Calibration curves for the pressures used are given in the Appendix. Room temperature was essentially constant - it was recorded, however, as a routine observation - but no temperature correction was required, As nozzles, standard Becton, Dickinson, and Company hypodermic needles were used, except that the ends were ground flat and the exit hole reamed. These nozzles were checked under a microscope to verify smoothness and lack of eccentricity, and the inside diameters are tabulated in Table I, L/D ratios were fairly large; however, many studies have indicated'' that this will not be a significant variable for the work considered here, The main effect of high L/D ratios is on discharge coefficient, and here the flow rate was measured directly. The needles were attached to the copper tubing by fabricating a connector using a Becton, Dickinson, and Company standard adapter

-29 TABLE I DIAMETERS OF HYPODERMIC NEEDLES USED AS INJECTION ORIFICES Size Designation Number 13 15 16 17 19 20 21 22 24 25 27 Inside Diameter, Millirmeters 1.87 1.42 lo 22 1.042 o642 o614.532.420 o317.277.229

-30 with a female "Luer-Lok" fitting for hypodermic needle on one end and a male thread on the other. The "Luer-Lok" fitting accepts the standard male "Luer-Lok" fitting on the hypodermic needle. The male thread was of a non-standard type, and so was filed smooth. The resulting surface was silver soldered into one side of a standard 1/4" copper tubing connector, which then was attached to the copper tubing from the reservoir, The sample cell which held the stagnant receiving phase was fabricated of 1/4" safety plate glass held in an angle iron frame, The five sheets of glass which comprised the bottom and four sides of the cell were held together with Carter epoxy resin glue. Some difficulty was experienced with leakage, and so the cell was also caulked on the outside with litharge-glycerol cement. This mitigated the problem, but no means was found to obviate it altogether..- a cell fabricated of a continuous piece of glass would do this but the cost is prohibitive. V.2 Lights and Time Delay System Photolights that were used were General Electric catalog number 9364688G. These lights give an extremely intense flash with a time duration of 1-2 microseconds. The lights were triggered with two time delay units constructed as shown in Figures 14 and 15. These units use number 2050 thyratrons for triggering, and can be adjusted to give time delays varying from about 10 microseconds to 1500 microseconds using the internal R-C network. Longer delays can be produced by adding an external capacitor. The two delay units were used in series,

POS PULSE NEG PULSE H I VERNIER Figure 14. Time Delay Unit.

5Y3GT 350-0-350 1002 20/450 4oon 10O -150v 20/450 20/450 EA 3VAC F igure 15. Power Supply for Time Delay Unit.

-33 with the trigger pulse to the first unit being supplied with a pushbutton. The first unit fired the first light and simultaneously supplied a pulse to the second delay unit. The second delay unit was set for the desired time delay, and upon receiving the pulse from the first unit delayed the desired interval and fired the second light, Time delays were measured each time the lights were fired by triggering a Hewlett Packard Model 524B counter (with a Model 526B time interval unit) from the pulse which triggered the lights. Prior to use of the light system in experimentation, checks were made using photocells to ensure that the response time of the lights, i.e., the time between receipt of the high voltage pulse and the flash, was negligible compared to the delays used. V.3 Camera, Film and Darkroom Equipment Two cameras were used - one with a magnification of 10X and the other with magnification of 2.6X. All counted data was taken using the 10X camera. Camera magnification, lenses, and depth of field calibrations are shown in the Appendix. Film used was Kodak Contrast Process Ortho 4" x 5" cut film. This is a fine-grained orthochromatic film with an ASA tungsten rating of 50. The film was developed for five minutes at 68~F. in Kodak D-ll developer, rinsed for 30 seconds, placed in Kodak Acid Fix for 10 minutes, rinsed for 30 second.s, placed in Kodak Hypo Clearing Agent for 2-3 minutes, rinsed for 10 minutes, and dried.

-34 V.4 Interfacial Tension Determination Interfacial tensions were determined using a Cenco (Central Scientific Co.) interfacial tensiometer type 70545. Manufacturer's serial number for this instrument was 410; the serial number of the Department of Chemical and Metallurgical Engineering was C7-80 The platinum ring used had a circumference of 5.998 cm. and was also manufactured by the Central Scientific Company (model 70542). It is interesting to note that in using a ring type tensiometer for interfacial tension (as opposed to surface tension) work it is necessary to lower the ring rather than raise it to avoid contamination by the second phase. This was not found to be an important consideration in work of the order of accuracy required here, but in more precise determinations an appreciable error can be introduced. Even though there was not a great difference in the readings obtained by raising and lowering the ring, all determinations were made from the values obtained by the conventional lowering method, Between each reading the ring was rinsed in potassium dichromate - sulfuric acid cleaning solution and rinsed in double distilled water as it was found that residual contamination after one reading affected reproducibility. Under very strict laboratory conditions, a ringtype tensiometer can be made accurate to.05 dyne/cm,, far in excess of the requirement for this work, The ring-type tensiometer has the advantage of speed over some of the other methods for interfacial tension determination such as capillary rise, drop weight, pendant drop, etc. A calibration curve for the interfacial tensiometer is given in the Appendix.

VI. EXPERIMENTAL PROCEDURE In taking data, the camera was first focused on the spray issuing from the orifice. This was done by using a ground glass screen in place of the film, and using a General Radio Corporation Model 1531A Strobotac for illumination. By setting the Strobotac for relatively low flashing rates it was possible to effectively "stop" the spray process for focusing purposes. This was a new technique in conjunction with the photographic method of analysis, and eliminated much of the trial and error focusing necessary when using a steady source of light. Most of the spray could be included in the field, so it was not necessary to traverse the spray to remove effects of non-uniformity. Experimental conditions during the course of a run were recorded on a standard mimeographed form, and pictures were normally taken in groups of 24. After developing and drying, each negative was stamped with an identification number and the corresponding number stamped on the data sheet. Approximately 1000 pictures were taken in the course of the investigation. The negatives were examined using a Jones and Lamson Bench Comparator, which projected an image of the negative on a ground glass screen, and gave a magnification factor of 10, so that the 2,6X negatives were examined at a total magnification of 26 and the 10X negatives at a total magnfication of 100o In Figure 16 through 19 are shown typical single and double flash shots, Figure 17 and -35

I! Figure 16. Print from Typical Double Flash Photo. Figure 17. Typical Double Flash Negative - lOX.

-37 I *sr 0) *ri O cAP a0 Ir O Q.-i 0 -H k P$ co CO H h0) p.

-38 19 show the appearance of the negative as it was counted; Figures 16 and 18 are conventional contact prints from the negative, Considerable detail has been lost in these prints over the original negative, but it is still possible to distinguish the inclusions nestling in some of the parent drops. The original negatives have sufficient detail to permit measurement of the diameters of the inclusions as well as of the parent dropso The drops were counted using a transparent template made by engraving a scale on a piece of clear photographic film. The same template was also used for distance measurements for the doubleexposure photographs. The appearance of the drops when magnified an additional 10 diameters over the magnifications in the photographs presented here is much as shown in Figure 20, It can be demonstrated that the inertial forces tend to control whether the inclusions rise or sink with respect to the main dropo The causes the clustering shown in Figure 20. Two remarks should be made at this point with regard to the human error in the analysis. First, the judgement factor as to whether or not a drop is in focus is much less important than in the usual spray analysis, because primarily relative areas, volumes, etc. are being measured, This will become apparent in the discussion of the analysis of the counted data, Second, the clustering of the inclusions in either the top or bottom of the parent drop makes analysis more uncertain, since it is difficult to estimate numbers and diameters of drops that are partially, or in some cases totally

-39Figure 20. Schematic Diagram of Drop Appearance During Counting,

-40 obscured, This tends to give results which may be systematically low for the included area and volume. The error should be more nearly self cancelling for diameter distribution measurements, but will still contain some bias since it is easier to obscure a small drop totally than-a large one, In effect, this would tend to skew the distribution toward the large size classes, Considering the relative numbers of drops in the small and large size ranges, however, coupled with the log normal form that the distribution takes as pointed out below, the effect on distribution measurements should be negligible. With some high rates of flow, difficulty was encountered in getting a sufficiently non-scattered light beam from the object drop to the lens, resulting in a loss of contrast, It was possible to overcome this difficulty to some degree by using the arrangement shown in Figure 21 to examine the negatives, The negative is illuminated by glancing light from an intense light source (in this case, light from a microscope illuninator)o This system makes the drops in focus stand out from the background, and also helps in discrimination between in-focus and out-of-focus drops, Typical drop travel data obtained from the double-exposure photographs is shown in Figure 22, Points shown are averages of many drop measurements; the velocity of drops of a given diameter will show a considerable range, and averaging facilitates the smoothing of the data, As can be seen from this typical run, velocity differences are more pronounced in the lower size ranges, as would be expected. Because of the shape of the parent distribution, the points plotted

SUPPORT NEGATIVE SOURCE H FLIGHT PATH M -LUCITE WINDOW Figure 21. Reflected Light Method for Examination of Figur~e 21. Reflected. Ligfht Method, for ~Examnation of Negatives.

.12.10 0.08 w ~ w.06.04.02 0 00.05.10.15.20 DROP DIAMETER, Cm Figure 22. Typical Drop Travel Data - Run Number 4. Io

-43 representing the lower siz.e ranges represent a larger sample of drops than those at larger diameters. From counting the single-exposure photographs, one obtains the distribution of large drops within a preselected series of size ranges, and the distribution of inclusions within another preselected series of size ranges according to the diameter of the parent drop, The counted data obtained can be depicted as shown in Figure 23. For M preselected size ranges we can characterize the diameter of the large drops by the mean diameter of the range, denoted by Dm(l < m < M; m = integer). Similarly we can preselect N size ranges for the inclusions and characterize them by their mean diameter dn(l < n < N;n = integer). Associated with the vector Di (i = 1,2,53.. M) there will be two vectors obtained from the drop counting process. The first is the distance vector, which we denote by i.' and which represents the distance traveled by drops in the respective size range obtained from the smoothed data as shown in Figure 22. Coupled with knowledge of the time delay used, this vector will yield our velocities, The second vector represents the number of drops, yi, of diameter Di which we observe in counting the single-flash photographs. We also obtain a matrix of values x.. (i = 1,2,3 o,, M; j = 1,2,3 o.. N), where xmn (1 m < M;1 < n < N) denotes the number of inclusions counted of size dn within a parent drop of size Dmo This data, coupled with the data on flow rate, interfacial tension, etc,, is fed to a computer program which carries out the routine calculations,

-44 LARGE DROP DIAMETER NUMBER OF LARGE DROPS DISTANCE OF TRAVEL OF LARGE DROPS I! I I I I I I I I 1 y1 2 l3 yi M! Yl Y2 Y3 i YM 1 ~2 85 i IM I I I I I dl'Xll X211 X31 INCLUSION DIAMETER d2 x12 X22 x32 d3 X13 X23 X33 r~~~~~~~~~~~ Xil x. xi2 xi3 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I,M1 _M2 s XM35 I I I I I I 1 j I I I I I I I I I dj | X2j tXj I Il I I.I I 1 I I I I I I I I I~~~~~~~~~~~~~~~~~~~~~~~ Figure 23. Schematic Diagram of Counted Data.

-45With regard to interfacial tension, it might be mentioned that checks were made on the fluids both before and after spraying to pick up any contamination effects from the equipment. No appreciable effects were found, and the interfacial tension of the fluids used would remain constant over extended periods of time.

VII. DISCUSSION AND RESULTS OF COUNTED DATA The experimental system used for the counted data was the carbon tetrachloride - water system. This system offers several advantages. First, it has been used by a number of investigators (8,37,67) working in the field of liquid-liquid sprays 3 ) Second, the non-flammability of carbon tetrachloride made it a convenient liquid to use in the open sample cell. Third, the first derivative of the interfacial tension - temperature curve for the carbon tetrachloride - water system is a known constant (d_ =.098)(89) permitting ready estimation of possible temperature effects. Fourth, the system offers a reasonable density difference. Finally, it was desirable to retain water as one component of the system since so much of emulsion technology utilizes water as one component. The selection of the independent variables to be studied is a sizeable problem in itself. For the moment, we will let it suffice to say that the independent variables used were nozzle diameter, velocity through the nozzle, density ratio of the two phases, and interfacial tension, VII. 1 Ranges of Variables Studied Three nozzle diameters were used: Q. 420 mm. (No. 22 hypodermic needle), 0. 642 mm. (No. 19 hypodermic needle), and 1.042 mm, (No, 17 hypodermic needle). Nozzle velocities ranged from 39 to 902 cmo/sec., and interfacial tension was run at two levels, 32.0 and 11.7 dynes/cm, Density ratio was varied by interchanging sprayed and receiving fluid -46

-47 with levels of.63 and 1.60 resulting. For the counted data, all runs were at a viscosity ratio of approximately 1,0; however, work done on mechanism was at a viscosity ratio of receiving fluid to sprayed fluid of about 1000, with the same mechanism operative, For this research, limits on the operating variables were these: 1) Nozzle diameters were limited at the low range by resolution of the camera system, and at the high range by the size reservoir and sample cell required, 2) Velocities through the nozzle were limited on the low side by cessation of multiple emulsion formation and on the high side by clouding of the sample cell. 3) Density ratio was limited by the combination of cost and physical and chemical properties of available liquids. 4) Viscosity ratios are limited both above and below by the combination of nozzle diameter and pressure required. Small diameter nozzles require excessive pressures to attain the required flow velocity, while large diameters have the limitation noted above.

-48 VII.2 Typical Raw Data Results Shown in Table II: are the results for a typical set of counted data.. (Complete raw data may be found in Appendix D. ) This information is fed into a computer program (see Appendix) which carries out the detailed mathematical manipulation, The diameter ranges for large drops and inclusions were the same for all runs, From the counted data it was possible to study two things. First, it was possible to determine a probability distribution function which would adequately represent the distribution of the large drops and that of the inclusions, It was then possible to correlate certain parameters of the process against the independent variables. Table III gives experimental conditions for the various runs and some of the more important derived data, VII,3 Determination of Probability Density Functions In order to use a given function f(z) as a probability density function there are two primary criteria that must be met: (z) - 0 (VIIo, o1) too -(z) dz- = I (continuous case) (VII, 3.2) Z f (7 AZi I (discrete case) If these two criteria are fulfilled, and if in addition we can demonstrate that, for the random variable Z: PR C Z.) = J fzz) t (VII..33) -oo

TABLE II TYPICAL RAW DATA SET - RUN NUMBER 10 System: Saturated Carbon Tetrachloride into Saturated Water Flow Rate: 130 cc/min. Nozzle Diameter:.0642 cm. Interfacial Tension: 32 dynes/cm. Viscosity of Flowing Phase: 1 cps. Density of Flowing Phase: 1.595 gm./cc. Time Delay: 1.55 x 10-3 sec. Numberr of JInclusions by Size Range,. cm. x 102 Large Drop Size Range cm. x 10-2 No., Large Drops Average Distance, cm. x 102 0.-.5.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-53.5 3.5-4.0 4,0-4,5 0.- 1 - 2.- 3.- 4.- 5.1. 2. 3. 4. 5. 6. 6.- 7.- 8.- 9.7. 8. 9. 10. 193 304 140 63 36 15 11 11 7 4 3 2 1.75 2.10 2.45 2.80 3.10 3.40 3.75 4.10 4. 40 4.75 5.10 5.45 4\kO I 0 11 17 5 11 15 11 14 4 0 2 14 12 9 13 9 6 3 0 0 8 13 28 4 15 17 22 0 0 0 6 6 6 5 5 10 0 0 0 2 7 5 1 5 12 0 0 0 0 1 1 0 1 0 0 0 0 0 1 2 3 2 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 10. - 11. - 11. 12. 5 0 0 9 0 1 6 6 8 5 11 4 4 0 0 2 1 0 1 1 2 O O O 1 1 0

TABLE III EXPERIMENTAL CONDITIONS AND DERIVED DATA Run Nozzle Flow Rate Velocity Interfacial Reynolds Weber Reynolds No. No. Diameter, cm3/sec. Through Tension Number Number x Weber No. cm. Nozzle Dynes/cm. cm/sec. System % Included % Included Volume Area Large Drops Inclusions D32 D10 Log Geom. d32 dlo Log Geom. cm. cm. Std.Dev'n cm. cm. Std.Dev'n 1.1042 2.1042 4.1042 5.1042 7.0642 8.0642 9.0642 10.0642 11.0642 13.0642 14.0o642 15.0642 16.0642 4.58 4.58 1.53.333 1.50 2.17 2.17 2.17.834.750 1.50 1.33.918 557 32.0 89.3 1500 1.34 x 105 CC14 into H20 537 32.0 89.3 1500 1.34 x 105 CC14 into EO 180 32.0 29.8 167 4.99 x 103 CC14 into EBO 39 32.0 6.49 7.92 5.14 x 101 CC14 into H20 463 32.0 670 32.0 670 32.0 670 52.0 258 32.0 232 11.7 463 11.7 411 32.0 284 32.0 47.5 687 326 x 10 CC14 into H20 68.6 1440 987 x 104 CC04 into H20. x 1 C14 into 20 68.6 1440 9.87 x 104 CC14 into H20 68.6 1440 9.87 x 104 CC14 into H20 26.4 212 5.60 x 103 CC14 into H20 23.7 470 1.12 x 104 CC14 into H20 47.5 1880 8.93 x 10 CC14 into H20 26.4 339 8.94 x 103 H20 into Ce14 18.2 161 2.94 x 103 H20 into CC14 5.33 5.59 0.00 0.00 2.68 5.05 6.76 6.01 0.00 3.05 7.50 3.64 2.21 17.9.0232.0305.309.0138.0164.262 17.4.0237.0304.295.0132.0154.250 0.00.0397.0678.379 0.00.215.220.060 -- -- - 10.4 16.2 17.5 16.9 0.00 10.6 18.9 13.2 8.88.0197.0295.379.00940.0115.294.0146.0186.314.00867.0103.272.0160.0206.314.oo843.0106.310.0153.0196.314.00854.0104.292.0367.0810.404 -- --.0159.0220.354.00861.0107.308.0159.0194.277.00840.00958.242.0153.0190.295.00899.0102.236.0177.0238 334.00894.0103.251 0 O 1 6.0420 12.0420 17.0420 18.0420.367 1.25.517.833 264 32.0 17.7 17.7 2.61 x 103 cc14 into H20 902 32.0 60.4 60.4 1.03 x 105 CC14 into H20 373 32.0 15.7 15.7 2.86 x 103 H20 into CC14 601 32.0 25.2 25.2 1.19 x 104 H20 into CC14 1.55 4.28 1.13 3.27 5.40.0246.0332.311.00727.00861.279 12.1.0133.0157.262.00662.00770.267 3.67.0220.0274.281.00904.0101.226 7.01.0136.0162.268.00996.0112.226

-51 we may say that f(z) is the probability density function for Zo An analogous definition holds for the discrete case. We will here restrict discussion to continuous random variables, since there is no discrete density function commonly used in particulate statistics, In addition to the probability density function, we can define a probability distribution function as a simple integral transformation of the density function: F (Z) \ -)c (VII.5.4) The random variable Z can be associated with any characteristic of the spray for which a probability density or distribution function can be determined. Most small particle statistics work has associated F(z) or f(z) with either the number or weight distribution dV dN S w of particles (f(z) = d or N). Since we can write: dz dz - - V (VII~35) dV dr4 dV dA dz dZ (VIIo3.6) (VIIo307) 6 dz dz where: N = number of drops z = diameter of drops V = volume of drops or, for estimates from our samples IT -_ = Z (VIIo308) A( Z9

-52 we can obviously transpose a number distribution to a weight distribution, and similarly for other diameter-related functions. It should be noted that although F(z) and f(z) are associated with the weight or number distributions the functions are still written in terms of the diameter, although this is not necessary. There have been many probability density functions proposed for use in spray research. Most of these are some specialization of a function of the type: (65 i -Ye (z = c - 6e (VII. 359) The decision as to which distribution to use must be made on purely pragmatic grounds - it is occasionally possible to justify a given distribution on theoretical grounds, but almost always by post hoc reasoning. We will consider here the use of the three density functions most common in spray work: 1) The Log-Normal Distribution'2NVt' (9 = -/ (VII..o10) where - and zg = geometric mean ag = geometric standard deviation. 2) The Rosin-Rammler Distribution (Z = Z (VIIo311)

-53 3) The Nukiyama-Tanasawa Distribution 2 -z V (L) caLZ (VII, 3512) The log-normal distribution arises as a natural successor to the normal distribution where ratios rather than differences are important, i.e, cases where the geometric, rather than the arithmetic mean is important. The Rosin-Rammler distribution was originally developed for particulate solids, but has found sOme application to sprays, and the Nukiyama-Tanasawa function was developed for liquid-into-gas sprays. 5) All three of these density functions are integrable as special cases of the incomplete gamma function:(7) \Q( jt e dt (VII. n.135) This is a tabulated function available in standard references, Transformations used for the integration are shown in Table IV, along with the resultant distribution functions, The Rosin Rammler function is usually applied to the volume distribution in the form given, and the Nukiyama-Tanasawa equation to the number distribution (65) The main difference in the above distributions is that the log-normal distribution has two parameters, the geometric mean and variance; the Rosin-Rammler distribution has two parameters plus a pre-exponential term; and the Nukiyama-Tanasawa equation has a preexponential term and three parameters, The data can be tested for fit to the various distributions in the following ways. The log-normal distribution is easily tested

-54 TABLE IV TRANSFORMATIONS AND INTEGRALS FOR DENSITY FUNCTIONS Transformation Distribution Fcto Log Normal Rosin Raimler Nukiyama-Tanasawa 1 2 z2 t 2= 2 F(z) = 2J- r2/2( 2 2 F~z/ F(z) = b n(l) = (1- e-bx bz t = bzn 3 = n t = bzn )nb/n bzn(n) TABLE V TYPICAL LARGE DROP AND INCLUSION DISTRIBUTION DATA - RUN NO, 13 Large Drops Size Range cm. 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 Size Range cm. 0-.'5.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 Cumulative Percent of Drops 21 7 42 7 63.2 74.9 83.8 89.2 91.5 93.0 95.2 96.8 Cumulative Percent of Inclusions 16.6 44.0 68.9 76.8 85.6 91.9 95.2 Inclusions

-55 by plotting on log-probability paper the estimates of the probability distribution function F(z). These estimates may be obtained from the computer program as the cumulative percent of drops observed below the given diameter (in this case, the upper limit of the size range): F( D we) = g - OM) (VIL3514) i1 A? / l. -~~JElJ —1 (14 ts' ~(VII5o315) Plotting the estimates of F(z) versus Di and dj respectively should yield a straight line on log-probability paper if a fit to the log normal distribution is obtained. A typical run is shown in Figure 24 and Table V. (Log normal plots for all runs may be found in Appendix D ) It should be noted that the end points have been truncated from the curves since it is impossible to fit a straight line to any finite consist using the infinite range distribution functions applied here. (Obviously there will be a maximum and minimum diameter for the particles, while the given distribution functions approach upper and lower limits asymptotically.) Since the Rosin-Rammler function shown is applicable to volumes, we require our estimates to come from the distribution weighted by the third power of our random variable, diameter: F ( GD =' (vI..6) i -, I ^(vII 316)

-56 99 Lu Z LJ 4 C z 5 Z UJ Lo -J U) (I a. O 1 I. 0 98 95 90 80 70 60 50 40 30 20 10 10 I0 DROP DIAMETER, Cm Figure 24. Typical Fit of Log-Normal Function to Large Drop and Inclusion Distributions - Run Number 13.

-57 1'3 A (d di-l 7- E d t a (VII 3. 17) i l \ig I 0 X These again are readily obtained from the computer program. Now, if we replace F(z) by (1 - F(z)) in the distribution function, we have: Cl-F(Z - eC - (VII,30,8) where G(z) = 1- F(z) taking logarithms twice, we have: (lT LCG(2iG = Q \l -Y - L - -,e (VII.3o19) This is a linear relationship in log log [G(z)] and log z, Hence a plot of log log [G(z)] against log z should give a straight line if the data follows the Rosin-Rammler distribution. Results are shown for the large drops of a typical run in Figure 25 and Table VIo Fits for inclusions are similar. For this particular run, values of n = 3.05 and = 865 were obtained, It is interesting to note that associating the given distribution function with the number distribution rather than the volume distribution gives as good a fit (see Table VII and Figure 26), with n = 1,14 and = 50.2. The variation in n reflects the skewness of the number distribution toward the smaller diameters and of the volume distribution toward the larger diameters, With the Nukiyama-Tanasawa distribution we once again are concerned with the number distribution, with estimates of f(z) obtained as the percent (rather than cumulative percent) of drops in the given size range. Here, however, we have three parameters to fit. Dividing the

-58 TABLE VI TYPICAL DATA SET FITTED BY THE ROSIN-RAMMLER FUNCTION APPLIED TO THE VOLUME DISTRIBUTION Data Set No. 13, Distribution of Large Drops Drop Diameter Cumulative Number Log Log [G(Dm)] cm x 10= Dm = F(Dm) x 100 1.019 -4.097 2.52 -2.646 3 2.77 -1.913 4 6.34 -1.546 5 12.04 -1.254 6 18.42 -l.054 7 22.87 -.958 8 27.29 -.859 9 36.64 -.703 10 46.27 -.569 Log Diameter -2. 000 -1.699 -1,523 -1 398 -1, 301 -1 222 -1,155 -1.097 -1o046 -1o 000

-59 0 -I.0 0 E -.j -3.0 -4.0 -2.0 LOG (Dm) Figure 25. Fit of Rosin-Rammler Function to Run 13 Volume Distribution.

-60 TABLE VII TYPICAL DATA SET FITTED BY THE ROSIN-RAMMLER FUNCTION APPLIED TO THE NUMBER DISTRIBUTION Data Set No, 13, Distribution of Large Drops Drop Diameter cm x 10-2= Dm 1 2 4 5 6 7 8 9 10 Cumulative Number % = F(Dm) x 100 21. 70 42,74 63.16 74.93 83080 89.23 91.52 93501 95.16 96,76 Log Log [G(Dm)] - 9737 -. 616o -o3628 -.2212 -. 1021 - o0143 00301,0628.1191.1728 Log Diameter -2 000 -1,699 -1.523 -1 398 -1 301 -1,222 -1 155 -1,097 -10o46 -1 000

0.4 r -0 — 2 ~ o, -0.6 -0.8 -1.0 " 2.0 -1.5 -1 LOG (Dm) Figure 26. Fit of Rosin-Rammler Function to Run 13 Number Distribution.

-62 density function by z2 and taking logarithms we have: 1[Z"b- ^1 = R+ ~-^-L Li e (VII.3.20) Our estimates have the form: f(DY, =,4 - 0 Ai) (VIo3.21) E1 VYi (i,) = -,~ ~~ I> e (vII. 3 22) Here we have a linear function in b and a given a valve of no Nukiyama and Tanaswa found n = 1/4 to give the best fit. Shown in Figure 27 and Table VIII is the result using n = 1/4. Values obtained are a = 5,75 x 109 and b = 31,08. These are of the same order of magnitude as those values obtained by Nukiyama and Tanasawa in their liquid-intogas sprays. In Table VIII and Figure 28 is shown the result of using n = 1/2. No appreciably better fit was obtained. Since the two more sophisticated functions show no better fit to the experimental data than the log-normal function, there is no justification for using the more complicated models on the basis of this worko It has often been said that the normal distribution is to statistics what the straight line is to geometry, and so it would be extremely unwise to abandon the log-normal form of distribution without well based justification, It is interesting to observe that the log-normal form of distribution will hold even down into the varicose breakup (see Section VIII) regime for the large drops (see Figure 29). The change

-63 TABLE VIII TYPICAL DATA SET FITTED BY THE NUKIYAMA TANASAWA FUNCTION, n = 1/4 and n = 1/2 Run Number 135 Large Drops Dm/2 1/4 1. 2DM Dm f(Dm)X 100 Log [1- w 7 D m n A f (D M) cm x 10 1.0 2.0 3.0 4. o0 5.0 6.0 7.0 8,0 9.0 10o0.1000.1414.1732.2000.2236.2449.2646.2828.3000.3162.316. 0375.416.447.473.495.514.532.548.561 7~ 21 7 21.0 20.4 11.8 8.87 5.43 2.30 1.49 2,15 1.59 m 5. 336 4,720 4.356 30868 3.550 3.179 2. 671 20367 2. 423 2 201

5.0 0 waE 0 3.0 0 2.2.,.31.35.40.45.50 114 Dm Figure 27. Fit of Nukiyama-Tanasawa Function to Run 13 Data, n = 1/4..55

E 0 -J ~0 \1!n I 112 DmFigure 28. Fit of ui Fuctio to Ru 1 Figure 28. Fit of Nukiyama-Tanasawa Function to Run 13 Data, n = 1/2.

-66 a w z Q4 CI Iw (I) () 0. 0 a I. 0 90 80 70 60 50 40 30 20 10 5 2 i I I I 1 A 1 - -. — I I L I I I I I I -- L I I O..1I 10 DROP DIAMETER, Cm Figure 29. Log Normal Function Fitted to Distribution Data from Varicose Breakup.

-67 from one type of breakup to the other is reflected merely in changes in the mean and variance of the distribution, We have determined above the probability density functions for the large drops and for the inclusions, We must note, however, that the distribution for the inclusions has been treated independently of that of the large drops. Our data for the inclusions, though, implies that there may be an additional consideration. The number of inclusions, xij, is classified not only with respect to the inclusion diameter, but also with respect to the diameter of the large drop within which the inclusion is found. The next question one might ask is whether the same form of distribution function holds for inclusions within large drops of a specified diameter as holds for inclusions irrespective of the large drops; in statistical language, are the marginal and conditional distributions identical? Based on the data obtained in this study, there is no adequate reason to reject the hypothesis that the marginal distribution function of the inclusions is identical with the conditional inclusion distribution, given a range of large drop diameters. Shown in Table IX and Figure 30 is a typical set of data, Note that all the mean diameters for the inclusions obtained from the conditional distribution lie within one standard deviation of all others in Table IXo Figure 30 is a plot of data for one conditional distribution as noted, VIIo4 Correlation of Multiple Emulsion Parameters The most immediate observation from considering the relationship of the distribution of inclusions to that of the large drops is that the large drops contain a much higher number of inclusions than

-68 99 Ic w a z I') C) U) z o0 u) o 0 U0*e 98 95 90 80 70 60 50 40 I111i I I I 11111. I ] -' —-- ---- --- -- -. -~-t -y / _c~~~~ 30 20 10 _1 5xl0 i6 la INCLUSION DIAMETER, Cm Typical Data for Conditional Distribution of Inclusions. Figure 30.

-69 TABLE IX CONDITIONAL DISTRIBUTION PARAMETERS OF INCLUSIONS FOR A TYPICAL RUN Large Drop Size Range cm x 10 4-5 5-6 6-7 7-8 8-9 9-10 Number Inclusions 63 47 44 52 53 33 Run Number 10 Inclusion Log Geometric Mean dm -1 9846 -2.0662 -2 o438 -2. 0025 -1o 8626 -1o9539 Inclusion Geometric Mean d cm x 10-2.1036.0859.0904.0994.1372.1112 Inclusion Log Geometric Standard Deviation o2633.3374.2920.3270 o2241.3067 the smaller drops. This can be seen graphically in Figure 31 and Table Xo Stating the matter in a slightly different way, we can say that here the smallest four size classes contained 835,96% of the large drops and only 15009% of the inclusions, a ratio of 5,6 while the largest four size classes contained only 665% of the large drops but 12,89% of the inclusions, a ratio of 5.2 x 10 2 The number of inclusions per drop is of the order of 10-20 in the largest diameter drops, but less than 1 in the smallest diameter drops. This observation fits well with the proposed mechanism discussed below. A second matter of interest arises with regard to what mean drop diameter should be used to characterize the distribution of large

-70 TABLE X NUMBER OF INCLUSIONS PER LARGE DROP AS A FUNCTION OF LARGE DROP DIAMETER Pooled Data From Runs 7, 10, 13, 14, 15, 1 Nozzle Diameter =.0642 cm. Dp Number Number r Large Inclusions Drops Large Drc Diametei cm x 10O 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 519 817 471 232 148 65 42 35 32 22 11 12 6 5 4 3 4 0 26 lo4 97 194 151 130 131 149 128 71 86 44 34 35 44 81 L6 Inclusions Per Large Drop 0.000.0318.221.418 10311 2, 323 3.095 3 743 4.656 5.818 6.455 7.167 7.333 6.800 8.750 14.67 20,25

-71 0 o 1.0(e z C) - -J z 0 z'10 0.01 0.01 0.1 1.0 LARGE DROP DIAMETER, Cm Figure 31. Number of Inclusions per Drop as a Function of Large Drop Diameter.

-72 drops and that of the inclusions, We can define the expectation, E(z) of a random variable Z as: E(7z = \ Z. ( L) \ (VII.4.1) Similarly, we can from the expectation write a generalized mean diameter as: [ E (_ ) ] (VII o42) Using this defintion, we can write immediately the mean diameters most commonly used in spray work: 7 E (Z) = "tLength" (here diameter) Mean (VIIo 453) Z Z ( 2) = Surface Mean (VIo 4,4) o30- E (L ) = Volume Mean (VII 4 5) Z3 i ) = Sauter or Volume-Surface Mean (VIIo 4 6) The Sauter mean diameter can be thought of as that diameter which, if the spray were made up only of drops of that diameter, would yield the same surface and volume as that possessed by the original spray. The Sauter mean can be related to specific surface by writing: 3 v_ f"~' to Lz3" (VIIo4.7) k... " V,, L z3-, (viio 48) where n = number of drops.

-73 Then: Aspray 6 Specific Surface = Vspr (VII. 49) spray z32 As can be seen from the above definitions, z20 and z30 are merely the second and third moments of the density function f(z)o Now the log-normal distribution is uniquely defined by the geometric mean and variance, and further, the estimated mean and variance are sufficient statistics for this distribution. In other words, based on a sample Y1, Y2' ~~. YM or xll, x12, o.. xMN we can estimate the mean and variance but no more information can be obtained from the data. This is a well known statistical result. What implication does this have for our analysis? It means that once we have determined the log-normal distribution to be the best fitting for the data, it does not matter in any essential detail what mean diameter we choose to correlate against, so long as we estimate variance along with our selected mean diameter, Certainly some means may give more convenient graphical representations, etc., but scatter of data will not be affected. This can be seen graphically in Figure 32, where the first six weighted distributions of typical data are plotted, with the only change being in 50% intercept (mean) and slope (variance). It is instructive to plot the points for zlO versus z32 obtained using the experimental results. Estimating zpq from the sample, we can write (for the inclusions): d —-- -i1 ^~ & J ~~ ^ m1 ~ x, lEditi&)U~~~~ L~g EVII.4.l) ctio A~z, Adam ja datia.z daze I td5 A&

-74 90 W. w 50 w 10 XA I,I —. _ 10 J. 0 0-011. I II. 0, a1, 6, OI.! - I' 7 - -t 0I.01 I', DROP DIAMETER, Cm Figure 32. Typical Data for Weighted Drop Distribution. Figure 132. Typical Data for Weighted Drop Distribution.

-75 and applying the Cauchy inequality: to each bracketed term on the right hand side, using, S, 1/ b,'d'-lb (viio 4 11) (Vii,,4,,12) and ~I/z V OL = 1?', = A = dg ti( (VIIo 4 13) we can see that: d^' d. (vIIo 4 14) The equality holds only for a point distribution, and the difference between ZlO and z32 is a measure of the spread of the distribution, Figure 33 is the plot of the data obtained here. The 45~ line represents the equality: dA a 32 (VI.4.15) There is insufficient data to make estimates using Figures 33 and 34; however, the apparent relationship of D32 and D10, and d32 and dlo suggests that the mean and the variance of the distributions may be related, If this relationship can be elucidated with more data, we may be able eventually to reduce our distribution functions to one parameter functionso That is, we can calculate some estimated mean diameter, and then use a relation of the form: = j (mean diameter) ( r- = std. deviation) (VIIo 4, 16)

015 E 0 0.010 dio, Cm Figure 33. d32 versus dl0.

.025 E I0.015 I I.015.020.025.030 Dlo,Cm Figure 34. D versus D0

-78 to calculate standard deviation directly. If such an approach is possible, it would be possible to characterize the spray completely by simply giving a mean diameter. Figures 33 and 34 suggest that standard deviation varies directly with mean. The parameters of most immediate commercial interest are, of course, the percent included surface area and percent included volume, defined here as: Includ Ara Total Surface Area of Inclusions x 100 ( ~.Included Area~............... x 100 (VII, 417) Inc d Aa Total External Surface of Large Drops % Included Volume Total Volume of Inclusions (vi4 ~ Included Volume..... x LO0 (vII. 4,18) Total Volume Enclosed by External Surface of Large Drops Definition was made in this manner so ready estimates of effects on existing data could be made. The question of what independent variables to correlate against becomes somewhat involved here. It is probable that there are at least seven important independent variables in the process: 1) nozzle diameter 2) velocity through the nozzle 3) density of sprayed phase 4) density of receiving phase 5) interfacial tension 6) viscosity of sprayed phase 7) viscosity of receiving phase To vary these seven factors at only three levels, using a complete factorial design with no replication (using higher order interactions to estimate error) would require 7 = 2187 experiments (21)

-79 Two of the above variables were (in effect) eliminated by working with liquid pairs of essentially the sane viscosity, This procedure will still give widely applicable results as many liquids used in dispersion processes have viscosities close to 1 cps, the value used. This will still leave 35 = 243 experiments necessary to test the variables separately. The obvious solution to the problem is to place further restraints on the system by dimensionless groupings of the variables, Two of the most widely used dimensionless groups in spray processes are the Reynolds number, representing the ratio of inertial to viscous forces, and the Weber number, representing the ratio of inertial to interfacial forces, here defined as: DR5, P U — (VII. 4. 19) (f,= P 6 VIi4.020) where Dn = nozzle diameter vn = velocity through nozzle p = density of sprayed phase Is = viscosity of sprayed phase y = interfacial tension An extremely naive model, but one which permits a reasonable correlation of the data is a linear model for the relationship of the logarithms:

-80 r (7e oNO"D vot^.) V, (-l"1; j(v 41 -' (VII.4.21) d (70 INCLUDED EAZSA) - an/ ".6 k -, i., (VII.4.22) A least squares fit was run on this model and the results are shown in Figures 35 and 36. These are the best fitting straight lines using maximum likelihood estimation. The 95% confidence limits are shown for each case. Correlation coefficients for these two models were ~88 and.83 respectively. A check on experimental error was made in runs 8 and 9 of the experimental worko We can estimate error variance using standard tables of the relative range.(7) The 95% limits for % included area were plus or minus 2.25% at about the 17% levelo Observed unexplained variation can be seen from Figure 36 to be of this order of magnitudeo This means the residual variation (scatter) can probably be explained by experimental error. A similar argument holds for the % included volume plot. The scatter is somewhat worse in the % included area case than for the % included volume correlation. This can be explained to a large extent by Figure 37, which shows a curvature when % included area is plotted versus % included volume on log-log paper, demonstrating that the proposed linear model cannot fit both cases, It is straightforward to fit a higher order model to % included area, but such models are notoriously untrustworthy for extrapolation, It would perhaps be preferable to estimate % included volume by the given function and

30 0 |o 1.0 dzo0.1 -.04, i2 3 104 15 106 2x106 (Re) (wE) I QXI I Figure 35. Percent Included Volume as a Function of Re x We.

30 950 % LIMITS-. 10 — __ ___________ _____ I7x 10 104 o1 2x10, (RE) (WE) Figure 36. Percent Included Area as a Function of Re x We. I Uo I

-83 20 I / III1 C,1 _1~~~~~~~~~~~~I ~~10 % INCLUDED VOLUME Figure 37. Percent Included Area as a Function of Percent Included Volume.

then use an estimate of mean diameter and variance to derive % included area using the log-normal distribution, since the mean and variance of the inclusion diameters appear to be quite insensitive functions, The linear model of the type: Area Log(% included )= ml, R 4[]4rE + (VI.4,25) Volume VII 2 was also fitted using multiple regression techniques, with no significant improvement in correlation, Consequently, the additional parameter was not introduced. With sufficient experimental results, a test of the model: Area Log(% included ra ) = a D + tM 3 PS (VII 4 24) Volume + ^ P ~ 4- +M LiS b' mV would probably suggest relationships applicable to a general liquid pairo Based on the correlations shown here, it is merely, possible to conclude that the linear relationship used can be utilized to correlate data for a liquid pair with viscosities about 1 cps, This model indicates that inertial forces play a much more dominant role in the inclusion forming process than do interfacial forces, Before discovery of the mechanism involved, it was surprising that a correlation based on nozzle parameters would prove adequate; however, in light of the mechanism discussed below, it is not surprising that such an approach yields a good first approximationo

VIII. DETERMINATION OF MECHANISM In most of the published literature on sprays, it is customary to distinguish about four stages in the breakup process of a jet exhibiting surface or interfacial tension: 1) Varicose breakup, where the jet is "pinched off" through the growth of symmetrical disturbances, (Figure 38). 2) Sinuous breakup, where the jet is broken into columns through a "flag waving" action, the columns then disintegrating by varicose breakupo (Figure 39). 3) Ligament formation, where initial disturbances are drawn out in the form of ligaments which detach and collapse into drops'(Figure 40). 4) Disruptive breakup, where the jet disintegrates immediately upon leaving the confinement of the nozzle. There are, of course, secondary breakup processes which involve the splitting of the larger drops after the jet has disintegrated, In the carbon tetrrachloride - water system used for the counted data, breakup was exterior to the nozzle, with a varying length of undisturbed jet, as shown in Figure 41, In low viscosity systems such as this, breakup of the liquid jet always took place over such a short distance that it was not possible to distinguish mechanism of -85

-86 B O N4 o v/ O 0 0 0 0 Figure 39. Sinuous Breakup. o O 0 0 o O Figure 40. Ligament-Type Breakup. Figure 38. Varicose Breakup.

Figure 41. Typical Photograph of Jet Breakup in Low Viscosity System - 2.6X.

-88 inclusion formation. Accordingly, runs were made using a low viscosity sprayed phase (carbon tetrachloride) and a highly viscous receiving fluid (glycerine). Results were immediate and gratifyingo Shown in Figure 42 to Figure 45 is a series of pictures taken with this liquid pair at progressively increasing nozzle velocities, As shown in the photographs, the high viscosity of the glycerine receiving phase kept breakup of the jet in the varicose regime, A most embarrassing point in the analysis of the data to this time had been the question of how the inclusions could penetrate the relatively stable large drop configuration in order to get inside. The answer yielded by this set of photographs was that the inclusions were present in the jet before it disintegrated - the inclusions literally pre-date the large drops. Next, pictures were taken closer to the nozzle, to attempt to catch the inclusions forming. Results are shown in Figures 46 and 47, The mechanism can be seen to be the sequence of events shown in Figure 48. A ligament or sheet is drawn out from the jet, but instead of breaking off, it recoalesces with the jet, pinching off some of the external phase in the process. This elongated form then collapses to yield a drop or drops within the jeto The same mechanism is operative at various nozzle diameters, as can be seen in Figures 49 through 55. Figure 52 shows an inclusion just beginning to form, while Figures 53, 54, and 55 show to what lengths the penetration of the jet can reach, as well as the teardrop shape exhibited by the inclusions after detaching from the external phase and before being forced into a spherical configuration by the surface forces, It is interesting to note that a similar appearance can be distinguished in Figures 7 through 12, the transient case.

I CC \I I Figure 42. Carbon Tetrachloride into Glycerine - No. 19 Hypodermic Needle, 5-1/2 cm. From Orifice - lOX - Re = 7.4. Figure 43. Carbon Tetrachloride into No. 19 Hypodermic Needle, From Orifice - 10OX - Re = Glycerine - 5-1/2 cm. 35.9.

0 O! Figure 44. Carbon Tetrachloride into GlyceriLe - No. 19 Hypodermic Needle, 5-1/2 cm. From Orifice - lOX - Re - 48.6. Figure 45. Carbon Tetrachloride into GlycerineNo. 19 Hypodermic Needle, 5-1/2 cm. From Orifice - 10X - Re 653.4.

,:::::,i:,:s-: F,Z ::I Ir::Q,, I::,:i'iii A 8: a:::::::::-:: i:::':'::'::::::::::::i::-::::i::i: i~::::::::il:,:::,,,::::,::::::::,-:::: i::::::::~: iii::I:s:::::,:_,:::::::::::ii:i:iji::::::::::-:ii:'i:ii~.:::::':ii:'':i':::"ii.::ii:i':'ii-~ii:.:n:a: ~::':::::::~:::: iii::::.::-::'iil:::i:::i::::ii::::iiiC.i~ig ii::::::::,::i:l::::s::: i: i:,:.:::; ii:i:'::::::::i::i:::ii":il:i'::::::: i::::: ii::::':':::':'::-' I H Figure 46. Carbon Tstrachloride into Glycerine - No. 19 Hypodermic Needle, at Orifice - lOX - Re - 39.6. Figure 47. Carbon Tetrachloride into No. 19 Hypodermic Needle, From Orifice - 10X - Re = Glycerine - 2.5 cm. 47.5.

-92 Figure 48. Schematic Depiction of Mechanism.

I \O k~ Figure 49. Carbon Tetrachloride into Glycerine - No. 22 Hypodermic Needle - lOX - Re = 8.88. Figure 50. Carbon Tetrachloride into Glycerine - No. 22 Hypodermic Needle - 10X - Re = 30.6.

I Figure 51. Carbon Tetrachloride into Glycerine - No. 22 Hypodermic Needle - 10X - Re = 42, o.

::ri;:::i —ihrii;i'ilirl~~-~~,~,::li:~~i~i'l-~li~i":':~:rl~i~'i-i'!a:~i:-iai:i~~i- i:'j-iiiifi$i- iI.':S~:':::~:'';:::::::.:::-D: ~i:i~iiii::iii~:''~':::::;-:'.::':: i~':i:'ii~::i-::::ii-ni::::~::::~ -i;li::ii-~i:~:i:-:: l~~.::i::::i::ii:-: -.~:::::::,~::::::1::-:::;::: i,.:~ia,~iai:-iI\ F igure 53. C~~~~~~~~~~~~~~~~~~~~~~~ebon T~~~~~~~~~~. etaeoid;~~:~ii_.~.:::::::~ ~:~i:ii~.:',.:-~iil-`: e:::: into Gii~ ly er~.i::~:.iiine-: No. I~:i-,i.lFi~::~~: 17 Hypodermi:~;ic Nedl:::i-::::ij.-ii 1 0 X - 4 cm. From, Orif..,:ice:: -::;: R e:-:::::":: 33..::_:.i;:i: Figure 52. Carbon Tetrachloride into Glycerine - No, 17 Hypodermic Needle - lOX - 4 cm. From Orifice - Re = 24.6.

I Figure 54, Carbon Tetrachloride into Glycerine - No. 17 Hypodermic Needle - 10X - 4 cm, From Orifice - Re = 60.,3 Figure 55. Carbon Tetrachloride into GlycerineNo. 17 Hypodermic Needle - 10X - 4 cm. From Orifice - Re = 71.4.

-97 Another important observation that could be made using this viscous system was that the coalescence of the inclusions was extremely rapid. From a jet literally packed full of included drops as shown in Figure 45, a large drop would detach with much the appearance shown in Figure 56a, The inclusions coalesce rapidly out through the large drop wall, and by the time the drop reaches the bottom of the cell, it has an appearance much as shown in Figure 56c, all in a time of the order of one second. The rapid coalescence rate indicates that this is perhaps the reason that multiple emulsions are so seldom observed in liquid-liquid work, Measurements are usually taken on a stagnant system rather than a dynamic one, and by the time the observation is made, the inclusions have disappeared. The systems where multiple emulsions have been observed, as in the work by Boll and that by Pavloshenko and Yanishevskii discussed earlier, have either been very viscous systems or heterogeneous systems with possible stabilizing surfactantSo A logical conclusion would seem to be that the flow pattern which spawns inclusion formation probably occurs in very nearly all liquid-liquid processes, but that coalescence is so rapid in most cases that the inclusions are never observed, For any sort of macroscopic approach, inclusion surface area would merely be lumped in the mass transfer coefficient, and coalescence would give observed effects which would be regarded as anomalies in the transfer coefficient rather than the interfacial area, It is instructive to examine some more of the counted data in light of the proposed mechanism, Since the inclusions are formed

-98 a. b. c. Figure 56. Schematic Diagram of Inclusion Coalescence.

-99 more or less independently of the large drops, we would expect little or no relationship between the diameter of a large drop and the mean diameter of the inclusion within that drop, other than the obvious limitation that inclusion diameter cannot exceed large drop diameter. Shown in Figure 57 is such a plot, with the observed relation very nearly flat as would be expected. The specific flow field which leads to inclusion formation would seem to be an eddy which forms in the receiving phase at the jet boundary, and rotates similarly to the vortex rings which exist in the atmosphere. Such a flow will obviously be induced by the moments existing in the viscous fluids, This type of rotating motion would be supplied with energy by the deceleration of the jet; the magnitude of this deceleration is obvious from the jet swelling observable in Figures 46 and 47. Such an eddy would also give a velocity field which tends to return the free end of a ligament to the jet body. Strong interfacial tension would tend to prevent such recoalescence, in agreement with the observed data. It is also interesting to note that inclusion mean diameter does not change with (Re)(We) (see Figure 58). Since we observed that the percent included volume and area do change with (Re)(We), this indicates that the number of inclusions increases but not the diameter, In other words, we are led to the speculation that the scale of turbulence which forms inclusions is relatively constant, although the intensity must change to supply the energy for the additional surface formation.

.016.015.014.013.012.011 E.o.010 0 ro.009.008.007.006.005.004.0 0 0O~~ 0 0 I i II I II I I I I I IILLIXI2ILI2ILIL. H 0 I 15.020.025.030.035 D|O. Cm Figure 57. DL~ versus d-0,

2x1 2xlO -2 I0 E o_ I'0 0 o 0 0 i LI I I 1 L —---- - -_ -------- -- X - 1 —-- I 0 II 1I 11 m o3 104 1i 3xo10 (Re)(We) Figure 58. dlo versus Re x We.

-102 We should note at this time that a lower limit for inclusion formation is observable. We must also say there may be an upper limito It may be that at sufficiently high injection pressures the internal pressure of the jet will cause disruption before the flow field observed here has time to develop. Equipment limitations prevent investigation of possible upper limits at this timeo A further understanding of the interfacial forces involved will be necessary before it will be possible to construct a realistic mathematical model for the mechanism proposed, particularly with regard to coalescence and with regard to the interfacial tension of an interface under dynamic conditions, It is well known that interfacial tension can show a strong time dependence, The extreme length to which the external phase can penetrate the jet may indicate that the interfacial tension drops sharply when an interface is being strained- When it is possible to make some reasonable assumptions with regard to surface forces, one can postulate a variety of eddy strengths and initial jet disturbance configurations and attempt to see what configurations will grow and bend back toward the jet. The existence of the large velocity gradients in real systems will probably require that such modeling be very naive at the outest,

IX. CONCLUSIONS This work, as is typical with investigations in relatively unexplored fields, has frequently grown back two questions for every one that has been cut off. There are, however, several general conclusions which appear well motivated, Both the mechanism proposed and the data taken indicate that multiple emulsion formation is not only possible in pure phases, but probably exists in many present day operations with rapid coalescence preventing its observation as such. It appears that hydrodynamics controls multiple emulsion formation, although stabilization is necessary to its observation, The application of the log-normal distribution to the large drops, and to the inclusion marginal and conditional distributions seems well indicated, The possibility of a one-parameter characterization would seem worthy of further investigation. The proposed model for percent included area and volume as a function of nozzle parameters will probably furnish order of magnitude results for a given liquid pair; however, caution should be used in extrapolating. It can be said that inertial forces predominate in the inclusion formation process, and that the five variables in Reynolds number and Weber number must all be considered in future work. -103

X, RECOMMENDATIONS FOR FUTURE WORK There are several directions in which future work should be directed. First, since the experimental error is fairly large compared to the differences one desires to measure, there are three alternatives: 1) Re-design of experimental equipment to permit work over a wider range of independent variables so that changes in dependent variables are larger with respect to experimental error. 2) Improved analytical technique, 3) Experimental runs with many replicates so as to permit reduction of experimental error by averaging. Alternatives 1 and 2 are preferable to alternative 3; however, to redesign the equipment to permit working over a larger range requires certain additional knowledge. The most important limitation is the clouding of the sample cell at high liquid velocities through the nozzle. In order to circumvent this, a larger, deeper, sample cell could be used to permit photographing the spray farther from the nozzle where spray density is less. To do this, one must know the coalescence rate of the inclusions, and the validity of the spray sample taken. It will probably be necessary to traverse across the spray to get a representive sample. Longer focal length lenses will be required, To improve analytical techniques will be very difficult unless some way is found to eliminate the human factor in counting, perhaps by a light transmittance technique, -104

-105 In order to remove variation by averaging, it will be necessary to determine experimental error precisely. This also involves consideration of variation of error at high percent included area or volume because of obscuring of inclusions, etc. After resolving the experimental error problem in one of the three ways suggested, the next logical step is a designed experiment, probably a partial factorial, to test a model of the form: log (% included volume) = vA ^ o A + M\S L1 ^5 i VA Lw ^Y + KAI-%,V 4-)' (X 1) Results from checking this model at two or three levels should suggest more realistic dimensionless groups for correlation purposes, With respect to the suggested mechanism, the first step should be an investigation of dynamic, as opposed to static, coalescence. Initial study can probably be done with a drop approaching a flat interface at various velocities~ Finally, there are any number of independent variables which suggest themselves for study, such as: 1) nozzle configuration - producing sheets, cones, etc,. 2) nozzle roughness and wettability, 3) sharp versus blunt edge nozzles, 4) vibration of nozzle, 5) effect of surfactant type, 6) effect of chemical properties of the liquids.

APPEND ICES -106

APPENDIX A BIBLIOGRAPHY -107

A. BIBLIOGRAPHY 1. Allan, R. S., and Mason, S. G. "Effects of Electrical Fields on Coalescence in Liquid + Liquid Systems," Trans. Far, Soc., 57, (1961) 2027-40. 2. Albers, W., and Overbeek, J. T. G. "Floccuation and Re-Dispersion of Water Droplets Covered by Amphi Polar Mono Layers," Colloid Science, 15, (1960) 489-502. 3. Asset, G. M., and Bales, P, D. "Hydraulic Jets at Low Reynolds Numbers and Constant Weber Number," Research Report 69, Chemical Corps Medical Laboratory, Army Chemical Center, Maryland (June, 1951). 4. Balje, 0. E., and Larson, L. F. "The Mechanism of Jet Disintegration," Air Material Command Engineering Division Memorandum Rep. MCREXE-664-531B GS USAF Wright Pat. No. 179 (August 29, 1949). 5. Baron, T. "Atomization of Liquid Jets and Droplets," Tech, Rep. No. 4 on Contr. N6-Ori-71, Eng. Expt. Station, University of Illinois (1949). 6. Batchelor, G. K,, and Davies, R. M. Surveys in Mechanics, Cambridge: New York (1956). 7. Bennett, C. A., and Franklin, N. L. Statistical Analysis in Chemistry and the Chemical Industry, iley ew York (1954) 8. Boll, R. H, "A Rapid Technique for Determining Specific Surface in Liquid-Liquid Sprays," Doctoral Dissertation, The University of Michigan (1955). 9. Borisenko, A. J. "The Problem of the Influence of Turbulence of a Liquid Jet on Its Atomization," Zhur, Tekh. Fizik,, 23, (1953) 195-6. 10. Borodin, V. A,, and Dityakin, Y, F. "Unstable Capillary Waves on the Surface of Separation of Two Viscous Fluids," NACA Memo 1281 (April, 1951). 11. Boucher, P. E. Fundamentals of Photography, Van Nostrand: New York (1947). 12. Brown, E. B. Optical Instruments, Chemical Publishing Company: Brooklyn (1945). -108

-109 13, Chamberlain, Katherine, An Introduction to the Science of Photography, MacMillian: New York (1951)o 14, Charles, G, E., and Mason, S. Go "The Coalescence of Liquid Drops with Flat Liquid-Liquid Interfaces," Jo Colloid Sci,, 15, (1960) 236. 15. Charles, G. E., and Mason, So Go "The Mechanism of Partial Coalescence of Liquid Drops at Liquid/Liquid Interfaces," J. Colloid Scio, 15, (1960) 105. 16o Cheesman, D. F. and King, A, "The Properties of Dual Emulsions," Trans. Far. Soc., 34, (1938) 594-8, 17o Christiansen, R. Mo and Hixson, Ao No "Breakup of a Liquid Jet in a Denser Liquid," Industrial and Engineering Chemistry, 49, No. 6, (1957) 1017-24. 18. Clay, P. H. "The Mechanism of Emulsion Formation in Turbulent Flow," Proc. Nederlo Akad. Wetenscho, 42, (1940) 852-65, 979, 990, 19. Clayton, W, The Theory of Emulsions and Their Technical Treatment, 5th ed., Churchill: London (195-4)o 20, Clerk, Lo P. Photography Theory and Practice, Pitman: New York (1954). 21. Cochran, W. G., and Cox, G, Mo Experimental Designs, 2nd edo, Wiley: New York (1957)o 22. Colloid Science (Symposium), Chemical Pubo Co: Brooklyn (1947), 23, Dallavalle, J. M., Orr, Co, Jr,, and Blocker, H, Go "Fitting Bimodal Size Distribution Curves," Industrial and Engineering Chemistry, (June, 1951) 1377-80o 24. Debye, P., and Daen, J. "Stability Considerations on Nonviscous Jets Exhibiting Surface or Body Tension," Phys, Fluids, 2, (1959) 416-21. 25. De Juhasz, Ko J. (ed.) Spray Literature Abstracts, ASME: New York (1959). 26. Du Nouy, P. Surface Equilibria of Biological and Organic Colloids, The Chemical Catalog Co,: New York (1926)o 27, Eriksen, J. L. "Thin Liquid Jets," Journal of Rational Mechanics and Analysis, 1, (1952) 521-38,

-110 28. Fraser, D. A. S. Statistics: An Introduction, Wiley: New York (1958). 29. Fuhs, A. E. "Spray Formation and Breakup, and Spray Combustion," Air Force Office of Scee Res., Rept. TN-58-514, AMF/TD No. 1199, Tech. Note 4 (February, 1958), 30. Gelalles, A. G. "The Effect of Orifice L/D Ratio on Fuel Sprays for Compression Ignition Engines," NACA Tech. Rept. 402 (1931). 31. Gelalles, A. G., and Marsh, E. T. "The Effect of Orifice L/D Ratio on the Coefficient of Discharge of Fuel Injection Nozzles," NACA Techn, Note 369 (1931). 32. Gelalles, A. G. "The Effect of Orifice L/D Ratio on Spray Characteristics," NACA Tech. Note 352 (1930). 33. Gel'perin, N. I., and Vil'nits, S. A. "Dispersion of Liquids Flowing Through Nozzles Into Air and Liquid Media," Trudy. Moskov. Inst. Tonkoi Khim. Tedhnol. Im. M.V, Lomonosova, 6, (1956) 111-16. 34. Giffen, E,, and Muraszew, A. The Atomization of Liquid Fuels, Wiley: New York (1953). 35. Glasstone, S. Textbook of Physical Chemistry, 2nd ed., Van Nostrand: New York (1948). 36. Harmon, D. B. "Drop Sizes from Low Speed Jets," Journal of the Franklin Institute, 259, No. 6 (June, 1955) 519-22. 37. Hayworth, C. B,, and Treybal, R, E. "Drop Formation in Two Liquid-Phase Systems," Industrial and Engineering Chemistry, 42, (June, 1950) 1174. 38. Herdan, G. Small Particle Statistics, Elsevier: New York (1953). 39. Hermans, J. J. Flow Properties of Disperse Systems, Interscience: New York (1953). 40. Hill, T. L. "Concerning the Dependence of the Surface Energy and Surface Tension of Spherical Drops and Bubbles on Radius," Journal of the American Chemical Society, 72, (1950) 3923-27. 41. Hinze, J, O. "Critical Speeds and Sizes of Liquid Globules," J. Appl. Sci, Res., Vol. Al, (1949) 273-88. 42. Hinze, J. O. "Forced Deformations of Viscous Liquid Globules," J. Appl. Sci. Res., Vol. Al, (1949) 263-72.

-111 435 Hinze, Jo 0. "Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Processes," AoIoChEo Journal, (September, 1955). 289-95. 44. Hinze, Jo 0. "On the Mechanism of Disintegration of High Speed Liquid Jets," 6th International Congress on Applied Mechanincs, Paris (July, 1946)o 45. Holroyd, H, B, "On the Atomization of Liquid Jets," Journal of the Franklin Institute, 215, (1933) 93-70 46. Hughes, Ro R., and Gilliland, Eo Ro "The Mechanics of Drops," 1951 Heat Transfer and Fluid Mechanics Institute, Stanford, 53-720 47. Jacobs, Do H, Fundamentals of Optical Engineering, McGraw HillNew York (1954). 48. Jirgensons, Bo, and Straumanis, Mo Eo A Short Textbook of Colloid Chemistry, Wiley: New York (1954). 49. Keith, Fo Wo, and Hixson, A. No "Liquid-Liquid Extraction Spray Columns - Drop Formation and Interfacial Transfer Area," Industrial and Engineering Chemistry, 47, No, 2, (January, 1955) 2580 50. Knelman, Fo H,, Dombrowski, No, and Newitt, Do Mo "Mechanism of the Bursting of Bubbles," Nature, 173, (February 6,.1954) 261-2, 510 Lange, N, Ao Handbook of Chemistry, 8th edo, Handbook Publishers: Sandusky (1952), 52, Lapple, Co Eo Fluid and Particle Dynamics, Stanford Res, Insto, Menlo Park (1951). 535 Magarvey, R, H., and Taylor, Bo Wo "Free Fall Breakup of Large Drops," Jo Applo Physo, 27, (October, 1956) 1129-355 54o McDonald, Jo Eo "The Shape of Raindrops," Scientific American, 190, (February,.1954) 64-8, 550 McDonough, Jo Ao "Formation of Interfacial Area in Immiscible Liquids by Orifice Mixers," AIoChE. Journal, 6, (1960) 615-18, 56, Merrington, A, C., and Richardson, Eo Go "The Breakup of Liquid Jets," Proc, Phys, SOC. (England), 59, (1947) 1-135 57, Miesse, CO C. "Correlation of Experimental Data on the Disintegration of Liquid Jets," Industrial and Engineering Chemistry, 47, (September, 1955) 1690-1701o 58, Miesse, Co C, "Recent Advances in Spray Technology," Applo Mecho Rev., 9 (August, 1956) 321-53

-112 59. Mugele, R. A., and Evans, H. D, "Droplet Size Distribution in Sprays," Industrial and Engineering Chemistry, 43, (1951) 1317-24. 60. Newitt, D. M., Dombrowski, N., and Knelman, F. Ho "Liquid Entrainment - The Mechanism of Drop Formation from Gas or Vapor Bubbles," Trans. Inst. Chem. Engrs., 32, No. 4, (1954) 244-61, 61. Null, H. R., and Johnson, H. F. "Drop Formation in Liquid-Liquid Systems from Single Nozzles," A.o.Ch.Eo Journal, 4, No., (September, 1958) 273-81. 62. Pai, S. Fluid Dynamics of Jets, Van Nostrand: New York (1954), 63. Pavloshenko, I. S., and Yanishevskii, A. Vo "Interfacial Surface Area of Mechanically Stirred Mutually Immiscible Liquids," Zhur, Priklad. Khim., 32, (1959) 1495-1502. 64. Perry, J. H. (ed,) Chemical Engineers' Handbook, 3rd ed., McGraw Hill: New York (1950), 65. Putnam, A. A, et'al, "Injection and Combustion of Liquid Fuels," WADC Tech. Rept. 5-344 (March, 1957)o 66. Ranz, W. E, "On Sprays and Spraying," Bulletin No, 65, Dept.of Eng. Res., Penn State U. (1956)0 67. Ranz, W, E, "Some Experiments on Orifice Sprays," Can, Jlo of Chem, Eng., 36, No, 4, (August, 1958 ) 68. Redding, To Ho Flow Through Orifices and Parallel Throated NozzlesA Bibliographic Survey, Chapman and Hall: London (1952), 69. "Reversal of Emulsion Type," Chem, Soc. Jlo, (September, 1934) 1360-1, 70. Richardson, E. G. "Mechanics of the Disruption of Liquid Jets," Appl. Sci, Res,; 4, Section A, (1954) 374-80. 71. Rideal, E. K. An Introduction to Surface Chemistry, Cambridge U. Press: Cambridge (1926), 72. Robertson, G, R, (ed.) Modern Chemistry for the Engineer and Scientist, McGraw Hill: New York (1957)o 735 Rouse, H., and Abul-Fetough, A. "Characteristics of Irrotational Flow Through Axially Symmetric Orifices," Jl. Appl. Mech,, 17, No, 4, (December, 1950) 421-6. 74. Rumscheidt, F. D., and Mason, S. G. "Particle Motion in Sheared Suspensions," J. Colloid Sci,, 16, (1961) 210-61.

-115 75. Rutgers, A. J, Physical Chemistry, Interscience: New York (1954) 76, Savic, P, "Circulation and Distortion of Liquid Drops Falling Through a Viscous Medium," Repto No, MT22, National Research Council of. Canada (July, 1953)o 77, Savic, P, "Hydrodynamical and Heat Transfer Problems of Liquid Spray Droplets," National Research Council of Canada, Div, of Mecho Engo Quarterly Bullo (January - March, 1953)o 78. Schlicting, Ho Boundary Layer Theory, 4th ed,, McGraw Hill. New York (1960). 79. Schwartz, Ao M,, and Perry, Jo Wo Surface Active Agents, Their Chemistry and Technology, Interscience: New York (1949)o 80. Schwarz, N,, and Bezemer, C, "A New Equation for Size Distribution of Emulsion Particles," Kolloid Zeitschrift, 146, No, 1-3 (1956) 139-51. 81. Scott, Lo S,, Hayes, Wo Bo, and Holland, Co Do "The Formation of Interfacial Area in Immiscible Liquids by Orifice Mixers," AoIChE, Journal, 4, No, 3, (1958) 346 82, Shafer, M, Ro, and Bovey, Ho Lo "Applications of Dimensional Analysis to Spray Nozzle Performance Data," NBS Jl, of Research, 52, Noo 3 (March, 1954) 141-7, 835 Siemes, W,, and Kauffmann, J. F, "Drop Formation in Liquids on Nozzles at High Rates of Flow," Chimie-Ingo Techno, 29, No, 1 (1957) 32-8. 84, Squire, Ho B."The Round Laminar Jet," Quarto Jlo Mech, Apple Math,, 4, pt, 5, (September, 1951) 321-29, 85, Squire, H, Bo "Some Viscous Fluid Flow Problemss Jet Emerging from a Hole in a Plane Wall," Philo Mago, VIIth Series, No, 344, (September, 1932) 942-5, 86~ Treybal, R, Eo Liquid Extraction, McGraw Hill: New York (1951), 87. Tyler, E,, and Watkin, Fo "Experiments with Capillary Jets," Philo Mago, 14, Series VII, Noo 94, (1932) 849-81, 88. Van Deemter, Jo Jo, and Van der Laan,.E To "Momentum and Energy Balances for Dispersed Two-Phase Flow," Applo Scio Res,, 10A, (1961) 102-8,

-114 89. Washburn, E, W. (ed,) International Critical Tables, McGraw Hill: New York (1928). 90. Wiley, R. M, "Limited Coalescence of Oil Droplets in Coarse Oilin-Water Emulsions," J. Colloid Sci., 9, No. 5, (October, 1954) 427-37. 91, Woodman, R. M, "Notes on Dual Emulsions," Jo Phys, Chemo, 33, (1929) 88-94, 92, Woodman, R. M, "Studies in Dual Emulsions," Chem. Age, 25, (1931) 146-7. 935 York, J. L, "Photographic Analysis of Sprays," PhoDo Dissertation, The University of Michigan (1949), 94, Zucrow, M. JO "Discharge Characteristics of Submerged Jets," Purdue Univ. Eng. Expt, Sta. Bull, No 31 (June, 1928),

APPENDIX B COMPUTER PROGRAM -115

COMPUTER PROGRAM Shown on the following pages (Table XI) is the computer program used in this work. The program is written in the MAD language developed at the University of Michigan. Information regarding this language and instructions for its use can be obtained from the Computing Center, University of Michigan, Ann Arbor, Michigan, Execution was by an IBM 709 machine. Shown in Table XII are the input variables for the program. In Table XIII are the corresponding values for Run 10o In Table XIV is the computer output for Run 10, Note the raw data for Run 10 is contained in Table IIo We will consider in order the calculation of the items shown in the computer output for Run 10. The nozzle diameter, flow rate, interfacial tension, and viscosity are input variables. The Reynolds number is calculated as: (co-,T -7) C4.5 CFLt (CrST -) \<= (8^3.^4s^} C)o(4O ^ (S^) (B.l) and the Weber number as: L 3 s Cot = ^(G9AVA) &ITZD) (B02) Velocity through the nozzle is given by: Nozzle Velocity =, - (B 3) SH\50^ ( tlo 0 Z'D7

-117 "SCOMPILE MAiD EXECUTE, DUMP, PUNCH OBJE.CT. PRINT OBJECT I o'1 DI MENSI ONt CELL.3i0), MOME-T (2A0), ENiPT;.35),S DI M.30) t, E N20, DPK *o ONUMC 1 0:),DENt( l, ISTc.30::'.:NU BERf.3O), PCT:30, CUMPCT::30),PCTINT.2DPK *001 _ (.31 0:, F30), CX(.3O>) Y(30::',, ELI('r30),iWC30_:)_, SPEED( 30)>,G 30)PRC 30) _ 3DPK *001 2, CUPR C.30::, 1, EM1 C'::':, REM2 (60), REM3 CGO), REM4:60), REM 5(60) 4DPK *001 DIMENSSIONN IN lC600, D),. I,:%O, D0 ) DPle *002 DIMENSION EDiPTIt(i 20), l1,:20 1). FLPHA, 3), BET C'20"^),S SIZINC 20) DP< *003 START CONTINT lHUE 5DFPK *004 RERiD FORMAT.DCRlRD 1 HEIGTH,.iDTH DEPTH, CONSTl CONST2, COiNS T C 6 DPK +*0055 OOHNSST4 _ 7OF 7DPK *005 VECTOR VALUES DOCFliRD1 =$4iE20. 5)* - 8D'FPK *006 * READ FORMAT DCARD2,M',,S, TL,DOGEr,, ENtDREM, PHOTO. 9PDPK *007 VECTOR...LIUES DCARD2=E6 3, F1l0. E...5* ODPK *.008 INTEGER M, S, OGEM, I, T, H, L, ENDRF.EM 1.1 DPK 009 INTEGER N,J,DOLOG,MOMI'N" 110DPKA *010 _ INTEGER REM1I,REM2,REM3, _EM4. REM5 ___ _ 12DPK *011 READE FORMAST ODCRD.3, NUMBER C1::.... NUMIBER CM) 1 DPK *012 VECTOR VALUES DCARD.3.=$C4. F20..5*$ 5* 16 DP'*01.3 READ FORMAT 0CRARD4,DI0STC )...DIST(M) 17DPK *014 VECTOR VALUES DC!1RD4=-$::4E20.5 *, 18DPK *015 READ FORMAT DCAlRDS,DEL'..'(1.l...DELAY(:M 19DPK *016 ___________VECTOR V'__LUES DCRD=C4____________ __________20PK 017 READ FORMAT DCARDi, ENDPTC:1.... ENDPTCM+ ) 21DPK *.018 VECTOR ViLUES DFCARD6=C,::4E20. 5 )* 22DPK *019.REEAD FORMFT DCJ1ARDC17,NUTMCT.. NUMC.T>5 23D-PK *020 VECTOR VALUES DClRRD7=$C4E20.5)>* - 24DPK *021 - E- F'-M'l T~.:iA'D8S, C7ErT,Tr... DEN T) 25DPK C22 *VECTOR'VALUES DCARD8=$'~:4E20. 5:*$. 26DPK *'023 REiD FORMAT DCARD9, REM1 1:l... REMC1 (ENDREM) 27DPK *024 VECTOR VALUES OCARD9=T( 1 3C6;* 280PK *025 RERD FORMAlT Df:AR1.,REMta2I::..R EM2CEtNDREtM.29DPK *026..VECTOR VALUE$ 0CPR1OF~~ 1'0=$ 1.3:*~; 30D0PK 1-027 READ FORMAT DCAR1 1,REM3. 1...REM3(ENDREM) 310PK *028 -VECTOR VALUES DCAR11=$C13C6)*$ ~ 32DPK *029 READ FORMAT OCAR 1 2,REM4 1 )... REP14 CEDREM 33DPK *030'VECTOR VALUES CA.R12=E,:1'3C:6*$ 34DPK *031.READ FORMAT iCARR13, REM5' I:..REM5(:EtDREM) 35DPkF *032 VECTOR.VALUES DCAR13=$C13C$S')*s 36DPK *033.READ FORMAT DCAR 1 7,DENSTY, COiNSTS, CON-IST6 - - - - 420PKA *034 VECTOR VALUES DCRR17=$3E20. 5*$'.42DPk< -035 READ FORMfT DCAR1 8,N, OOOG,MOM IN I PK *036 VECTOR VALULES 0CAR18=.3I.3*. $ - *037 VECTOR VALUES 0=2, 1,0 *038 DC2)=N * DPK. *039 READ FORMAT DCARI 9,NIN"1,: 1:... NIN CM, N) DPK *040 VECTOR VALUES OCAR1 9=$C 4F20. 2)*$ P__K *041 READ FORMAT DCAR20,EDPTI(1':,...EDPTINCN+1). DPK *042 VECTOR VALUES DCAR2=,C-:.4E20.5,*, DP OK'*043 RElD FORMAT DCAR21,NtiOZD,FLO,.GAfMM1fA,VISC DPK *044 VEC:TOR V.ALUES D:A21=4E.5 ______________PK *045 READ FORMAT 0C:AR22,CONST7,C0NST8, CONST9 DPK *046 VECTOR VALUES C FR22=$-3E20O. 5*$ -DPK *047 PRINT FORMAT SPAFCE *048 VECTOR VALUES SPRACE-=IH1*$ *049.___PIR —-----------— MT____________ ________ _ _______ _-___ —__-_____E_-____- -*__0 PRIN T FORMfAT R~1 ES1.REMt1 R, 11.:1>...REM1 -CE-DREt )- 43DPK *050..

' Er CTO..R VAL.UES... RES1'=: —1 1 C: 1 HO, 1 3 C:: *......... 44DF.*051 RE=C-,CONST7*4. *FLOW*I!7.N:'Y:.,:"3. 14.1 59 *N Zi.D ISC:) * 052 IE__l' CFLOw*4..'.. 3. 141 5 9._. E Fr:-E!H. Y..:.'.rI,'.C. _NZD_, 3..).._..,. DF'Pk *053 PRIN T FOR MFT E 43FF.3 FL.., Ni -, S C R E O I.E DPI:054'. VECTOR' ViLUES RES4.3= 1i -9HONOZZLE DIHtiETER =,E20.5./, DPK *055' 1 2 H F LO.,R FR RTE = E 2'.5'! < *l.55 122H INTERFFCIARL TENSIION -E20.. DFPK' *055 212 H V I SCOS I TY =, E20.5-., D Fk *055 ___ ^.31 8H REYNOLDS NUJMiBER -, E'20. 5. —, ___FK, *055 415H WEIEI NU 8 ER =,E2Q, *:!. D F K * 055 SPDN 4. *FLO I J...'c.3. 141 59': N.O 2'D. P'. 0::: 56PRINT FORMRT SPDNFSF' IPD' *057 V.'ECTOR'.'RLUES SFDNF =-E27H.'ELOCIT'.' THROUGH NOZZLE =,E20.5*2: *058 AD.I U S T=-. *0.59 THROFUGH RET1.,FOR =1, 1 I G.M 11 45DPK *060.O IR E IST,.J U T JST+N LMBE R:.EF: I) — I0 —...061 E L LC I': =E FT C:: I + 1:: -E i F'T:: I: 46IDPK *062 l HENEVER DIOGEM.E.:,"'iR'li-F ER'TO RMEE'f:i..N.... 47 F... 063.... I'I.': CENDPTCF'TI.ENDF'T: I+!.:, F'.:. 5': 48DP'K *064.WHENEVER I.G. I TRRfNSFEr TO WY'I fl.'l 065 PR_ INT FIFRMFT RES 1 49DPKO *pS6 -* * fl yflrf "* *"**"'*C O N T IN UE - ***** * ** -. *- * *............................. ~',~...-.^.-...... V'IECTI:iR''LUEiES'RES2=1 3'i: ITHI' COMPUTATION USES RIEOMETRIC MEtN-S.:5DPK *073 510 F:-*067 f[WR 2 CONTINUE I074 TRANSFER TO OUT 52DPK' *069.... —- --' —-R N.q'-F.i..-.........-;' "'D;................................................................ I E 1*. O. *070 IWJHE 1N' EVEFR IL. I. T ANSFER TO 1 AI. -R2 ______ 071 PRINT F!-ORMT RES2 54DFK *0.72 VECTORF V'LUE' S RES2=E' 4HOTHIS I': COMPF'UTlTION USES F.RITHtETIFC MEAN 5 K_ *_073....s F073.......... O.C.ONT I NU.E *07.4 ---------- — l- r oy~ - -- -- -- - - -- --.....-.........,-:.'......:.......... X______.s C I: =)' CNUMBl ER C I ) *D I ST C' I::* *C ONST 1:'.-*' lPHOTOS* DEL AYS C~ I':= D F 5.DPK, 081 C I =X C I + If, C GODPK *082 HENRETER EV L G E _T R."'_'_' E O T F.: OT L IT 14 4P _*3 _ ___ PRINT FORMFIT RES.3 6 0 77..84 VECTOR VRLUES RES4=.5=44HSTHIZES R:-IES24,IT HIONUBSES L-I THIC 0, SPEED, 65DPK*08 RE_-_-_ —_i__08,7HPECENTS2,18HCUfilULT TI'EFL ERCE J ITS21 SHPERCENUTE'SIZE R10GE GGDPK #088 1YS - -- - - _._.....-~.-._.-.-..,?.0)~.. =0~~7., 8Dp' * 0 8 8 THROUGH RET2,FR'I=1:1,I..FM'DPK *089 - - ------------- - - -_______^___ —------------- - __- - --- - —.-.- -- _ ) HENECTOER DOLOG.LIES RES.3=OHR.'ELF T'HO OUT 12ETE'ERCENTFES*',F'. 8591 WICI)= ELOG. Ch':C) 0 9-2 PR1INT FOR M: T REl1 8., RE1',1:. 1.. RE09312E:"E':':E F'k -—. —-PRI-NT FI RiT RENS4 4( *07 PCT10CI)=XCI1*-100./CM) T5DF'K *098 THROUGIT FHRMAT RES5,' ENCIPTHi,: EDPTC+1, NMEI.. I74DPK *099 I OCT I) CUMPCTCI CTINT - L0G'.'.:l i iDPK "*099 I........... F=CT'C'i'J-;:-1'LT I)PC —''-'iu'T'INT,:I-...............................F..........~ DI:!....r0i-.....

-119-.'ECTOR IRALUES fRE 95=1EH,F10.5 4H TO, F1 0.5,56,F10 1. 5, F10. 5, 760DPK *100 iDS,* -.F 1 0i, f.. 5,'~' F o.s.s1, 10 F li 91. 15,.;1, F:1'i.' -;0$1 f 0 RET2 C:ONTINUE _77DPKFi *101'MOMENT O:=1. 77DPKB *1.02 THRF.i Li0H G ET, FOR F= 1 FOR I, 1 G.' 78DPK _*103!10HE ENT C) A. 79DPK -'104 G O.......................................................................................1 0 5 THROLUGH RET4, FORJ I1 1, r.G.! ~ 10 IOP:' *106 F C I = CPCTI I':* ICUi.I P. 100. P. R:: 0082DP 107 MOMENTCR:: =F CI)'+MIMENT::' 3DPK *1.08 RET4 GCI')FCI)+GCI -1) 4DF' *109 ^ —--- -------- GSJ2^FSI}L+GC^ - __ -~ - -. -_ _ _ _ _-______ —.__~ ^'^'^.l0? —WHENEVER CONST37G. 10., FR:1r.ISFER T-i" RETi3 "='-j'-...*110 PRINT FORMAT RES:, R' 8.SF'K, *111 -_ —---------— J-'-^Iyj-^0?! —^5-3'-7- -._ _____-________~ - -_ _ - ---— _ —--— _J_-_'..IECTOR VALUES RESS=:.OH'2F'ROE:AEBILT'.' DENtSITY AND DISTRIBUTION 8GDPK 112 OFUNCTIONS WEIGHTED BEV,I.3,27HTH POWER OF RANDOM'...'ARIABLE*$ 87DPK *112 PRINT FORMRT RES''30OFK 113 VECTOR VfLUES RES9-1 1H0SIE. RANGES1:9, 1 1HPROBABILITY,SS, 91Dk _ _ 114 022HCUMULATIyE PROBA6EILiT'I $ 92DPK *114 THROUGH RETS_ FOP I=l,, 1 1.. 94DPFI' *115 CUPRCI)IG I).GC ) ___96DPK *117 PRINT FORMAT RES10, ENOPT I:', ENDPT,:.I+ ),PRCI),1 CUPRF'I: 97DPK *118 VECTOR VALUES RES10='1H,F10.5,4H TO.FlO.5,56,F10.5, S20,F10. 9SDPK *119 05*$ 99DPK *119 RET5 CONTINUE IOODPK.*120 RET3 CONTINUE 101DPK *121 Q=50. *122 INI CONTINUE *123 PRINT FORMAT RES11 102DPK *124 VECTOR VALLIES RES1 1-.33.H4MO1,ENTS OF WEIGHTED ISTRIBUTION"* 103DPK *125 PRINT FORMAT RES18,REM,'1l'...REM3CE.:DREM) 104.DPK *126 WHENEVER Q.G.25, TRANtSFER TO OULIT5 *127 THROUGH RET6, FOR R=0, 1,R.G.MOMIN' *128 OUT5 WHENEVER Q.L.25. TRANSFER TO OUT6 *129 THROUGH RET6, FOR RP-O,1,R. G.S 106PK *130 OUTf6 PRINT FORMRT RES12, RMOkENTC'R)'107DPK *131 VECTOR VALUES RES12=-1H I3, 12HTH MOMENT =,E15.5*. 108DPK *132 RET6 CONTINUE 109DPK *133 PRINT FORMAT RES'13 1100DPK *134 VECTOR VALUES RES13=$14H4MiOMENT RATIOS*$ *135 THROUGH RET7,FOR 1=1, 1,I.G.T 112DPK *136 K=MQMENTCNUM( I))/MOMENT CDHENC I)) 11 3DPK *137 PRINT FORMAT RES14,NU'lJC',DENCI),K 114DPK *138 VECTOR VALUES RES14='E10H RATIO OF.FS.2..13HTH MOMENT TO'F5.2 115DPK *139 0,12HTH. MOMENT= E15.5*+... 116DPK *139 RET7 CONTINUE 117DPK *140 OUT7 PRINT FORMAT RES15 118DPK *141 VECTOR VALUES RES15= $3H4COMPUTRTION OF MEANS, VARIANCES. AND 119DPK *142 0 STD.- DEVIATIONS*$ 120DPK *1142 PRINT FORMAT RES18, REM4l1)...REM4CENDREM) 1"20DPKA *143 WbJHENEVER Q.G.25, TRANSFER TO OUT8 *144 THROUGH RETS, FOR I=0, 1, I.G. CMOMIN-2) *145 OUT8 WHENEVER Q.L.25,. TRAHSFErR TO OUT9'*146 THROUGH RETS, FOR I=0,I1,I.G.CS-2): *147 OUT9 MEAN=M0MlENT C I +1) /MO, MENT,:I 122DPK *148 VAR =CMOMENTCI+2) /MOMENT'::I P )-C~CMOMENTCI+I1*./MOMENTC.I-':,.P.2.) 123DPK *149 WHENEVER ADJUST.L.2., A lDJUST = 2. *150 VAlR=VAR*ADJULST-/,(ADJUST-1.': *151 WHENEVER VAR.L.O., VAR = 0:0001 *152 DEV=CVAR.P. (.5):) 124DPK- *153

-120 CHECK4 CONTINUE *154 PRINT FORMAT RES35, I 125DPK *155 -__~__ V~'.P LLES REC'S-TO FOR....'THE RANOM VARIALE DI AETER ON...........126P OTHE, I5,24HTH WEIGIHTEo DISTRIE:UTION* 127DPK *156 PRINT FORMAT PRES'.3,, fR.N t.E.. DE*1'ECTOR'VAiLUES'RES'36=,7H ME'Rnt =, E15.5,S5, 1 O-fViARIPNCE =,E15.5, 129DPK *158 ~OS H T DI..T O..! 5..................... 5.. HST.. EV.I.AT O.. E.1..5.................................... __.' _1 58._... RETS CONTINUE 131DPK *159 __HENEER G.25 TNFR... TO O.UT0................1 0 THROUUGH RET11, FOR 1=0, 1, IG3. (NOMIiN.t.2) *. 161.OUT10. WHENEVER Q.L..5. T:.FRISFFR TRNFR OUT1 1.... *1(62 THROUGH RET11; FOR I=O, 1,I.G.(S2) *163 OUT1 1 PRINT FORMf T RE'S$19, I 133DPK _ *164 VECTOR V!ALUES RES19=.47H FOR THE RANDOM VARIABLE (DIANETER TO 1""" 34DPK *165 0 THE POWER, I5,.34H) ON THE NON-WJEIGHTED DISTRIBUTION*. 134DF'PKA 165 MEAN=MOMENT I) 134DPKB *166 VAR=NMO1ENT C2.*I)- (CNMOMENT<TI)).P.2.) 134DPKC *167_ VAR-VAR*DJ LIST., /CA J UST-1. ) * 1G68 WHENEVER VFR.L.O. VlR =. 0001 *1659__ DEV=VRR.P~C.'~5) 134DPK0 *170 PRINT FORMAT RES36,MEA N VAR, 0DEV 134DPKE *171 RET11 CONTINUE 134DPKF *172 WiHENEVER Q.L. 25., TR!NS'-ER TO OUT1 *173 W.HENEVER Q-'.G.'75., TR NS ER TO OUT.2"'............*....... 174 PRINIT FORMAT RES22 135DPK *175 VECTOR VALUES*RES22=2 136DPK *176 PRINT FORMAT RES1 8, REM5C1::,... REMSCENDREN) 137DPK *177 PRINT FORMAT RES50 *178 VECTOR VALUES RES50-$9H DIARMETER,S16., 12HSURF.CE RPTE.,S13, *179 011HVOLUME RATE*S *1799 SUMSUR=0. *180 SU MVOL= O. -.......................,.........18 1 ~THROUGH RET2.3, FOR I=11,I.G..M *182 SUR=C3. 1415S'* (fLPHACI:). 2.:, *SPEED(I)*NUMBER:CI)),: (FPHOTOS*HEIG *183 OTH) *183 VOL=.C3. 14159* ACALPHA('CI).'..3.:.*SPEEDCN I)*N*UMBERCI)'.. /C6.*PHOTOS*H * 184 OEIGTH) *184 SUMSUR-'.iUR+SUSUJR * 1 85 SUMVOL=V'OL+SUMVOL *1 86 PRINT FORMAfT RES31,.FLPHqCI),SUR,VOL *187 VECTOR VALLUES RES24=, 1H'S2URFACE RATE_= E5.5.2.. 1 42DPK. *188 ORATE =,E20.5*$ 143DFPK *188 RET23:CONTINUE,*189 PRINT FORMAT RES51 *190 VECTOR VALUES RES51-='1 2HITOTAL RFATES*,,191 PRINT FORMAT RES24,SU-lSUJR, SULMVOL *192 PRINT FORMAT RES29 164DPK *193 VECTOR VfALLUES RES..-.,5.-T'MH,,-NMENTLIUM AND ENERG.Y TRRNSFER RATES T 1 SDPFK+ 1 94 OHROUGH SAMPLE SP':E*. 166PKDFK *194 PRINT FORMIRT RES1.8, RE5...REMSEDRE) 167DPK *195 PRINT'FORMIT RES32 169DPK -196 VECTOR VALUES RES32='9HOODIRM!ETER,S20,8HMOMENTUM, S10. 170DOPK *197 014HKINETIC ENERGr.Y*E 171DPK -?1'97 SUMOM=O..198 SUE —-— i —-- _EN=O. *1 99 THROUGH RET1OFORI-=1,1, I.G.N. " ""'172DPk *200 V C I ) =3. 141 59* (CALPHA CI....3.::) *DENSTY*CONST5*SPEED CI::* NUMBERI ( [:.'201 0/C6. *PHOTOS) *201 X:;CI)= VYCI')*SPEED(I)[*CONST.-2. 174DPK *202';tSU 0 MO i)+SLi-rO,..........-....2-03- ---

-121 S Li, E N =: I + _ __ i1 E *204_ FPRINT FORt RT RES 31, Wb::I)'', CI':' * 205'I.,:ECTOR.'LUES RFES31=. 1H:.iEl5.5,-., E 5.5. S9, E..5.............PK 206 RET1 0 CONTINUE 177DPF' *207 PRINT FiORMAT RES51 *208 FR I NT FORMRT RES52, SU,10,, SUIMEN *209. VECTOR VFLLUES RES52= I11LI MNIMENTLIU =E20. 5, S1 0, 1 GHKINETIC ENER 21 0 OGY -,E20. 5*i *210 WHENEVER L.E.O. TRANSFER TO END 211 THROUGH RET12,FOR I-1,1tI.G.N DPK *212 W1 cIl=)-EDPTIT' I; C+EDF'T I':."' +1_: ).'2.. +DP1k * _213 SIZINCI)-EDPTItiCI+1)-E0D'TIN(I'::1','. 214 EBETR { I).=W _...........__.....(- -21____ WHENEVER DOLOG.E.O, TRRA'tFER TO OUT13 *,216 W1 CI)= ELOG..1 I': CI' 21 7 SIZINCI)=ELOG. CEDPTIN':I+1:': - ELOG. CEDPTINCIM:.) *218 OUT11 3 C-ONTIN I'tUE *219 RET12 CONTINUE DPK *220 ADDI=O. *221 DD02=0.- *222 THROUGH RET 13, FOR H=1, 1,H. iG.N M DPK *223 WHENEVER CONST.9.L. (C5.),:;, TRANSFER TO N01 *224 PRINT FORMT RES37,ALPHF'CH':,. *225 VECTOR VRLUES RES37=;49'H4C:LC.ULLTIONS FOR INCLUSIONS IN DROPS DPK *226 0 OF DIAETEFRE20.5*.x. DPK *226 WHENEVER NULMBER CH);. L. C:.:05'::, TRANSFER TO NOGO *227 PRINT FORMAT RES.38 DPK *228 VECTOR VALUES RES38= DIARMETER, S1 4, 7HPERCENT-, S7, DFPK *229 018HCUMULATI VE PERCENT, 7, 18HPERCENT.'S: IZE RANGE* *229 UCH, 1)=NINCH, 1i * 2.30 THROUGH RET14,FOR J-2,1,J.N.t OPFK *231 UCH,.J)=NINC:H,.J)+UL'H, H.J-1) DPK *232 RET14 -CONTINUE *233 WHENEVER UCH,N).L..CONST2. TRANSFER TO NOGO *234 PO.DJUST=O. *235 THROUGH RET15, FOR J 11, 1,JG.N. N P *236 RDJ UST=RDJ UST+N I N CH, J: *237 PCT (J) = 1 00. *N I N CH,.J,'.U CH N)'' *238 ~CUMPCT CJ:' =U CH, J).1 00....U H, N "::1 DPK *239 RET15 CONTINUE DPK *240 __1M2: CONTINUE *241 THROUGH RET20, FOR J,1,.1. G. N *242 PCTINT(J)=PCTC.J)/SZIN C..: *24.3 PRINT FORMAT RES39,!.l:..";, FPCT C.J), CUMrPCTCJ), PCTINTCJ::, *244 VECTOR VALUES RES39='-i1H.E1.5.5,S9,Fi5.5,S10,F15.5,S10,Ft5.7*S *245 RET20 CONTINUE *246 MOMENTCO)=-1 DP *247 W.UHENEVER Q.G.75, TRHNSFERF TO OUT3 *248 THROUGH RET17, FOR F.'. 1,1,R.G.MOMIN *249 OUT3 WHENEVER Q.L.75, TRANSFER TO OUT4 *250 THROUGH RET17, FOR R=IIR.G.S DPK *251 OUT4 MOMENTCR')=O. DP *252 GCO)=O OP *253 THROUGH RET16, FOR J=1,1,.J.G.N DP *254 F C.JF =PCTCJ')* (W1 C.J). P. R- 1 00. DP *255 MOtMiENT CR) -=FCJ ) +M0 MENT CR": DP *256 RET16 G CJ)=FCJ)'+GC:J-1) ODP *257 WHENEVER CONST4.G.10., TRANSFER TO RET17 *258 PRINT FORMAT RES8,R DP *259 PRINT FORMfT E40......... D.4P *260

-122 VECTOR VRLUES RES4_='i,1 -.l'O IICLUSION DI FAMETERS1 SO 1 1 HPROBB BILIT 6_ _..__.*21 OV, S3,22HC UMLtULT I''E PROBqEE:.IL I TVY* DP *261 THROUGH RET17, FOR J=1 1 J.. G.._.................N....... D_ *262 PRCJ)=FCJ.G (CN) DP *263 I.U P F.: C) = G )fJ (N) DF *264 -.F. —---- r t 1 5.- _ t - t -... - - - -.-_ —--------.____ *X 4__ PRINT FORMAT RES41, BETC::.I, FPR'F'J), CUPRCJ) * 265 VECTOR VALULES RES41=;1H,E15.5,S9,F15.5,S1O,F15.5*$ OF' D 2P 6 E:TP- LSESRE_41 1_H_, E.= * m........................................... Et.......____ ____ ___P__ 2_ _ RET17 CONTINUE DP *267 W.HENEVER Q.G. 75., TRANSrER TO INt1 *268 N01 CONTINUE *269 VYH) =O. *270 X:H) =0. *271 THROUGH RET9, FOR J=1,1.J.G.1N *272 XC(H) = (CBETPJ).PF'.2..*HI:INCH, J: SPEEDC(H)) + XH) *273 _' YCH) =CCBET iCJ). )...^ t I CHJ )*SF'EEDCH))+VY C H) *274 RET9 CONTINUE *275 ADD1 =. CH:: +ADD 1 *276 PDD2=V (H) +DD2 *277 XCH:)=: (.. H) *1. oo. C ALPHHP2 UMBER (H::. P..;N E(H) *SPEED.:H) ) *278 VC (H = ('V YCH) * 100.. ) / ( LPHC (H. P. F. 3 *NMBER (H) SPEED H:) *279 Q=l. *280 WHENEVER CONST8.L. (5.>, TRANSFER TO RET13.281 WHENEVER Q.L.25., TRANS.ER TO IN1 *282 OUT1 CONTINUE *283!NOGO CONTINUE *284 RET 1 3 CONT I NUE DP *285 Q=100. *286 SUM=O. DP *287 PRINT FORMPT CHECK *288'T-ECTO —R'LT-S'CHECK^. 3H1 TOTPL NLUMBERS OF DROPS* *289 PRINT FORMAT CHECK2 *290 " ----— T ECTT-F;- 1HOI ZE RRNGE, 521,9H.NOI. DFROP-:., SI, *291 01 4HNO. INCLUSIONS*$ *291 THROUGH CHECK1, FOR I=1,1,I.G.M *292 PRINT FORMAT RES10, ENDPFTCI::, ENDPTCI+1, NUMBERCI),UCI, t) *293 F-CC 1 r —---- MONfINV f *294 ADJUST=O. *295 h_____ UC. _0 _________ _____________ ___- _______- _____.- ________- __ —-------- -------------- -- TR —0UGH RET8, FOR J 1 1, J.G. I DP *296 Uc 1, J)=O. DPK *297 THROUGH RET19, FOR I=1,1,I.G.M DP *298 ADJUST=ADJUST + N(I..J) *299 -------------- - - P P - - - - - -- ----------------- - - --- --- - - - -- UC1,J)=NINCI,.J*SPEEDC:I)/PH3OTOS+UC:I-.1, J *300 RET19 CONTINUE DP *301 SUMNUC, J) +SUJJMP DPK *302 RET18 CONTINUE ODP *303 CUMPCTCO:)=0. DP *304 THROUGH RET21, FOR J=1,1,J.G.N DP *305 PCTCJ)=100. *JJC(1 J)/SUM DP *306 RET21 CUMPCT CJ) =PCT C.J) +CUMPCT C J-1) DP *307 ~ -~~~~ ~RItiT FORMAT RES42 DP *308 VECTOR VALUES RES42=:49H1 CLCULRTIONS FOR INCLUSIONS BASED ON DP *309 0 WHOLE SPRAY*$ DP *309 PRINT FORMAT RES38 DP.K *310 WHENEVER Q.G.75., TRFANS:ER TO IN2 *311 OUT2 CONTINUE *312 PRINT FORMAT RES25 *313 ADD.3=O. *31 4 pAD4=0. *315 THROUGH RET22, FOR I=1,1, I.G.M *316 - DD-3=CAL IPHR (I. P.2-. N-*UHBE.:,R I::, *SPEED CI)+Do, ---- -31 37

-235 ADD4=C(PLPHII).P. 3. 3)*NLU'1EERC I)>*SPEEDO. -)+PDD4 *318 RET22 CONTINUE 319 PRINT FORMAT RES25 * 320 VECTOR V''ALUES RES25='.71H'-:ARLCULATION OF PERCENT OF SURFPCE AN *321 OD VOLUME REPRESENTED BY I NCLUiSIONS*! *321 PRINT FORMAT RES26 *322 VECTOR VALUES RES26=$14HODROP DIAMETER,S 14,21HPERCENT INCLUDE *323 00OD FRE, S6' 2.3HPERCENT INCLUDED VOLUME*.23..................3...THROUGH CHECK.3, FOR H==1,1,H. G. M *324 PRINT FORMAT RES27, 3LPHqCH::'XCH'i- Y(H' f).. *325 VECTOR VALUES'RES27=1H F10.5,S10,E20.5: S7,E20.5*,.*326 CHECK3 CONTINUE -327 ADD1=ADD1*1'OO,./.ADD3 *328 ADD2=PDD2*.1 0..." D D 4.*3........................29 PRINT FORMAT RES44,ADD1, RDD2 *330 VECTOR VALUES RES44=;44H' PERCENT SURFACE REPRESENTED BY INCLU *331 OSIONS =,FlO.5.'/,43H PERICHT VOLUME REPRESENTED BY INCLUSIONS = *331 1,F10. 5*,$ *3.31 END C.ONTINUE *332 TRANSFER TO START 178DPK *333 END OF PROGRAM 179DPK *334 THE FOLLOWING NAMES HPVE OCCURRED ONLY ONCE IN THIS PROGRAM. R- -— LLT. —~ BE ASSIGNED TO THE SAME LOCATION, ND COMPILATION WILL CONTINUE. CHECK4 CONST9 DEPTH WIDTH - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -.... - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - -- -- - - - - ----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

-124 TABLE XII INPUT VARIABLES FOR COMPUTER PROGRAM HEIGHT - Dimension of camera field of view in the direction of spray flow. WIDTH - Dimension of camera field of view normal to spray flow and normal to camera lens principal axis, DEPTH - Dimension of camera field of view normal to spray flow and parallel to camera lens principal axis. CONST1 - Arbitrary constant which can be used to change units in which spray drop velocity is printed out, CONST2 - Control variables calculations for inclusion conditional distriN butions are not calculated if total inclusions Z N,N(mJ) < J=l CONST2 (1 < m < M)o CONST3 - Control variables for CONST3 > 10, calculation and printing of weighted large drop distributions is suppressed. CONST4 - Control variable- for CONST4 > 10, calculation and printing of weighted inclusion conditional distributions are suppressed, M - Number of large drop size ranges, S - Highest moment of large drop distribution to be calculated, T - Maximum number of moment ratios to be computed., L - Control variable: for L = 0, no calculations involving inclusions are made, DOGEM - Control variable: when DOGEM = 0, arithmetic means of diameter size intervals for large drops are used as Di - for other values of DOGEM, geometric means are used.

-125 TABLE XII INPUT VARIABLES FOR COMPUTER PROGRAM (Continued) ENDREM - Control variable: ENDREM controls the length of the remark statements REM1.. REM5o PHOTOS - The number of photos counted for the drop distribution data, NUMBER(l).o (M) - Total number of large drops counted from the single exposure photos: Yl.oYM in Figure 23, DIST(l),. (M) - Distance traveled by the large drops in the respective size ranges, obtained from a plot such as Figure 22 - 1.o.'M in Figure 23. DELAY(1)..o(M) - Time delay used: for this work, DELAY(l) = DELAY(2) = o00 = DELAY(M)O ENDPT(l).. (M+l) - Endpoints of the large drop size ranges, NUM(l)...(T) - Selected moments for numerator of moment ratioso DEN(l)... (T) - Selected moments for denominator of moment ratioso REMl(l)... (ENDREM) REM2(1),... (ENDEM) Remarks which may be printed out REM3(1)..o (ENDREM) at various places in the output REM4( 1)... (ENDREM) REM5(l).0..(ENDREM) DENSTY - Density of flowing phase. CONST5 - Arbitrary constant used to adjust units on momentum for output, CONST6 - Arbitrary constant used to adjust units on energy for output. N - Number of inclusion diameter size ranges,

-126 TABLE XII INPUT VARIABLES FOR COMPUTER PROGRAM (Continued) DOLOG - Control variable: for DOLOG not equal to zero, log (Di) is substituted for Di and log (dj) for djo MOMIN - The highest moment to be calculated for the inclusion conditional distributions, NIN(l1,)..o (M,N) - Total numbers of inclusions counted from the single flash photographs: xlloo xMN in Figure 235 EDPTIN(l)...(N+i) - Endpoints for the inclusion size ranges. NOZD - Nozzle diameter, FLOW - Flow rate of sprayed phase, GAMMA - Interfacial tension. CONST7 - Arbitrary constant which may be used to rationalize units in Reynolds number, CONST8 - Control variable: when CONST8 < o5, conditional distributions of inclusions are not calculated or printed, CONST9 - Not used in program: eliminated in a revision,

-127 TABLE XIII COMPUTER INPUT DATA FOR RUN 10 HEIGHT = 1,2 WIDTH =.96 DEPTH =.10 CONST1 = 1.0 CONST2 =.50 CONST3 = 1.0 CONST4 = 100o M= 12 S =3 T = 4 L= 10 DOGEM = 0 ENDREM = 26 PHOTOS = 7.0 NUMBER(l).. (M) = YloYM in Table II DIST(l)..o(M) = 1..e M in Table II DELAY(l)...(M) = all values are 1.55 x 10-3 ENDPT(l)...(M+l) = 0, 1 x 10-2 2 x 102 o. 12 x 102 NUM(1)...(T) = 1, 2, 3, 3 DEN(1).o.(T) = 0, 1, 1, 2 REMl(l)...(ENDREM) = RUN NUMBER 10 NO 19 HYPO, 130 CC/MIN SEE RUNS 8, 9 CGS UNITS SAT. CCL4 INTO SAT. H20 REM2(1)...(ENDREM) = LENGTH = CENTIMETERS MASS = GRAMS TIME = SECONDS REM3(1)...(ENDREM) = blank REM4(1)... (ENDREM) = blank REM5(1).. (ENDREM) = same as REM2 DENSITY = 1.595 CONST5 = 1.0 CONST6 = 1,0 N = 9 N=9 DOLOG = 0 MOMIN = 3 NIN(1,1)...(M,N) = see x11 o.x in Table II

-128 TABLE XIII COMPUTER INPUT DATA FOR RUN 10 (Continued) EDPTIN(1),. (N+1) =0,.5 x 10-2, loO x 10-20. 4,5 x 10-2 NOZD = 6.42 x 10-2 FLOW = 130, GAMMA = 32. VISC = 1.0 CONST7 = 1.0 CONST8 = 1000, CONST9 = 1,0

RUN NUMBER 10 NO. 19 HYFPO, 1.30 CC.tN. -- - SEE RUNS' 8, 9 C CGS UNITS SAT. CCL4 INTO SAT. H20 NOZZ..'-.LE DIA!',TER -- - 42-O —- - ----------------------------------------------------------------—. — NOZZLE DIAI~ETER.6420.E-01l ~FLOW RATE.21700E _1 INTERFACIRL TENSION =. 32000E 02 VISCOSITY =.10000E 01 REYNOLDS NUMBER.68643E.02 REBEOLD NUMBER =.48^43E 04 —2 —---------------------------------------------------------------------------- JWEBER NUMBER =.14380E 04 VELOCITY THROUGH NOZZLE =.67035E 03 THIS COMPUTfATION US-IES'FRITHMETIf MENs VELOCITY WEIGHTED PERCENTAGES — ___.. LENGTH CENTIMETERS MASS.= GRAMS TIME SECONDS SIZE RANGE NUMBER SPEED PERCENT CUMULATIVE PERCENT PERCENT/SIZE RANGE.00000 TO 01000 193.0 1 -.12) 1 e:1-:10L1 1 2::'_ -------- -- —...-_... —--—..__ _ _,., 0: — ~ -._-, _____ _5 -l5 —-.01000 TO.02000.304.0 13.54838t 35.06729 5.3.61989 3506. 728- 94. 02000 TO.03000.140.0 15.80645 a1 8.4098 72. 46086 1884.09778 03000 TO.Q4000 6.3.0 18.06452 9.68965 82.15051 968.96461 ~ 040.00 TO.05000 L6.0 2 O 0~0000 6.13018 88. 2'O 9 613.01839 ----- _ — ------- --------- 3 - ------- ~ —-----. 05000 TO.06000 15.0 1.93548 2.80143 91.08212 280. 14218.06000 TO.07000 11.0 4. 1399_ L. 25=._. A 1'.82. 5.07000 TO.08000 11.0 26.45161 2.47734 95.82532 247.73415 ~ 08000 TOf 09000 7.0 328.710 1. 8 4 97. 5717 1 69.:42".09000 TO.10000 4.0 3 0.64516 1.04367 98.5608.3 104.36694 10000 TO ~11000.3.0 2'0.323.81043''.401'26 84. 04285. —-- -— ^I C)0 0 _ — __ —-- L —— _-._____ —_ —-_-_ ____ —0 3 - --- ---- - - ^ - ----— __ __ _ _ _..0 2 5 _ _ * 11000 TO.12000 2.0 35.16129 C.59874 100.00000 59.87.366 ""PROfBflBILITY DEN ITTV PND DISTRI'TiNF1'^fN EuiE Y HPItE F NDMVRPL SIZ FRfNGE PRf1BHBIIIT" CUMULATIVE P~ROBABILITY.0 0000 TO.01000.03579.073579.01000 TO. 02000.20294.2.3872 —-.0 200.0 TO.03000.18172 4204.03000 TO. 0.4000 1n.1..13084........... 55128...04000 TO.05000 _ 10_643 95771 *d'5000~~~~~~ —- -------------— " """"~ "".77 ------- ----------------------------------------.05000 TO b.6000 * n0944 71719.06000 TO..07000 05682 77 3:*:]8.07000 TO.08000 071'8.-. —-----.08000 TO.09000._05548_.90114.09000 TO. 10000.. 03825. " 93939.10000 TO.11000*..03405..97344 - - - —.1100- f0 ~ 2 —-76 —----------- T20.U -----------------------------------------------------.1100 TO 1200.0266 1.oOO~ H \,0 I

-130 PROBABILITY DENSITY AND DISTRIBUTION FUNCTIONS WEIGHTED BY 2TH POIW.IER OF RANDOM UIVARIABLE - SIZE RANGE.00000 TO.01000 TO.02000 TO. —- 03000 TO.04000 TO n.050n TO PRIOBABILIT'Y.01000.03000.04Q00.05000. nrnnn.00403 10 22.10774 m 73 9 CrUMUULATIV E PROR I I TY.00403,17470. —--------—, —, —-I,872-4.38545. 4scl rnn _._ _. _ w ~' _' -.,....! _*''-'-v,.06000 TO.c0700,.08309,54209.07000 TO.08000.1 2094 _____33.08000 TO.09000.10609.76911.09000 TO 1 0000.08175. 85086 ------- ------------------------------------------------------------.10000 TO.11000;08042. 93128.11000 TO.120002.06872. 100000 PROBRBILITY DENSITY' AND DISTRIBUTION FUNCTIONS WEIGHTED BY 3TH POWER OF RSNDOM VARIAELE ~~-Sl' ~WANE-~?~~~~E PROBAFILITY CUMULATIVE PROBBI LI TY.00000 TO,01000.00032.00032.01000 TO.02000.01612.01644.02000 TO.03000.,04011.05655.03000 TO.04000.05660 ~'113153-~.04000 TO.05000.07611.18926 ----— 500 -TO. 06000.'06350. 322~~76 ~. 06000 TO..07000.08478, 33753.07000 TO.08000.14239.47992.08000 TO.09000.14156.62148.09000 TO.10000.12191.743 9.10000 TO.11000.13255. 8759.4.11000 TO.12000.12406. 1,00000 PROBABILITY DENSITY AND DISTRIBUITION FUNCTIONS WEIGHTED BY 4TH POlJERO-.F RANDOM. VA RIABLE SIZE RANGE PROBABILITY CUMULATIVE PROBCBILITY'.00000 TO.01000.010002.00002. 01000 TO.02000 ~ g. -t,3i _ 1.02000 TO.03000.01283.01595 03000 TO _______.04000.02535 ___ 4130 ______________.04000 TO.05000.04383.08514.05000 TO.06000.04470.12984.06000 TO.07000.07053.20036.07000 TO.08000.13668.33704.08000 TO.09000.15400 49104.. 09000 TO. 10000.1482.3 _ 3927.10000 TO.'11000.17813.81740. 11000 TO..12000.18260 1.00000 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _- - _ _ _ _ _ _ _ _. _ _ _ _ _ _ _ _ _ _ _ _ -_ _ _ _ _ _ _ _

MOMENTS OF WEIGHTED DISTRIBUTION OTH MOMENT =.1 OOOOE 01 1 TH MOMENT =.25920E- 1 2TH MOMEIT =. 1 1522E-02 4TH PiMOMENT -.573._'-4E-0- -— 5 a —--------------------------------------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ---- - MOMENT RATIOS RRATIO OF 1.00TH MOMENT TO.OOTH MOMENT =.2592OE-01 RATIO OF 2.OOTH MOllMEtt TO 1.00TH MOMENT =.44453E-01 9 — — RfiT --- ---- _3 -------------------------- ---------------—. RATIO OF 3. 0TH MOMENT TO 1.00TH MOMENT -.2'31'8E-02 iRATIO OF 3.OOTH MOMENT TO 2.OOTH MOMENT =.6702E-01____ 3-_ _ _ _ _ _ _ _ _ _ _ COMPUTATION OF MERNS, VAR I ANCES, NAt- IT- FU D. T rEVIATTI N FOR THE RANDOPM VR I ABLLE DIAMETER O THE _ ITH. EIG HTE_ __T I BUTIO ---- -- MERN =.25920E-01 VRIANCE =.4l808E-03 STD. DEVIATION.21931E-01 FOR THE RANDOM VA'RIABLE DIAMETER ON THE 1TH t.EI_!.HTED J __T E. TI __T__i__UT_-_ ____ _ MEAN =.44453E-01 VARIANCE =.85677E-03 STD. DEVIATION =.29271E-01 FOR THE RANDOM VARIABLE DIAMETER ON THE 2TH.WEIGHTED DISTRIBUTION MEN =.63702E-01 VARIANCE -.92042E-03 STD. DEVIATION -.30338E-01 lFOR THE RANDOM VARIABLE DIAMETER TIO THE F'IWER._) 11_ THE NON-WEIGHTED DISTRIBUTION MEAN =.10000E 01 VARIANCE. OOOOOE 00 STD. DEVIATION =.OOOOOE 00 FOR THE lRANDOM VARIABLE CDIAMETER TO THE POWl.ER 1) OFN THE NONJ-I.EIGHTED DISTRIBUTION MEAN =.25920E-01 VARIRNCE =.48037E-03 STD. DEVIATIONI.. 21917E-01 FOR THE RANDOM'V.'ARIABLE CDI!METER TO THE -POER 2) ON THE NON-I..EIGHTED DISTRIBUTIl.O MEAN =.11522E-02 VARIRNCE =.44073E-05 STD. DEVIATION =.20993E-02 SU RFCE AND VOLUME RATES LENGTH = CENTIMETERS MASS GRAMS TIME = SECONDS DIAMETER SURFACE RRF.'ATE VOLLME RTE.5OpODE-02.'2031.74E —01 _ _.197O8E 04. 150OOE-01.34659E 00.6 rS47E-03.-25000E-01.51726E 00 21553E-02 *35000E-01.52140E 00.3C0415E-02.45000E-01.54529E 00_ ~ 4089'7E-02_Q.55OOOE-01.37225E 00..34123E-02 -65000_E-01-_.420.52E 00..45557E-__. 75000E-O1.61 212E 00. 76515E-02 -.E50 —- E-01.5-3694E 00 -.70 —-767E-02.95000E-01 ~.41.375E 00.655 11E-02 __10500E 00.40_'701E 00. 71227E-02.11500E 00.34782E 00..66666E-02 TOTAL RRTES SURFACE RATE - _.50613E 01 - - - - - - -VOLUME RATE -= -5._-.__, — 37.36,E-01

-152 MOMENTUM AND ENERGY TRASFER _RT__ ___ ____L_._E__ _______ ____ —--- LENGTH = CENTIMETERS MASS = GRAMS TIME = SECONDS DIAMETER.MOMENTUM KINETIC ENERGY _ —-- 5P-QE- -_ X_ E X —----------- 2aE. —----------------- _ 3 4.25000E-1.412s2E-02-.32602E-01.35000E-01.58215E-02.52581E-01 -45000E-01,z-.E=-Q2.. —---------— _ -- Q! _------- Ep g__ —----- ___ ______7*2_;2__________ 7___7 - Ql.55000E-01.65.311E-02.71632E-01.. ~OOlE 0_____oo _E-J-__,y___-_2 O__.____-_4 _.O_ _.7500E-01. 1 4645E-01. 1 369E 00.85000E- 01.14559E-01.206rr.5E 00 95000E-01. 125.39E-01.'19213E 00 -.105OE OQ -&_ —-L —----....l ——..-.1 —o.11500E 00.12760E-01.22433E 00 TOTAL RATES MOMENTUM =..1t0285E 00. _ KINETIC ENERGY-' =.1.39.31E 01 CALCLULATIONS FOR INCLUSIOcTS IN DOROPS OF IAMETER. 50000E-02 IOCLLISIOT DI METRF PFERC ENT CLiMUL TIE PERCENT CALCULATIONS FOR INCLUSIONS IN DROPS OF DIIMETER. 1500sOE-01 INCLUSION DIAMETER PERCENT__ _ CulMULiLATlyE PERCENT 25000E-02 84. 615.3S 84.61538.75000E-02 15.38462 _ _ __ __ 100. 00000 12500E-01.00000 100.00000., 1 7500E-0_1.._00000 1_00. 00000. 22500E-0.00000! 100.00000.27500E-O1 __ _______-2_____,__QQQD0aD._ -tO-_O_ -OQQ- ______D._ ___. 32500E-01.00000 100.00000 ~37500E_ —01 QQ -_ —-----------—.. —---- _ _ —.-Q —2-_ ___ —Q,__. 42500E-01. 00006 0 100. 00000.7-50OOE-02..15.38462 100.00000~~~~~~~~~~~~~~~~~~~~~~~. MOMENTS OF WEIGHTED DISTRIBUTION OTH MOMENT _= -____...lQOEl_________________ —----- 1TH MOMENT =.32692E-02 -----— 2TH MOMENT = --— _ 14 2E-04 3TH MOMENT =.78125E-07 4TH MOMENT'=.51983E-09 ___ __ MOMENT RATIOS RfTIO OF' 1.00TH MOMENT TO.00TH MOMENT =.32692E-02 RATIO OF ~2.00TH MOMENT TO 1.00TH MOMENT -.42647E-02 RATIO OF 3;00TH MOMENT TO 1.00TH MOMENT =.23897E-04 RATIO OF 3.00TH MOMENT TO 2.00TH MOMENT =.56034E-02

-133 L:-OMi-jTP- lT-I —- ON OF tEiN —,-.F I i-N.-CE- -,- N - -T- -. EI -1 —---- - RT I -N ---------------- - --- ----- C:OMPU:LITAiTION OH0F tMiE tt'S.'.,~~ ZA::E S. ANH D S -Tr. D E V I ~i T 1 H':. FOR THE RfAiNDOM R...RIRBELE DIRMtETER ON THE.iTH WIEIGHTED DISTFR:IEBUTI ON MEAN =.. 3269 2E-0 2 V'ARIR NCE = T. E TIO. 1777E-02 -FOR THE RFNHiDOMN O...'RIRELE OIktNiETER tN~ THfE i 1TH iEIGH2TE- DISTRIE:UTION MEANH =.42 i47E-02., R IAICE --.- 61 -IS51E- 05 STDL-. DE lPTIN -= 24_870E-02 FiiF.R THE RF.NfDOIM VC'RIBLE DIRMETER ONIH THE:2TH l EI GHTED DISTFRIB LTII-O3N MEFN =.560.34E-02_'VAiRIAEflE = 7 G 3 E -, E0 TD. iDEVIT'ION.25251E-02 FOR: THE RF RNDOM VfIRIF:BLE CDIRMETER TO THE FPOl.iEFR 0::.' ON- THE tN4N-i.-!iEI i3HTED DIST:TRIBUITIO MEA 1r. I 0000E 01 V RR I NCE -I Qtl COE 01. S*T D. D E,'ITI'- 1000IE 00._______ E________ __ __ __ _____,- - ^- - ____.__ __-_-_-_- -,- --- ---- --- - _____ —7- - - - - - -i_ -___ - _ - Tg.. p FOR THE RIlHDOiM V'A'RIBFELE CDIt:IMlETEF. TO THE FOEIIE-F.ER 1) -ON THE NON-i IEIGHTED DIST F.TIBLTIITHN MEiiN - __ __ 31'26-E-2''IR II:E 2544E-1.,____ _I. _S E II _H i FOR THE RFNDO-tM.V RIRBLE CDIIIMETER TO THE PO Ii.ER 2: OtN1 THE NON-lt-EI GHTED EII:'' IB. LtTI ON FERN -.13942E-04. V' -RIfNC:E =..32544E-9_ 1'_ -- STE. DIE'u'IlITI ON. " CALCULALTTIiitS FIR INCLUSIINS IN DRiOPFS i'F DII iETER_.25IOOE-iI01 INCLUSION DIPAMETER PERCENT-:T C:lJMULT I.EF PERCENT.25000E-02 43. 5 E'-, 74 43.5 - 974,75000E-02.35.89744 7' 4871 1 —— 2500E-01 20. 5122E 1.-________00____.. --—..00S —--. 12500E-0 1 20.51282 100. 00000 17500E-01 225 OE-0.1..27500E-01.32500E-01 - 37500E-01. 42500E-01. 00 0. 00000.00000. 00000 1 —-—. _____0000000 ___________ 100.00000 100.00000 100.00000 100.00000 10co.0o00o0 MOMENTS OF lWEIGHTED DISTR I ITION OTH MOMENT =. 10OOE O1 1TH MOMENT =.6.3462E-02 2TH'MOMENT =.54963E-04 3TH MOMENT =.55889E-06 4TH MOMENT. 61609E-0, MOMENT RATIOS RA:TIO OF 1.00TH MOMEN'T TO O0-oTH MOMENT -- =.-3462E-02RPiTIO OF 2.00TH MOMENTT TO 1.. 00TH t OMET = ". 86S l GE-02 RiTIO OF 3.00TH MOMENT TO. 1.00TH tMOMENT =.8_8068E-04 RRTIO OF 3.00TH MOMENT TO 2.00TH MOMENT =.101 68E-01 ------------- ------------------— E —-- --— _ --— _-_ D- - - - - - - - COMPLITTION OF MEANS, VARIANCES, AHND STD. DEI.TIONI FOR THE RFNDOPIl'VRIrE:LE DIAPMETER ON THE OTH WEIGHTED DISTRIBLITIONLMERN =.63462E-02 VflRIAiNCE =. 15081E-cl4 STD. DEVIFITIO. 38834E-02 FOR THE Rf:lNDOM _VAlRIABLE LIAIiMETER ON THE ITH W.EIGIHTED DISTF.TIEBUTION MEfN =.8S61 6E-02'.'fR IA:NCE = 1.3.1:33:E-04 STDE. IEVIPTIONH=...36589E-02 FOR THE RANDOM VRRIfBLE DIRMETER ON THE 2TH WEIGHTED DISTERIE:UTICON MERN =.101S68E-CI1 I f'RIANCE =. 892,12cE-0.5 STD. DE'ITION =.29881E-02 FOR THE RNILDOM VAi)RIAiBLE (DIIiMETER TO THE POlilER 0ci: ON THE NtON-!l.EIFHTELD DISTRFIEBTION ~ —---------------------- i 2 -— O 2 —---- - A -R Pi = —- - -- -- -- - - - -- - - -- - MEiRN =. I 0000E 01 V1RIf'NTCE -.L- iOOcL-IE 00 STD. DEVI E TI O =.00CIiIIo-liE 00 FOR THE R!-]HNEIOM',,'FIRIPBLE CDIItRMETER TEi THE _PgldIEFR 1:: ON_ THE NiONliiEIGHTE _L ISiiTFI _TIO[' MEN =.- 63462 E-02 Y':RRI NHC:E =. 14.94E - 04- STD. DIE'TVITIiON = 38333E-02 FOR THE RANDO*M VYAPRIRBLE CDIIMETER TO THE PCIW.IERF 2) ON THE NON-WEIGHTED DISTRIBUTILiN MERN =.5496'E-04'VARINCE =..3'8 —.I4E-I1-8 STD. DEVI.TION =.:5603E-04

___2500_____I______ 15__________3. 15789 ______________________________ C AL:U LATIONHSF FOR INC LU z";I!S I It]1 D Rf'F'S 0 F DlI R H E TER.3 5000 E - 1 1 I NC:LULSIlO DIAMIETER PERCENT CU:lULATI. E PEF:CENT 25000E-02 1.3. 15789 1 3 1578.,. 7.500E-0i.31. 578',544.73684 _ 125;OE-01.34.21153 78.94737 ----------------------------------------.1750OE-0 1 5.789'.47 94.73684 ----— E^ —------—.- ----------- -- ----- - -- ------ --------,27500E-01..oo 00000 100.00000. 32500E-01. 00000 1 00. o0000.37500E-01.00000 100.00000 42500E-01.00000 100.00000 MOMENTS OF WEIGHTED DISTRIBUTION OTH MOMlENT = 10000E 1 _____________________________ ___' 1TH MOMENT ~= ~l 1. -09~21 E-0 1 2TH MOMENT. 1 4704E-!.3__ 3TH MOMENT =.22492E-05 4TH MOMENT.37654E-07.. —.,,,, —-,, —j-i'ti -y ---------------- MOMENT RATIOS RATIO OF 1.00TH MOMENT TO. —-OOTH MOMENT =. 1021E-01 RATIO OF 2.00TH MOMENT TO 1.00TH. MOMENT =. 1.3464E-01 RRTIO OF 3.00TH MOMENT TO 1.00TH MOMENT =.20595E-03 -_______-R__IIOF___._OQ_ T__MQNT__ g____0_______ COMPUTATION OF MEANS, VARIfNCES, AND ST. DEVIATIONS FOR THE RANDOM VFRIABLE DIAMETER ON THE OTH WEIGHTED DISTRIBLUTION MEAN =. i10921E-01 VARIANCE =.28521E-04 STD. DEVIATIAON-.53405E-02 - FOR THE RANDOM VARIABLE DIAMETER ON__ THE 1TH WEIGHTED DISTRIBUL-TIOHN MEAN - 13464E-01 VAFiRIANCE 253 4'0E-04 STD. DEVIATINI -.503.3_9E-02 FOR THE RiNFDOM VPRIABLE DIAMETER ON THE TH WTHEIGHTED DISTRIBUTION MEAN =._15296E-01 VARIANCE =.22699E-04 STD. DEVIATION =..47643E-02 FOR THE RANDOM VARIABLE COIAMETER TO THE POW1ER O) ON THE NON-WEIGHTED DISTRIEBUITION MEAN_____. ______ OOOO__ E 0_____1 VARIAC__E=__.OCLOE.00E _ ____STD. DEV__IATION ____.OOOOOE_ 00 FOR THE RRANDOM VARIABLE CDIAMETER TO THE POWER 1) ON THE NON-WEIGHTED DISTRi:IBUTIONN — iE~rL —-|0fi1PJlST~lDN~0|r-iN1Erlolts'D —-yiIiritisi 5_ ___ r*2ZJ7Jl-EllISTI-C}-ri-,l__ ______ —— _-?_g___ MEAN =.10921E-O1 VARIANCE = 27770E-04 STO. DEVI'TION =.52697E-O2 FOR THE RANDOM VARIABLE.l DIAMETER TO ITHE POWER 2) ON THE NON-Wi:IEIGH.TED DISTRIBUTION MERN =.14704E-03 VARIANCE =. 1,034E-07 STD. DEVI.TION = _ - 1`2662E-03 CALC.ULATIONS FOR INCLUSIONS INM DROPS OF DIARMETER.45TOOE-01 INCLUSION DIFMETER PERCENT CUMULATIVE PECEC~NT_.25000E-02 17.46032 17.46032 75000E-02 12 85 7 1 1- 746-03 ~ —---— ^ —-^gO Q2 __ _________J-Z —----------------- j --- ------------—,46- — ___-___-.12500E-01 44.44444 76.19048 ~17500E-01 9.52381 85.71428 ------------ 5E __________________ 238____.728 —----------------------------.22500E-01 11.11111 96.82540.27500E-.01 1.58730 98.41270.32500E-01 1.58730 100.00000.37500E-01.00000 100.00000.42500E-01.00000 100.00000

-135 MOMENTS OF WEIGHTED DISTR I BUT I N O'TH MOMEHN'T =. 1 O00OE 01 ------ -----— _ ---------------— I —-l-1-lE__-.- - _ - _ - _ - _-____ ____ ____Q_ _ ___ __-____-_-__ —-__ _ ____ ^ 1TH MOMENT =. 12183E-01:2TH MOMENT =. 1 9276E-03.3TH MOMENT =..358'21E-05 — 4TH MOMENtT =. 75505E-07 —---- MOMENT RRTIOS RRTI OF 1. 00l H MOMlENT TO.. 00 TH MOMENl1tET ------ 1 8 — E - 0. 1 —RRTIO OF 2.00TH MOMENT TO 1.o00TH MOMEHT -. 1 5: 22E-01 RFTIO OF 3.O0TH MOMENT TO 1 00TH MOMENT =. 2944E-0-.3 4:_____. RATIO OF 3. 00TH MOMENT TO 2J-1D T H MO tMEN'TT =. 18583E-01 COMPUTATION OF MEANS:', V'lRINC:ES ARND STr. DEI,'I ITIONS F-rz... _.. _ _g_ _ J -- Qt......P -LASE EJ.PEIEL_. TI.. —..E-... - L-~____ FOR TJ R jj_jDrt' Le-L. l__.IEFLT.IEJ-J —--— _I II.L MERfN.1218.3E-01 VFRIRNCE =.45059E-04 STD. DEVITIONI - 6.7126E-02 FOR THE RRfNOOM V.RF I E _LE-_ Ll T_. l_1.iTL-E_-_i- J] JESI E__LII l __ _J_ MEAN =.15822E-01 YAFRIPNCE =.44389E-04 STD. DEVIATION =.66625E-02 FOR THE RAtNOM V''RIA BLE DIAMETER ON THE 2TH WEIGHTED DISTRIBUTION MERN =.1858.3E-01 VARIRNCE =.47117E-04 STD. DEVIATION =.68642E-02 FOR- THE RAitNDOM VRRIBELE (,DIIAMETER TO THE FPOWER ) ii THE NON-Wl.EIGHTED DISTRIBUTION MEAN =.1000E 01 V RIRNCE =.001E1OE 00 STD. DE'.ITION =.OOOOOE 00 FOR THE RNftDOM VARIl:BLE (:DIIIAMETER TO THE FPOi'.ER 1) ON THE NOtN-WEIG1HTED DISTRIBUlTION_ MERN =.12183E-01 VRIFINCE =.44~344E-04 STD. DEVIlTION =.66591E-02 FOR THE RANDOM'VARIABLE CDIAMETER TO THE F'OlER 2) ON THE T NON-liWEIGHTED DISTRIEUTIIONt ME!N =. 1 9276E-0.3 V iRRItNCE =.3.3. 5 0 E - 07 STD. DEV I FTIONr =. 1 9583E-03 C LLCRiULfTIO C F OR- IIC:LUSIOS IN OROPS OF DIMETERF.55000E-01 ________2500E-02_______________. 1. 914._1 91489.750lOE-O2 27.6'957 59..57447 ~1 25100E-01 8:..51064 68. 08511.1 7500E-01 12.7u.9'' 80. 85106 ~ 22500E-01 10. 03.8: 3 0' 1. 48'-9361. 27500E-01 2. 1 27,'- -.6.61702..32500E-01 4 *255-2 97. 87234.37500E-01.1100000 97.:7234.42500E-01 -. 1276jO 100.00000 _____________________________________________________ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -_ MOMENTS OF IlE IGHTED DISTRI BLT I OTN 0H — MOMENT =. 1 -0000E 01 1TH MOMENT =.114.36,E-01'2TH MOMENT. =. 22.327E-0.3 3TH MOMENT =.57204E-05 4TH MO.MENT =. 1 7126E-06 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _- - - - - - - - - - - - - - - - - - — _ MOMENT RRTIOS -RATIOS O 1 0 H,T —-----------------—'-1 —-',' —, —---—........ —--—......... -..........................-.. RRTIO OF 12.00TH MOMENT TO 1.00TH MOMlENT =. 1 1436E-01 RATIO OF 2. OTH MOMENT TO 1.00:TH MO1MENT =.1 i952.3E-01 RAT I lJ OF.3. 00tTH MOMENT TOI 1.00TH tMlOMENT = 5:102CE-I 3 RATIO OF 3.00TH MOMENT TO 1.00TH MOMENT -..50020 E-03 ---— RTI-O O.-F__3.0TH MOMETTO -— 2.:TH MO0MENT _.5621-01

-136 COMPITRATION OF MEAltS, VARIANCES, FAND STD. DEVIATIONS FOR THE RANDOM VARIABLE DIRMETER ON THE OTH WEIGHTED DISTRIBUTION MEAN =.11436E-O1 VARIANCE =.9i449GE-04 STD DEV.IATION = f.9720'-E-02 -FOR THE RAlNDOM VARRIABLE DIAMETER ON THE ITH WEIGHTED DISTRIBUTION MERN =.1952.3E-01 VARIFNCE =.12163E-03 STO. DEVIATION= 1:10'2E- 01 — TR- ~HTERFi~-crtDOOM VtRI BLE DI AMETER ON THE 2TH WIjEIGHTED DISTRIBUTION MEAN -.25621E-01l VARItNCE. 11303E-03 STD. DEVIATION =.' 1032E-01 FOR THE RANDOM'tVRIABLE CDIlMETER TOHE POWER 0): O THE NON-btEIGHTED DISTRIBUTIOH MEAN =.1OOO0E 01'ARIANCE =.00000E 00 STD. DEVIATION =.O000OCE -0 FOR THE RANDOCM1 VARIREBLE DCOIRAMETER:E TO THE POFWlER 1) ON THE NON-dWEIGHTED DISTRIEBTIOtF MERN = 11436E-01 VARIRNCE'.2485E-04 STD. DEVIATION_. -961 69E-02 FOR THE RFNDOM V'RIFABLE (DtIMETER TO THE POWER 2) ON THE NON-WlEIGHTED DISTRIBUTION MEAN =__.22327E-____3 RIANCE =._. 12141E-06 TD. DEVITION.3__ 4844E-03 CALCULAT I OHS FOR I NCLUSI NS I N DROPS O F DI AMETER. 65000E-01 INCLUSION DI METER PERCENT CUMULATIVE PERCENT.25000E-02 25.00000 25.00000. 75000E-02. 20. 45455 45.45455.12500E-01.34.09091 79.54545.17500iE-01- 11.'3364 90.90909.22500E-01. 2.27273 93.18182. 275QOE-01. 00000 93.181 82.32500E-01 6.81818 100.00000.3 7500E-01.00000 100. 00000. 42500E-01. 00000 100.00000 MOMENTS OFWEIGHTED DISTRIBUTION______ _____ _________________________ OTH MOMENT =. 110000E 01 1TH MOMENT. = 11136E-01 2TH MOMENT =. 1 8466E-0.3 3TH MOMENT =.3. 39645E-05.4TH MOMENT =. 10153E-06'- MOMENT RA TIOS RATIO OF 1.00TH MOMENT TO.00TH MOMENT. =. 1 1 31.$6E-01 RTrio'rOF~~2.f00TH MOMENT TO 1.0TH MOMENT =. 16582E-01 RATIO OF 3.00TH MOMENT TO 1.00TH MOMENT =.35599E-03 RATIO OF 3.00TH MOMENT TO 2.00TH MOMENT =.21469E-01 _ _ _ _ _ _ _ _ -__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

-1-57 COMPUFLITT IOt O F MtER tNS,.. RRI ARNC E.S, FHtD ST 1. D-E r1, I RT I IO rMERN =. 111 36E-0 1'Vt.'RRIHS:E =.iS2051 E-04 STD. DEV'ATT I T =.I 787t72E-02 FOR THE RFlNEIOM VARIABELE DIMtETER lOl THE tTH I. L EIG'HTED DISTRIBlTIUCTl _ M ERN =. 1 tL 8 E i-'I 1 IR C A CE =.8 -I 2' E- -0 4 STD. DEVT I1 i E H 91065E-02 FOR THE RFAHDOM'..'RIRBLE DIMiETER ON THE 2TH I.lEIGHTED DISTRIBUTI ON MERN =.2..E -'1 VARIANCE = 8.. n' E - 0 4 STD. DEVITION =. 9 5376E-02 FOR THE RANHDtOM' VARIHELE DIAMETER TI' THE FIEF 0: OHi THE NOH-EEITHTED STRIBUT MEAIN =.1 9E-01 VR I HNCE E=. OI-''f-E 00 STD. DEV I T I I' -,"'95O37E 00 FOR THE RAHtCOM V'ARIABLE (DIAMETER TI: THE F'I.lI0ER 1:0 OH THE NtOH-iEIGHTED DI'iTR:.IBUTItION MEN = - 1 F1.3-1 E — 1V-IRIANCE =. 60401E-04 STD. DEVI TI O 1 l1 -7: 7?07:l2E-02 FOR THE RRHDOM V.'RI ABLE (DI iMETER TO THE F' POI.ER 2:' Ol 1 THE ON-I.E IIGHTED TE1!'W: U'iT. T O MEAN =.18466E-0O V10RI NCE =.6 74-3_2E-O7 STD. DEVIRTIO = CPLCULLT I -lNS FOCR II.LUSIOHS IN DROF'S OF DIAMETER.75000E —11 5__ 2.00E-022__.92.308 ___26. 92308____ 75000E-02 11.53846 38.46154 2fE 1 50E 12,. 2 923 1 7. 1 5385 - - - - - - - - - - - -125E-01 ----- - 2 2 --------------- 7115385 ---- 17500E-01 9.61538 80.76923.2251OE- 1 9.61538 90.38461 ____.32'500_E-01 _3. 84615__ __96. 15385',.37500E-01 1.92308 98.07692 -- 4125'00E — 11. 923. ——: 1 00:n4'. 00000. I._' ---------— 4 —------— O —----------------- ---- -— i.. — ----------------- ------— J — - - - - MOMENTS OF WEIGHTED DISTRIBUTION__ OTH MOMENT -.1 -00E 01 1TH MOMENT =.12788E-001 2TH MOMENT =. 25433E-03__ 3TH MOMENT =.65126E-05 4TH MOMENT =.. 1 967 10E-06 -. - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ----- ----- ---- - - - - - - - - - MOMENT RATIOS RAPTIO OF 1.00TH MOMENT TO-. J-0TH F1 —OMEHT =. -127 —E-01 RATIO OF 2.OOTH MOMENT TO 1.00TH MOMENT =,19887E-101 RATIO OF 3.OOTH MOMENT TO 1.00TH lMOMENT =.50926E-03 RTIO OF 3.00TH M,. I_E!"~T_ _ ___TL___2_ ___,___________, ___________ COMPUTfTION OF MEANS, VARIRiF. CES, AND STE'. EVIPATICONS FOR THE RMNDOM VAfRIABLE DIAMETER ON THE CITH WEIGHTED DISTRIBUTION MERN __.12788E-01 VRINCE =:, 562E-04 STD. DEVIATI-H =.-6209E-02 FOR THE RANDOM V'..'RIPBLE DIPMETER ONH THE 1TH WEIGHTED DISTRIBUlTIOH MEAN..19887E-01 VARIAHCE =.11.59E-0..3 STD. DE.VITILON =.= 10770E-01 FOR THE RFNDOM VPRIFBELE DIAMETER ON THE 2TH WEIGHTED DISTRIBUTION MEAN = _.25607E-01 VARIAfNCE = 1l'.'-.8E-0.3 ST.. 1DEVIATION =. 10'95-4E-01 FOR THE RfANDOM V'RIABLE (DIAMETER TO THE POW.ER. 0 ON THE NON-W.EIGHTED DISTRIBUTION MEAN =.10000E 01 VARIANCE =.S 1 ICOE 00 STD. DEVIATION =. OOOOOE 00 FOR THE R'NDOM VARIrBILE (DIAMETER TO THE POWFER 1:: ODN THE NON-WEIGHTED DISTRIBUTION -MEAN.12788 E-01 VARIA2CE -.' -07E82E-04 -STEI. EDEVITIOH =.9527280E-02 FOR THE RFNDOM VAtRIABLLE CDIMlETER TO THE PO.l E R 2: ON THE NON-W.EIGHTED DISTRIBUTION MEAN =. 25433E-03'.,'RR IANCE =. 1 3202E-06 STD. DE'VIt ATIIO =. 6334E-03 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

-138 CALCULATIONS FOR I tNCLU-SINS — E__i-_P.QE'_ _.Q_ QEIEE_:- — JODE_-O.1 INCLULSION DIAMETER PERCEFNT rl:IMLI!TT'.IF PFPRfFNT.25000E-02 7.54717 7.54717.________-,_ ~..aDJE-:Q2: —-----—. ---------—.i3 - 2.5 —-__ —--------------------------------------.12500E-01 41.50-.43 54.71698 ___ __ —-- - _. -------—.L —--—. ——._._. —-— __._ —---—..5_ —---------------— ___ —----.22500E-01 22.64151 96.22641.27500E-01. oonnnO 96.22641.32500E-01 3.77358 100.00000 -37500E-01 __ ------—. —------—._10i_, D —- -----—. — —..Q0 —-.42500E-01.00000 100.00000 ---— OENTS-O —-- - DITRI —TO —---------------- ------------------------------------------------ MOMENTS OF WEIGHTED DISTRIEIUTION O__ TH MOMENT _.1 E 01_______ 1TH MOMENT =.15425E-01 2TH MOMENT =.28078E-0.3 3TH MOMENT =.57214E-05 4TH MOMENT.12814E-06________________ MOMENT RATIOS RATIO OF 1.00TH MOMENT TO.00TH MOMENT =.15425E-01 RATIO OF 2.00TH MOMENT TO 1.00TH MOMENT =.18203E-01 RATIO OF 3.OQTH MOMENT TO 1.00TH MOMENT =.Y37093E-03 RATIO OF 3.OOTH MOMENT TO 2.00TH MOMENT =.20377E-01 COMPUTATION OF MEANS, VARIANCES, AND STO. DE'VIATI NS FOR THE RANPD_a_ VARI ABL_EtJRi~ _QU i 1iIBUI - ---------------- MEAN =.15425E-01 VARIANCE =.4.3686E-04 STD. DEVIATION = 660-.'E-02 FOR THE RANDOM.'VARIABLE DIAMETER ON _H. ]TH__IITHEIF___IQI_ r MEAN =.18203E-01 VARIANCE =.40327E-04 STD. DEVIATION =.63504E-02' FOR THE RANDOM VARIABLE DIAMETER ON THE 2TH WEIGHTED DISTRIBUTION MEAN =.20377E-01 VARIANCE =.41948E-04 STD. DEVIATION =,64767E-02 FOR THE RANDOM _VARIABLE (DIAMETER TO THE POI.ER 0) ON THE NON-WEIGHTED DISTRIBUTION MEAN =.10000E 01 VARIANCE =.OOOOOE 00 STD. DEVIATION =.OOOOOE 00 FOR THE RANDOM VARIABLE (DIAMETER TO THE. POW._ER 1) ON THE _NON-WEIGHTED DISTRIBUITION MEAN =.15425E~-01 VARIANCE =. 42862E-04 STD. DEVIATION =.654,'69E-02 FOR THE RANDOM VARIABLE (DIAMETER TO THE POWER 2) ON THE NON-WEIGHTED DISTRIBUTION MEAN =.28078E-03 VARIANCE =.49304E-07 STD. DEVIATION =.22205E-03 -~INCLUSIOtN DIAMETER. PERCENT CLUMLILATI VE PERCENT.25000E-02 15.15152 15.15152.75000E-02 27.2727.3 42.42424.12500E-01 18.18182. — --- 60606 —-.17500E-Crl 15.15152 75.75758.22500E-01 12.12121 87..87879.27500E-01 6.06061 93.93939' ~$.32500E-O01 3.03030 96.96970.37500E-01.00000 96.96970 -----------.42500E-01 ------------- 3.03030..._1_ - -j-Q-.JL_00 __________- - -. - - - - - - - - - - - L - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _ _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

-139 MOMENTS OF.EIJEIGHTED DISTFI EUTIO T — H -MOMENT -. 100-001E 01 1TH MOMENT =. 14015E-0 1 2TH MOMENT =.28504E-0.3'3TH MOMENT =.72921E-05 4TH MO'MENT =.2179'2E- _ _ MOMENT RATIOS RATIQ OF 1.00TH MOMENT TO.00TH MOMENT =.14015E-01 RATIO OF 2.00TH MOMENT TO 1.00TH MOMENT =.20338E-01 RATIO OF 23.OOTH MOMENT TO 1.00TH MOMENT =.520.30E-03 RATIO OF 3.00TH MOMENT TO 2.00TH MOMENT =.2558.3CE-0l COPTRAT TIO -F - ME- n. —l TH lOM ENltt TND S TD E T I-'-O - J COP TTI ON OF tMEH Ap R I AtC.ES, AND STO. DEV. I AT I OS FOR THE RANDOM VARIABLE DIRMETER ON THE OTH WEIGHTED DISTRIBUTION MEArN -.1401i5E-01 VARIiNC-E =.91383E-04 STO. DEVIATION =.9 55.94 E-02 FOR THE RANDOM V'AZRRIABLE DIAMETER ON THE 1TH WEIGHTED DISTRIBUTION MEN.20.3.38E-11 V!ARIANCE =.11001E-03 STD. DEVIATION =.10489E-01 FOR THE RANDOM VARIABLE DIAMETER ON THE 2TH WEIGHTED DISTRIBUTION MEFAN =.25583E-01 VRRIANCE =. 11 347E-03 STD. DE'VJITION =.....0652E-01 FOR THE RANDtOM VARIABLE (DIRMETER TO THE POWER F. o ON THE NON-tlEIGHTED DISTRIBUTION MEAN =.10OOOE 01 VARIJANCE -.OOOOOE 00 STD. DEVIT ION.O0tOOE 00__. —------------------------— _______ —-- ---— __-_____ —-- FOR THE RANDOM...RIABLE CDIAMETER TO THE FPOW.ER 1) ON THE NON-WEIGHTED DISTRIE:BUTION MERN =.1 4015E-01.PIRI tNCE =. 8__.613E-04 STD._____E_ DZ_.._EIRIN.-. 94.1.35E-02 FOR THE RANDOM'VARIABLE CDIAfIMETER TO THE POWER 2) ON THE NON-WEIGHTED DISTRIBUTION MEAN =.28504E-03 VARIAlNCE =.1 3667E-0~, $ TISTD. DEVIFITION =.36969E-03 CALCULAT IONS FOR I tN-:LLI INRPS I otsI - F DI RMETE.10............ _50_0E -00........... INCLULI ION DI RMETER _PERCENT_ CUMULATI' PE PERCENT _.25 00E'-02. 00f000. 0000 750OOOE-02 flOOOO.00000 12500E-01.30.00000.30.00000.17500E-01 55.00000 85. 00000.22500E-01.00000 85.00000.275OiE-01 5. 00000 90.00000.32500E-01 5.00000 95.00000 ~37500E-01 000Cooo0 95.00000 425 —--— E —01 -5. 1l00000 -- 1 - -00-. 00000 —- -----.42500E-01 5.00000 100.00000 MO1MFNTS IOF 1IiF rTf;-TFf nTr ITP. I TLITT ~IN OTH 1TH 2TH 3TH 4TH MOMENT = MOMENT = MOMENT = MOMENT = MOMENT =. 10 00E i01,18500E- 01.39625E-0.3.10128E-04.30641E-06 MOMENT RFTIOS RATIO OF 1.00TH MOMENT TO.00TH MOfMlENHT =.18500E-0.1 RATIO OF 2.00TH MOMENT TO 1. 00TH MOMET =. 21 419E-01 ---------- RATIO OF 3.00TH MOMENT TO 1.00TH MOMENT =.54747E-03 RATIO OF 3.OOTH MOMENT TO 2..0TH MOMENT =.25560E-01

-llo COMPIUTATIOH OF MEANS, YtR.'IPtHIC:ES_ ANDEL STEi. DEVIIATIONHS.............._______l__JHE_ __ ____ _________ __ _ _ __ J_____ _ _D J_ _ _ _ _ FOR THE RPANDOM VARIABLE DIAMlETER OH THE rH WEIHTEI_DISTRQ _BIeT!EI I[l__H MERN =.18500E-01 VARIANCE =.5r-';8'42E-04 STD. DEVIATION =.75394E-02 FOR THE RANDOM VARIAJIBLE DIAMETER OH THE ITH EIGHTEDISTLI ______IT___ MEANt =.21419E-01 VARIRNCE =.93364E-04 STD. DEVIATION =.96625E-02 FOR THE RANDOM VIARIABLE DIRMETER ON THE 2TH WEIGHTED DISTRIBUTION MEAN =.25560E-01 VARIlNCE =. 12629E-03 STD. DEVIATION =.11238E-01 FOR THE RANBDOM VARIABLE,:DIAMETER TO THE F'It.0ER 0:: OH THE NON-WiEIGHTED DISTRIBUTION MEAN =.10000E 01 VA'fRIFNCE =,IiOOOOE 00 STD. DEVIATION = OOOOE 00 FOR THE RiANDOM VAPRIABLE:CDIPMETER TO THE POllIdER 1) OH THE NON..-W.EIGHTED DISTRIBUITIOt__ MEAN =. 1.51I'IE-01',.,I'RIlNCE =-.5'$l00E-0C4'-STD. =DEVIF TION =-, 73485E-02 FOR THE RANDOM VARIRABLE (D.IAMETER T TE ER T2 T)HE ON THE NON-WiEIGHTED DISTRIBUTION MEFAN.3'6.25E-03 VFRIArNCE =.14'40E-06 STD. DE'.'I-TION =. 3:52E-03.25000E-02.00000.00000.75000E-02 6.6666 7 6.66667.1.250,E-01 53.333.3.3 60. 00000. 22500E-01.00000I 86.66667 ~ 2700CE-01 7.". 00000 86. 66667.322500E-01 13...33333 100.00000.37500E-01.00000 100.00000 42500E-0 1. C.i0000 100. CI00000 2TH MOMENT =. 30958E-0.3 3TH MOMENT =.70760OE-05 4TH MOMEN'T =. 18700E-06 MOMENT RATIOS.... RRATIO OF 1.OOTH MOEMENT TO.THMOENT.1616E-01 RATIO OF 2.00TH MOMENT TO 1.00TH-MOMENT =. 1914"9E-01 RAPTIO OF 3.OOTH MOMENT TO 1.00TH MOMENT =.43769E-03.RATIO OF 3.00TH MOLMENT TO. 2.00TH MOMENT = 22857E-01 COMPIUTiflTION OF MERNS~, VRIAHCESP AHD STEO. DIEVITIONS FOR THE RANDOM VARIABLE DIAMETER ON THE OTH WEIGHTED DISTRIBUTION MEAN = lt16167E-O1p VARIANCE = 5.1667E-04 STD. DEVIATION =.71880E-02 FOR THE RANDOM VARIABLE DIMETER ONF THE ITH WEIGHTED DISTRIBUTION MEN ____.19149E-01 VRIANCE = ____ 76061E-04 STD. DEVITION =.87213E-02 -FOR THE RANDOM,VARIABLE DIA METER ON THE 2TH WEIGHTED DISTRIBUTION MEAN =.22857E-01 VARIANCE =. 874.31E-04 STD. DEVIATION =._93505E-_02 FOR THE RFNDOM VARIABLE (CDIAMETER TO THE POWI.ER -0) ON THE NON-WEIGHTED DISTRIBUTION MEAN =.10000E 01 VARIPANCE =,.OOOOOE 00 STD. DEVIATION = -OOOOOE 00 FOR THE RANDOM VPRIABLE (DIAMETER TO THE POWtb ER 1) ON THE NON-WEIGHTED DISTRIBUTION MEAN =.16167E-01 VARIANCE =..48222E-04 STD. DEVIATION..69442E-02 FOR. THE RflNDOM VAlRIABLE CDlIRPETERTO THE OIER 2) ON THE NON-WEIGHTED DISTRIBULITION. MEAN =..30958E-03_ VARIlNCE =.91 1,56E-07 STD. DEVIFTION =.30192E-03 F0P TH RStTOiN fetFiP~iBE SI~P1EEF. T TH PllWE'; CN T E t~t4l~~lE~uHE~lEI'DTIPU~l-t4

-141 TOTRL NULIMBERS OF DROPS SIZE RANGE NHO_. i RO P S H_ _ ~'_NO. INCL S I FOi' NS.00000 TO. 01 000 1 93' 9. 00000 I00000 ~ 01000 TO.012000.3E04.O 1OO.00 1'O ~ 02000 TO. 03000 1 40. 0 1: - 0 E -. 3. 3'. 000 I * 0.3000 TO.04000 3. 00 00. I 38. 00.040010 TO.0D5000.36.00000:OC G i3. _00000 _ 05000 TO.00____________________. 0000 47. _. I-. I 0.06000 TO.07000 11.00000 44.00000. 07000 T 8 1-T.C l D O. O1 1. C O CIC~ 55. -.. 00 Cl 0 C!.087000 TO.0 1000 1 7.00000 53.00000.091n00 TO.10000 4. 000011110. 33..011 000. 10000 TO. 1 1000.3.00000 20.00000 ~ 11000 TO. 1 2r0O _2.00000 __15.00C 00___ CRLCULATIONS FORF INCLULSIONS BRSED ON WHOLE FSPRA.,. INCLUS IONf DIRMETER PERCENT _CU MULRAT I E PERCENT____ _.25000E-02 19.77868 19.77868.75 000 E- 2 1 7. 14 __ 1. 3. 12500E-01.31.365 4 68.32547 1 7500E-0 1 15. _6602 8.3.99349 --------------------------------------.22500E-01 9.13588 93. 12938.27500E- 01 1.6. 40.36 94.76973.3250-OE-01 3.8.3401 98.60374.375010E-01. 266' 8 98.8706.3.42500E-01 1. 129.37 100.00000 MOMENTS OF WEIGHTED DISTRIBUTI O OTH tMOMENT =. 1 000.OE 0 1 1TH MOMENT =. 12778E-01 2TH MOMENT =. 23120E-0.3 3TH MOMENT =.52.3.35E-05 4TH MOMENT -. 1 406OE-06 MOMENT RfT IOS __ RATIO OF 1. 00TH MOMENT TO.)00TH MOMENT =. t12778E-01 RflTIO OF 2.00TH MOMENTF TO 1.00TH MOMENT =. 1809.3E-01 RRTIO OF 3.00TH MOMENT TO 1.00TH MOMENT =. 40956E-0.3 RATIO OF 3..OTH MOMENT TO 2.00TH MOMENT =.22.37E-01 COMPUTATIlON OF MEItNS, ARF IINCES, ND -STD. _DEV I TI ONS — FOR THE RRIINOM_ VRIABLE DIAMETER ON THE OTH WEIGHTED DISTRIBTION —-------- ------- MERN =.12778E-01 VARIt-NCE =.68072E-04 STD. DEVIRTION =.82506'E-02 — FOR THE RANDOM._v'ARIELE DIAMETER_ O THE 1TH WEIGh' L ISTR_ I_ —BUTIL N — -ER- N =. -:18093IE-01 I.-1IARIPFNCE =.8-2408E-04 STD. DEVIRTION =.90779E-02 FOR THE RFINDOM VIRlRIRELE DIAMETER ON THE 2TH W.EIGHTED DISTRIBUTION MEfN =.226.37E-01 VARIANCE =.95945E-04 STD. DEVI.fTION =.97952E-02 FORF._ THE RN.: ADOM'VARIABLE CDIAMETER TO THE POWER O) O THE NON-WEIG HTED DISTRIBUTIO MEAN =. 1OOOOE 01 VfRIAfNCE =.00000E l0 STD. DEVIATION =.OOOOOE 00 FOR THE RANDOM VARIABLE (CIAMETER TO THE POldER 1) ION THE NON-WEIGHTED DISTFRIEUTIOFN MEfRN =.12778E-01 V RIA TNCE =., 7909E-04 STD. DEVIFTION =.82407E-02 FOR THE RfNDOM'VARIABLE CDIiAMETER TO THE POFI.EFR ) O THE NON-WEIGHTED DISTRIBUTION MEfN -.2.3120E-03 ViRItfNCE =.8714GE-07 STD. DEVIATION =.29521E-03

CALCLILATION OF PERCENT OF SURFAC:E flHD','LLiME REPRESENTED E'' INCLLUSIOINS DROPP DItlMETER PER ErCENT INCLUDIED FREEA PERCENT I IN:LUDED V..'OLUlME.00500.18:.345E-03.32496E-04.01500._- l. --------— E ------------- " —4 E_________________ 89 EQ.02500.24500E 01.99643E 00.03500.72400E 01 _.31C4E_6_2__E ___ _ -------------- 3 —------------------ --------------— ___ ________ -- - - -.04500.16658E 02.68792E 01. 05500.23127E 0212. 10773E 02.06500.17483E 02.57744E 01.07500.21374E 02._72976E 01.08500.29424E 02. 70538E 01.09500.26-056E 02.70168E 01. 10500.2.3961E 0:2.58327E 01..11500.17557E 02_. 34895E 01 PERCENT SURFACE REPRESENTED B' INCLUSIONS = 1 6.93234 PERCENT VOLUME REPRESENTED B' INCLIUSIONS - 6.01691 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -_ _ _ _ _ _ _ _ ----------------------- ------------------- -----------------------------— __ — __ -----------------------------.___________________________________________________________________________- ______ —-----------— _________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ____________________________________ —__________________-___________________________________________________ - - - - - - - - - - - - - - - - - - - - - - - - -. — - - -.- - - - - -. - - - - -... — - - - - - - - - - - - - - - — _______________________________________________________ —------------— __ —__ —--------------------------- _ _ _ _ _ _ _- - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

In the velocity weighted percentages, number is from input data. For the mth size range: Speed(m) UI- D ~I s c" k o r c- Cv,\` ) -- -~ I- I r-~- I oIC -~- --- - - L DG LS -uC)\ L (B,4) Percent for the mth size range is figured as: Percent(m) = o00o. L'0 \r "(LY\(l-eS - ( w. -- i (B.5) and, for the mth size range, cumulative percent is: Cumulative Percent(m) = Z?PZC~N U>~ Vli\ (B,6) Percent per size range is: Percent/Size Range (m) = N D PTvte* \) - Ei pT Cv) (B.7) The probability density and distribution functions represent various weightings of the velocity weighted distribution by the indicated powers of the mean diameter of the size range. For the mth size range in the density (probability) function weighted by the Rth power of the mean diameter, DM, of that size range: ( D ")PECCcT C Wc\e (0D?C- (C CAi ^-=lA %1 A F. sl^- cvv) ( - T CR TI},\ (B,8) (B.9) and: (C U~A 0~- I, T V L P(

The moments of the weighted distribution are calculated as, for the Rth moment: MCnA^KT R ^ -~ — A I TI ACC T (C^ (B.10) Moment ratios are self-explanatoryo Means, variances, and standard deviations are calculated for the Rth weighted distribution as: Mean = Moment (R + 1) (Bl) Moment (R) Variance = L~o T(Z) I -J L (B.12) tAG^^T C^ Ao NT U M|(I^x1- L 1/2 Standard Deviation = (Variance) / (Bo 13) For the mean of the variable diameter to the power R on the non-weighted distribution, we have: Mean = Moment (R) (Bo14) tA Variance =(Moment (2R) - [Moment (R)]) 2-() — (Bol5) It should be noted that whenever the variance = 00, the computer sometimes will retain a very small negative number instead. This is always replaced automatically by a value of 10-6 for the variance to avoid stopping the machine by attempting to take the square root of a negative number in computing the standard deviation. Surface and volume rates are calculated as, for the mth size range (Note Dm comprises the diameter column):

Surface(m)= "L (53.\Q s<) ( D8 eSPE w L L IkJ; pji l (p;.i\.' (pCATo S) (Hi\G-TH) (B 16) and ( ~, ~4, 03 ( \ i ^( 0,,,, s ~6 ( v,) I(",E. sr:-'. ~,,,,,t' Volume(m) =.....4 )......V\. and the total rates are simply: (B,17) Total Surface = Total Volume Z Surface (I) t-V Z Volume (I) ~- I (B.18) (B.l9) Note these represent the total volume and surface of the large drops passing through the camera field per unit time without regard to the inclusions. Similarly, the momentum and energy (kinetic energy) transfer rates are calculated without regard to the inclusions as: Momentum(m) = Energy(m) (.s \4 \S,,o 3 (o6 ~ cT' ^ 5 )C, 0 )[. LS )3 [seer (,,, ___,',o ~\k rJ,4.T.^ t,,..c,3 % CD c ~,3 C Lc..<:T, ~3 (B,20) (B.21) (2c) and for the total rates: Total Momentum = Z Momentum (I) r-M \ (B 22) Total Energy Z Energy (I) T., (B.23 )

Now, for the inclusions in the mth size class of large drops, ie., drops with mean diameter Dm, we have for the nth inclusion diameter: V - (\ k* — - A- lp (B 24) and as in the calculation for the large drop distribution: E~oo.7AC.^ i C^^U 12 ^?~^csET G = ---- (Bx 25) Z, CMJeAL)TVL4 PE ce\ CAN = E E LcEC6 L3G (Bo26) Although space does not permit the inclusion of the weighted conditional inclusion distributions, the program will also figure these in a fashion similar to that for the large drop distribution; eogo, for the nth inclusion range in the mth large drop range, we have for the Rth weighted distribution: c, = CLd ~l P&^c=^T(,v3 _ _= (Bo 7) r2Lv] =Pv, W and Cumulative Probability(n) = j P?( ) (B.28) J3=1 Again, as for the distribution of large drops, the Rth moment: I'\ TA[tE(TCI- -^ — ^ C~?^ ^^^(B029) Note that in the above we have used PERCENT (n), and for the large drops we spoke of PERCENT (m). For inclusions, PERCENT (n) is

-147 defined in Equation (B.25); for large drops, PERCENT (m) is defined in Equation (B. 5 ). Moment ratios, means, variances, and standard deviations are calculated as for the large drop distribution, except the last factor in the variance becomes: E. <( -' -'I ~..., -------—. ~j~ —,;(30)(B.30) Note that whenever there are no inclusions in a given large drop class, the computations are skipped to save computer time. Total numbers of drops are tabulated by large drop diameter D.o For the mth size class: Fo Drops = Number (m) (Bo,31) lo Inclusions = E NIN (m,J) (B.32) In the calculations for inclusions based on the whole spray, we aus-.st vseight the inclusions by the velocity of the large drop which contains them. Therefore, in these calculations, for the nth size class of inclusions, of diameter dn: (c.) ZEpSP x l s L?cG2cr(> = A ------— ) —--- (Bo55) tCEo^JL-AT\ OeuC'ls Pet R1= (^- ^. ((Bo33) C c- C c (B, 34) Jz1

-148 Again, there are no weightings of the marginal distribution shown; however, the calculations can be done using this program as they could for the conditional distributions. Calculation of moments, moment ratios, means, variances, and standard deviations is the same as for the conditional distributions, except the last factor in the variance becomes: LILns N3r_(Tr3') (Bo35) i —I J ~ Percent surface and volume represented by inclusions is classified by large drop diameter, Di., and is calculated, for the mth size class, as: 4 2 A7,0 \-Aa (=Ba36) (l "ORJ=l (- 37) ( ^00^ tea R buzz L [l,,,4 and for the overall spray (last two lines of output): OVEeMA' S AEu- -. (900)'1' — (B038) - PCSE C Z t>, (I YQ9t~bFI, ) L )I ^ 3 1 0v1ER~AL L-'9 c-, VoL UM E15 =41 D'So'A V~ce- L 0 3 ^ 3(B 39)

APPENDIX C EQUIPMENT CALIBRATIONS -149

-150 Co o Rotameter Calibrations Shown in Figures 59 and 60 are the calibration curves for the Manostat Corporation FM1043T Flowmeter used to measure flow rate of the dispersed phase through the orificeo Flow rate was measured by measurement of the flow of displacing nitrogen, and curves are presented for nitrogen pressures (measured on upstream side of rotameter) of 3457 psiao and 49,9" mercury absolute, Calibration curves were drawn from volume-time measurements with a fluid actually flowing from the liquid reservoiro The timing device used was a Hewlitt-Packard counter with an accuracy of o001 second, and samples of the liquid were collected in a graduated cylinder in such quantity as to reduce both time and volume measurement errors to less than 1.o Readings were reproducible, and the presence of two different floats permits averaging the two readings (when both are on scale) while using the calibration curves, It is possible to make a mathematical prediction of the calibration using a "Predictability Chart" which is supplied by the manufacturero The values calculated with the aid of this chart for the 34-,7 psia pressure are shown in Table XVo Although the agreement is good, the calculated curve falls somewhat above the measured points, and so the measured calibration, since it was representative of actual conditions, was the one used in all caseso Co 2. Calibration of Tensiometer The tensiometer used in this research was of the DuNouy type, manufactured by the Central Scientific Company, and bore the serial

c HE 0 I. 260 240 220 200 180 160 140 120 100 80 60 40 20 0 ( STAINLESS FLOAT I I II__ I I I I__ __ I I ____ IIAPI LA _ ~~__ ~__ ~_ _ ~ ~__ ____ ____ ___ SAPPHIRE FLOAT _ __ _ __ _-_ _ /_ ^^^^^ ^^^^^^^/ / __ __ _ ^/ /n__ _ _ _ _ _ _ _ _ _ _ _ _ _ I Ln 1I 3 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 SCALE READING Figure 59. Calibration of 1043B Rotaaneter at 52.7 Psia.

400 350' 300 250 E 20 /RD LF 150 100 / 50 0 2 4 6 8 10 12 14 16 18 20 SCALE READING Figure 60. Calibration of 1043B Rotameter at 49.9" Hg Absolute.

-153 TABLE XV CALCULATED CALIBRATION CURVE FOR ROTAMETER TYPE FM1043T WITH NITROGEN FLOWING AT 70~F AND 34.7 PSIA Flow Rate - ml./min. @ 70~F, 34,7 Psia Scale Reading Stainless St. Float Sapphire Float 1 5352 1.79 2 7.95 4o04 3 15.4 7.6 4 26.3 13.2 5 41.6 21.1 6 60.6 32,4 7 78.4 42,7 8 99.0 56,6 10 137,0 83 8 12 17350 110,0 14 222.0 142,0 16 269.0 170 0 18 318 0 181,0 20 359.0 251,0

-154 number C7-8 of the Department of Chemical and Metallurgical Engineering Department of the University of Michigan. The platinum ring used with the tensiometer had a circumference of 5o998 cmo, and was also manufactured by the Central Scientific Company, Company catalog number on the interfacial tensiometer is 70545 and on the ring 70542. Calibration method was as follows: the ring was attached to the tensiometer in the normal fashion, and a small piece of stiff paper placed across the top of the ring to act as a pan for weights, The instrument was zeroed, and then weights from 100 to 1100 gm, were placed on the paper and the tensiometer re-zeroed. This gave a scale reading in dynes/cm. (the instrument is designed to read directly)~ Knowing the weight added to the ring, and the diameter of the ring which it was proposed to use, and assuming the gravitational 2 acceleration to be essentially 980 cme/seCo, one can calculate what the scale reading should actually be, Since the ring is used to rupture two liquid surfaces, the force (mass of weight times acceleration of gravity) is distributed over twice the circumference of the ringo In other words: CalcId Scale Reading = (C.2,1) L cC. where: Calcsd Scale Reading = Dynes/cm, m = mass in grams a = 980 cm/sec2 c = circumference of ring, cmo 1 gmom.cmO g = dynesec2 (conversion factor) c dyne seco,2

-155 Results are shown in Figure 61, and the corresponding values shown in Table XVI, TABLE XVI CALIBRATION OF TENSIOMETER Ring circumference: 5,998 Mass of Weight Calculated Scale mg. Reading, Dynes/cm. 100 8,2 200 16.3 300 24,5 400 32. 7 500 40,8 600 49,1 700 57.2 800 65,4 900 73 6 1000 81 7 1100 90.0 C7-8 cm. Observed Scale Reading, Dynes/cm. 8.3 16, 4 24.3 32.4 40,7 48.5 56.7 64,6 72.8 81 1 89,1 Co3. Calibration of Pressure Gauges Pressures involved in the course of this research were measured in two ways - first, by dial-type pressure gauges, and second, by mercury manometer. The mercury manometer obviously needs no calibration other than assurance that the scale is properly graduated and that the proper fluid is used. A commercial mercury manometer was used, model M184 manufactured

-156 90 85 - --- 7 80 —75 - 70 _-/ 65 -- - - - - ---- E 0 55 -— 50 45, 40 030 25... 20 15 -_ ---- 30 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 SCALE READING, DYNES/Cm Figure 61. Calibration Curve for Tensiometer.

-157 by the Meriam Instrument Company, serial C17 201 of the Department of Chemical and Metallurgical Engineering of the University of Michigan, The dial-type pressure gauges used were 0-60 psi, serial C2 111 and 0-30 psi, serial C2 495 - again both serial numbers are from the Chemical and Metallurgical Engineering Department of the University of Michigan. These gauges were both calibrated using a standard dead-weight gauge testing apparatus, with the results shown in Table XVII. TABLE XVII CALIBRATION OF DIAL-TYPE PRESSURE GAUGES Observed Pressure psi Serial C2 111 4.5 10, 15. 20. 25. 30, 55. 40, 45. 50. 55. 60. Serial C2 495 4.8 10, 15.2 20,2 25,2 29.9 True Pressure psi 5. 10. 15, 20. 25, 30, 355 40o 45. 50, 50. 55. 60o 5 10. 15. 20. 25. 30. Co 4. Camera Calibrations Two calibrations were made on each of the cameras used in this research - one for magnification and one for depth of field, Both cameras

-158 used 50 mmo Argus lenses, the 2.6X camera having f/2,8 to f/22 stops and the 10X camera remaining fixed at f/355. Magnification calibrations were made by photographing the barrel of a hypodermic needle which had been measured with a micrometer, The resulting negative was enlarged by a factor of 10 diameters and the distance measured using a ruler with 01" subdivisions, It should be further noted that camera magnification will vary slightly depending on the focus setting of the lenso This was checked and not found to be an appreciable consideration, but in order to be systematic all magnifications were measured and all data taken with the lens focus setting on infinity. Depth of field measurements were made similarly, except that the barrel of the hypodermic needle was inclined at about a 60~ angle with the camera axis. From knowledge of the angle and by measuring the length of the barrel shown in focus on the negative, depth of field measurements were obtained. Results are summarized in Table XVIIIo Depth of field was also calculated, and it was found that drops which would appear to be in satisfactory focus can correspond to a sizeable circle of confusion as compared to the sizes of circle of confusion commonly used in photographic worko TABLE XVIII DEPTH OF FIELD CALIBRATIONS FOR 2, 6X AND 10X CAMERAS f stop depth of field, mm, 1OX camera 3~5 1-2 2,6X camera 2,8 2,4 4o 309 5,6 4 4 8, 504 11, 6 9 16. 8,3 22, 10o3

APPENDIX D RAW DATA AND DISTRIBUTION PLOTS -159

-160 TABLE XIX RAW DATA - RUN NUMBER 1 System: Saturated CCl into saturated H20 Flow Rate: 275 cm3/m.n. Nozzle Diameter:.1042 cm. Interfacial Tension: 32.0 Dynes/cm Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.595 gm/cm3 Time Delay: 2.54 x 10-3 sec. Large Drop Size 0. - 1.- 2.- 3.- 4.- 5.- 6.- 7.- 8.- 9.- 10.- 11.- 12.- 13.- 14.- 15.- 16. - 17.- 18.- 19.- 20.Range, cm.x 102 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. No. Large Drops 36 86 99 65 32 19 12 6 5 4 7 1 0 0 3 6 0 1 0 0 1 Avg. Distance, cm. x 102 3.9 5.3 6.4 7.2 7.7 8.1 84 8.7 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.8 0.-.5 0 0 0 1 0 Number,5 -1.0 0 0 0 0 1 of In- 1.0-1.5 0 0 1 0 7 clusionsl.5-2.0 0 0 0 1 1 by Size 2.0-2.5 0 0 0 0 1 Range, 2.5-3.0 0 0 0 0 0 cmx l2 3.0-3.5 0 0 0 0 1 3.5-4.0 0 0 0 00 4.0-4.5 0 0 0 0 0 0 5 0 0 1 1 0 0 0 0 3 2 2 0 3 6 13 0 0 0 5 3 7 1 8 6 18 0 0 0 5 14 3 4 1 2 2 5 0 0 0 0 6 4 2 1 7 8 10 1 0 0 11 9 2 0 1 1 2 0 1 0 0 0 4 1 1 1 3 0 3 0 0 0 4 4 0 0 0 0 1 2 1 0 0 0 1 0 0 0 1 2 4 0 0 0 6 3 O 0 0 0 0 3 0 0 o 4 0 0 0 6 0 0 0 6 0 0 0 2 0 0 0 0 0 0 0 O O O 0 4 0 0 o 0 o 3 0 o 2 0 4 0 3 Large Drop Size 0.- 1.Range, cm. x 102 1. 2. No. Large Drops 16 57 Avg. Distance, cm. x 102 3.9 5.3 Number. -.5 0 0 of.5-1.0 0 0 Inclu- 1.0-1.5 0 0 sions by 1.5-2,0 0 0 Size 2.0-2.5 0 0 Range, 2.5-3.0 0 0 cm. x 3.0-3.5 0 0 102 3.5-4.0 0 0 4.0-4.5 0 0 TABLE XX RAW DATA - RUN NUMEER 2 System: Saturated CC1l into Saturated H20 Flow Rate: 275 cm3/min. Nozzle Diameter:.1042 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phasez 1.595 ng/cm3 Time Delay: 2.54 x 10-3 sec. 2.- 3.- 4.- 5.- 6.- 7.- 8.- 9.- 10.- 11.3. 4, 5. 6. 7, 8. 9, 10. 11. 12, 70 40 19 9 7 4 3 3 6 1 6.4 7.2 7.7 8.1 8.4 8.7 8.8 8.8 8.8 8.8 0 1 0 0 0 0 0 0 1 0 0 0 1 1 2 0 3 1 12 0 1 0 6 3 6 0 4 5 15 o 0 1 1 3 3 1 1 2 4 0 0 0 0 2 1 0 1 3 6 1 0 0 0 2 0 1 0 3 0 1 0 0 1 1 0 0 0 0 3 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 1 1 4 0 12.- 13. - 13. 14. o o 14.- 15.15. 16. 0 4 16.- 17.17. 18. 0 1 8.8 8.8 8.8 8.8 8.8 8.8 0 0 0 3 0 0 0 0 0 5 0 3 0 0 0 14 0 4 o o o 5. 6 0 0 0 7 0 6 0 0 0 3 0 2 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 3 0 4

99 98 95 w z w I,J 41 U) o 0 0.L. 0 oQ 90 80 70 60 50 40 30 20 10 ~ < 2 z z I I-J CD 0 I, a U. 0 I. 98 ---- 95 90 — 80 - 70 1 1 1 I. ) 60 --- 50 rey ^ — 40 - /7 t"ca 30 20 10 / / 2 1 1 H V 2 5xl? - I Sx1O 10 10 DIAMETER, Cm Figure 62. Distribution Plot for Run 1, DROP DIAMETER, Cm Figure 63. Distribution Plot for Run 2

TABLE XXI RAW DATA - RUN NUMBER 4 System: Saturated CC14 into saturated H20 Flow Rate: 92 cm3/min. Nozzle Diameters.1042 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.595 gm/cm3 Time Delay: 2.52 x 10-3 sec. 7. - 8.- 9.- 10.- 11.- 12.- 13.- 14.- 15.- 16.- 17.- 18.- 19.- 20.- 21.- 22.- 23.- 24. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 3 1 3 0 1 0 0 0 0 0 0 0 4 1 0 1 0 1 Large Drop Size Range, cm. x 102 No. Large Drops Avg. Distance cm. x 102 0.- 1.- 2.- 3.1. 2. 3. 4. 3 1 6 1 4.5. 5 5.- 6.6. 7. 4 3 I ro! 2.4 3.2 4.3 4.8 5.0 5.1 5.3 5.4 5.4 5.6 5.6 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 6.8 7.0 7.0 7.2 7.2 7.4 TABLE XXII RAW DATA - RUN NUMBER 5* System: Saturated CC14 into saturated H20 Flow Rate: 20.0 cm3/min. Nozzle Diameter:.1042 cm. Interfacial Tension: 30.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.595 gm/cm3 Time Delay: 2.52 x 10-3 sec. *For Distribution Plot See Figure 29. 0. - 1. - 2.- 3.- 4.- 5. - 6.- 7.- 8. - 9- 10. - 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 1 0 2 3 1 4 3 0 0 2 3 Large Drop Size Range, cm. x 102 No. Large Drops Avg. Distance, cm, x 102 3.9 3.9 4.2 4.3 4.5 4.6 4.8 4.8 4.8 5.2 5.3

99 98 95 < _90 80. 780 w /660 -J z 50 — to cn 40 00 ~2 ---------------- -- -- ----------------— i i I10 10' 5x160 DROP DIAMETER, Cm Figure 64. Distribution Plot for Run 4.

TABLE XXIII RAW DATA - RUN NUMBER 6 System: Saturated CC14 into saturated H20 Flow Rate: 22 cm3/min. Nozzle Diameters.0420 cm. Interfacial Tensions 32.0 Dynes/cm. Viscosity of Flowing Phases 1.0 cps. Density of Flowing Phases 1.595 gm/cm3 Time Delay: 2.52 x 10'- sec. 2.- 3.- 4.- 5.- 6.- 7.- 8.- 9.3. 4. 5. 6. 7. 8. 9. 10. 126 78 41 37 30 33 25 25 Large Drops Size Range, cm. x 10' No. Large Drops Avg. Distance cm. x 102 Number 0 -.5 of.5-1.0 Inclu- 10-1. 5 sions by 1.5-2.0 Size 2.0-2.5 Range,.2.5-3.0 cm. x 3.0-3.5 102 3.5-4.0 4.0-4.5 0.- 1.1. 2. 61 132 2.4 3.2 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.3 4.8 5.0 21 13 13 15 16 9 1 6 3 1 2 3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 5.1 5.3 5.4 5.4 5.6 8 8 6 12 10 9 21 19 12 22 10 13 14 20 13 3 5 8 6 8 2 4 8 8 4 1 2 1 1 3 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 10. - 11. - 11 12. 8 1 5.6 5.8 1 0 7 3 2 0 1 0 2 1 1 0 0 0 1 0 1 0 TABLE XXIV RAW DATA - RUN NUMER 7 System: Saturated CC14 into saturated H20 Flow Rates 190 cm3/min. Nozzle Diametert.0642 cm. Interfacial Tensions 32.0 Dynes/cm. Viscosity of Flowing Phases 1.0 cps. Density of Flowing Phase: 1.595 gm/cm3 Time Delays 1.10 x 10-3 sec Large Drop Size O.- 1.- 2.- 3.- 4.- 5.- 6.- 7.- -8 - 9.- 10.- 11.- 12.- 13.- 14.- 15.- 16,Range, cm, x 102 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12, 13. 14. 15. 16. 17, No, Large Drops 40 67 50 31 17 12 6 6 8 5 4 4 3 3 2 0 1 Avg. Distance, cm. x 102 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 0.-.5 0 0 0 0 0 0 2 1 2 6 5 4 1 1 1 0 2 Number.5-1.0 0 0 2 2 4 5 1 1 11 6 6 6 4 3 1 0 0 of 1.0-1.5 0 0 0 2 1 1 2 1 5 4 6 4 5 7 6 0 5 Inclu- 1.5-2.0 0 0 0 1 0 0 0 0 0 2 2 5 4 1 4 0 0 sions by 2.0-2.5 0 0 0 0 1 1 1 2 3 1 4 5 1 4 2 0 0 Size 2,5-3.0 0 0 0 0 0 0 1 1 0 0 3 0 1 0 0 0 Range, 3.0-3.5 0 0 0 0 0 1 1 2 1 0 2 0 1 0 0 cm. x 3.5-4. 0 0 0 0 0 0 0 0 0 1 0 0 2 2 0 0 102 4.0-4. 5 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0

99.9 99.8 995 99 98 99 98 95 1. w 4 z (D z Ix uj -J o I) LL 0 <S?0 95 90 80 70 60 50 40 30 20 w - Q 2 4 z z IoI -I -J 3) a. 0 0 0 o~R 90 80 70 60 50 40 30 20 10 ____ _ __A. / v' Y, 1 —4, ^- - ~ -: "/ "..I 0I 10 5 2 5 2 5x 10 DROP DIAMETER, Cm Figure 65. Distribution Plot for Run 6. 10 DROP DIAMETER, Cm Figure 66. Distribution Plot for Run 7. 10

-166 TABLE XXV RAW DATA - RUN NUMBER 8 System: Saturated CC14 into saturated H20 Flow Rate: 130 cm3/min. Nozzle Diameter:.0642 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.595 gm/cm3. Time Delay: 1.55 x 10-3 sec. Large Drop Size 0, - 1.- 2.- 3.- 4.- 5.- 6.- 7.- 8- 9.- 10.- 11.Range, cm. x 102 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. No. Large Drops 108 151 61 31 19 6 6 4 1 3 1 1 Avg. Distance, cm. x 10 1.8 2.1 2.5 2.8 3.1 3.4 3.8 4.1 4.4 4.8 5.1 5.5 Number 0 -.5 0 7 13 1 5 4 3 7 0 5 0 0 of.5-1.0 0 1 9 8 1 2 7 0 0 9 0 0 Inclu- 1.0-1.5 0 0 7 7 17 1 14 5 4 5 0 8 sions by 1.5-2. 0 0 0 4 5 2 5 3 3 5 10 2 Size 2.0-2.5 0 0 0 1 3 0 1 2 3 0 0 Range, 2.5-3 0 0 0 0 0 1 0 0 1 0 2 0 0 cm. x 3.0-3.5 0 0 0 0 0 0 1 0 0 1 0 0 102 3.5-4.0o 0 0 0 0 0 0 0 0 0 0 4.0-4.5 0 0 0 0 0 0 0 1 0 0 0 0 TABLE XXVI RAW DATA - RUN NUMBER 9 Systems Saturated CClh into saturated H20 Flow Rate: 130 cm3/min. Nozzle Diameter:.0642 cm. Interfacial Tension: 32,0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phasei 1.595 gm/cm3 Time Delay: 1.55 x 10-3 sec. Large Drop Size 0.- 1.- 2.- 3.- 4.-.-5 6- 7.- 8.- 9.Range, cm. x 102 1. 2 3. 4 5. 6 7. 8. 9. 10 11 12 No. Large Drops 85 153 79 32 17 9 5 7 6 1 2 1 Avg. Distance, 1.8 2.1 2.5 2.8 3.1 3.4 3.8 4.1 4.4 4.8 5.1 5.5 cm, x 102 Number of 0.-.5 0 4 4 4 6 11 8 7 4 0 0 0 Inclusions.5-1. 0 1 5 4 8 11 2 6 3 0 by Size 1.0-1.5 0 0 6 11 3 1 12 18 1 6 Ranage, 1.5-2.0 0 0 0 0 2 1 4 0 2 7 0 1 2 Range, 1.5-2.0 0 0 2 cm. x10 02 1 4 2 1 4 102 1 0 0 2,5-3,00 0 0 0 0 1 0 0 0 0 1 0 2.5-3.0 0 0 0 3.0-3.5 0 0 0 0 1 2 2 2 2 0 1 2 3.5-4.0 0 0 0 0 0 0 1 0 0 0 0 4.-4.5 o 0 0 0 0 1 0 0 0 1 1 0

995 99 99.9 99.8 995 99 98 LAJ I.Z w 43 3E z w Co t. 0 0 IbE 4 a z a 0 qc IW. Q -J Co o 0 U. 0 Oi I DROP DIAMETER, Cm Figure 67. Distribution Plot for Run 8. DROP DIAMETER, Cm Figure 68. Distribution Plot for Run 9.

99.9 99.8 99.5 _/ 99 —--- I 98 - 95 ----- 90 ZiI 80 -- 70 — 0 o~ 40 Figure 69. Distribution Plot for Run 10. (For Raw Data See Table II)

TABLE XVTII RAW DATA - RUN NUMBER 11 Systems Saturated CC14 into saturated H20 Flow Rate 50 cm3/min. Nozzle Diameter:.0642 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.595 gm/cm.3 Time Delays 2.19 x 10-3 sec Large Drop Size 0.- 1..-.- 5.-.-2.- 3.- 410- 51- 6- 1.- 84.- 15. - - - 1.- 16.- 17.- 18.- 19.- 20.Range, cm. x 102 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11 12. 13. 14 15 16. 17. 18. 19 20. 21. No. Large Drops 22 7 5 1 1 1 3 3 9 10 9 5 1 5 8 5 3 1 2 1 Avg. Distance, cm. x 10-2.1.5 1.9 2.2 2.5 2.8 3.1 3.4 3.7 4.0 4.3 4.6 4.9 5.2 5.4 5.5 5.6 5.7 5.8 5.8 5.9 6.0 TABLE XXVIII RAW DATA - RUN NUMBER 12 System: Saturated CC14 into saturated H20O \0 Flow Rates 75 cm3/min. Nozzle Diameter:.0420 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.595 gi/cm3 Time Delays 1.70 x 10-3 sec. Large Drop Size 0.- 1.- 2.- 3.- 4.- 5.- 6.- 7 — 8.- 9.- 10.Range, cm. x 102 1. 2. 3. 4, 5. 6. 7. 8. 9. 10. 11 No. Large Drops 139 229 103 54 15 10 4 4 2 0 1 Avg. Distance, cm, x 102 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 Number of 0.-.5 0 14 30 27 14 10 5 0 4 0 1 Inclusions.5-1.0 0 6 17 36 24 8 10 8 4 0 1 by Size 1.0-1.5 0 0 6 17 9 15 6 16 8 0 4 Range, 1.5-2.0 0 0 0 8 4 5 4 8 2 0 3 cm. x102 2.0-25 0 0 0 1 4 5 2 2 2 0 2 2.5-3.0 0 0 0 0 0 0 1 1 0 0 0 3.0-3.5 0 0 0 0 0 2 0 0 0 0 1

l Iz 0 a: z 4 U) en 0 L-. 0 0I at z z 4 z UJ I0 99.9 99.8 98 -____-Z =/_ _ 9 0 __ __ X? -- _______ 80 6 0 - _ _ _ _' I 50 -- 0 40 20o - - -- _10/- I 0 I / 2 5xl 5xl -2 10 DROP DIAMETER, Cm DROP DIAMETER, Cm Figure 70. Distribution Plot for Run 11. Figure 71. Distribution Plot f or Run 12.

-171 TABLE XXIX RAW DATA - RUN NUMBER 13* System: Saturated CC14 + 6.6 cm3/gal. "Alkaterge C" into saturated H20 Flow Rate: 45 cm3/min. Nozzle Diamter:.0642 cm. Interfacial Tension: 11.7 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.595 gm/cm3 Time Delay: 2.61 x 10-3 sec. *For Distribution Plot See Figure 24. Large Drop Size 0.- 1.- 2.- 3.- 4.- 5,- 6.- 7,- 8.- 9.- 10.- 11.- 12.- 13.- 14.- 15.Range, cm. x 102 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. No. Large Drops 104 96 87 48 34 20 8 5 7 5 0 3 2 1 2 1 Avg. Distance, cm. x 10 4.0 4.2 4.5 4.7 5.0 5.2 5.5 5.7 5.9 6.1 6.3 6.5 6.8 7.0 7.3 7.5 Number 0. -.5 0 1 4 0 8 4 4 2 5 7 0 1 0 0 3 2 of.5-1.00 0 1 3 6 7 6 10 8 10 0 1 4 2 4 3 Inclusions 1.0-1.5 0 0 4 3 7 9 2 3 10 5 0 7 3 1 4 2 by Size 1.5-2.0 0 0 1 0 2 5 1 3 0 2 0 3 1 0 0 1 Range, 2,0-2.50 0 0 0 1 2 0 0 0 3 0 4 4 0 2 3 cm. x 102 2.5-3.0. 0 0 0 1 3 0 0 3 0 0 1 3 1 0 2 3.0-3.50 0 0 0 0 0 0 1 1 1 0 0 1 0 3 0 3.5-4.oo 0 0 0 0 0 0 0 0 1 0 1 2 0 1 0 4.0-4.5 0 0 0 0 0 0 0 0 1 0 0 2 0 0 1 1 TABLE'XXX RAW DATA - RUN NUMBER 14 System: Saturated CC14 + 6.6 cm3/gal. "Alkaterge C" into saturated HR20. Flow Rate: 90 cmD/min, Nozzle Diameters.0642 cm. Interfacial Tension: 11.7 Dynes/cm. Viscosity of Flowing Phases 1.0 cps. Density of Flowing Phase: 1.595 gm/cmp Time Delays 2.60 x 10-3 sec. Large Drop Size 0.- 1.- 2.- 3.- 4.- 5.- 6.- 7 — 8.Range, cm. x 102 1. 2. 3. 4. 5. 6. 7. 8. 9. No. Large Drops 95 162 71 25 24 5 5 2 1 Avg. Distance, cm. x io2 1.5 2.2 2.8 3.5 4.0 4.9 5.5 5.5 5.5 Number of 0.-5, 0 2 5 3 7 7 4 4 0 Inclusions 5 -1.0 0 5 5 6 29 17 11 4 2 by Size 1.0-1.5 0 0 7 3 17 8 13 4 3 Range, 1.5-2.0 0 0 1 7 10 4 5 1 2 cm. x 102 2.0-2.5 0 0 0 1 3 1 1 2 1 2.5-3.0 0 0 0 0 2 2 0 2 0 3.0-3.5 0 0 0 0 1 0 0 0 1

-172 99.9 99.8 99.5 4 5 z'I L3 -I z ~1 4% (I, x -i C) U) 0~ 0 LL O 99 98 95 90 80 70 60 50 40 1X-P/ /1 I_ I I__ 1 1-_ _ _ _ I I 7 I —----- Z:^ Z:: 30 20 10 -_ 5xVc 10' 10 DROP DIAMETER, Cm Figure 72. Distribution Plot for Run 14.

-173 TABLE XXXI RAW DATA - RUN NUMER 15 System: Saturated H20 into saturated CC14 Flow Rate: 80 cm3/min. Nozzle Diameter:.0642 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.0 gm/cm3 Time Delay: 1.51 x 10-3 sec. Lag Do Sz 0.- 1..... 5- 6- 7- 8- 9- 1. 1- 1. 3- 1 5- 1. Large Drop Size 0.- 1.- 2.- 3.- 4.- 5.- 6.- 7.- 8,- 9. - 10o. - 11,Rangej cm. x 102 1. 2. 3. 4. 5. 6, 7. 8. 9. 10. 11. 12. No, Large Drops 55 119 66 36 14 7 7 3 3 1 2 2 Avg. Distance, cm. x 10 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2,0 2.0 2.0 2.0 2.0 Number of 0.- 5 0 0 2 4 5 2 3 3 1 0 0 1 Inclusions.5-1.0 0 2 13 10 5 5 7 6 9 1 10 18 by Size 1.0-1.5 0 0 3 8 2 2 6 1 5 2 4 2 Range, 1.5-2.0 0 0 0 0 1 0 1 5 4 1 3 1 cm, x 102 2.0-2.5 0 0 0 0 1 0 0 2 1 1 1 1 2.5-3.0 0 o o o 0 2 0 0 0 0 1 0 5.0-3.5 0 o 0 0 0 1 0 0 1 0 0 3.5-4. o 0 0 0 0 0 0 0 0 0 0 1 0 4.0-4.5 0 0 0 0 0 0 0 0 0 1 1 0 12.- 13.- 14.- 15.- 16.13. 14. 15. 16. 17. 0. 0 1 1 2.0 2.0 2.0 2.0 0 0 0 0 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 4 0 0 0 1 O O O O 0 0 0 1 O O O O 2.0 0 0 25 25 0 0 0 0 0 TABLE XXXII RAW DATA - RUN NIBER 16 System: Saturated H20 into saturated CC14 Flow Rate: 55 cm3/min. Nozzle Diameters.0642 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1,0 cps Density of Flowing Phase: 1.0 gm/cmp Time Delay: 1.51 x 10-3 sec. Large Drop Size 0.- 1.- 2,- 3.- 4.- 5.- 6.- 7.- 8.- 9.- 10.- 11.- 12.- 13.- 14- 15,- 16.Range, cm. x 102 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. No. Large Drops 34 69 57 29 23 6 5 8 6 7 2 1 1 1 0 1 2 Avg, Distance, cm. x 10' 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2 2 2.0 2.0 2.0 2.0 Number of 0.-.5 0 1 2 0 3 0 0 2 0 3 0 0 1 0 0 3 0 Inclusions.5-10 0 2 13 4 6 4 6 8 5 19 0 0 4 4 0 5 11 By Size 1.0-1.5 0 0 2 2 2 1 7 5 4 6 1 0 2 0 0 2 5 Range, 1.5-2.0 0 0 0 0 4 0 1 4 2 5 0 0 0 0 0 5 cm. x 102 2.0-2.5 0 0 0 0 1 0 0 4 3 0 3 0 2 0 0 2 2 2.5-3,0 0 0 0 0 0 0 1 0 1 6 1 0 0 1 0 0 1 3.0-3.5 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 5.5-3.0 o o o o o o o 0 0 o 4.5-4. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.o-4.,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

99.9 99.8 f~t% K 99 98 ---- A - 95 90. - _ _ _ _ I -- 99.9 99.8 99.5 99 98 CL Iz w o z Io) 0. 0 IU 0 / / ( / 80 70 60 50 40 30 20 0T, I C/, /I —- I I II — / i[f ~ a I0 z 4 CO z o IL Ii Ax 95 90 80 70 60 50 40 30 20 I 10 5 10 2 10' & 1 I5 5xl - 5xl0 _2 10 DROP DIAMETER,Cm Figure 73. Distribution Plot for Run 15. id DROP DIAMETER,Cm Figure 74. Distribution Plot for Run 16.

-175 TABLE XXXIII RAW DATA - RUN NUMER 17 System: Saturates HO0 into saturated CC14 Flow Rate: 31 cm /mln. Nozzle Diameter:.0420 cm. Interfacial Tension: 32.0 Dynes/cm. Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phase: 1.0 gm/cm3 Time Delay: 1.51 x 10-3 sec. Large Drop Size 0. - 1.- 2.- 3.- 4.- 5.- 6.- 7.- 8.- 9.- 10.- 11. 12- 12 3Range, cm. 7.9 102 1 2 4 5 6 1l 12. 13. 14. No. Large Drops 5 51 37 26 17 7 5 7 5 3 1 1 0 1 Avg. Distance, cm, x 102 2.0 202.0 2.0 20 20 20 20 2.0 2.0 2.0 2.0 0 2.0 2.0 Number of 0. -.5 0 0 0 0 0 0 0 0 1 1 0 0 0 0 Inclusions 5.-1.0 0 0 4 1 0 2 1 1 10 3 0 6 0 0 by Size 1.0-1.5 0 0 0 3 0 1 0 0 3 3 0 3 O O Range, 1.5-2.0 0 0 0 1 0 1 0 1 2 0 0 0 0 2 cm. x 10 2.0-2.5 0 0 0 0 0 0 0 0 1 2 0 0 0 0 2.5-3.0 0 0 0 0 0 0 1.0 0 0 0 0 0 3.0-3.5 0 0 0 0 0 0 0 1 1 0 0 1 0 0 TABLE XXXI RAW DATA - RUN NUMBER 18 System: Saturated HOI into saturated CC14 Flow Rate: 112 cm3/min. Nozzle Diameter:.0420 cm. Interfacial Tension: 32.0 Dynes/cm, Viscosity of Flowing Phase: 1.0 cps. Density of Flowing Phaset 1.0 gm/cm3. Time Delay: 1,51 x 10-3 sec. Large Drop Size Range, cm. x 10 No. Large Drops Avg. Distance, cm, x 102 Number of 0 -.5 Inclusions.5-1.0 by Size 1.0-1.5 Range, 1.5-2.0 cm. x 102 2.0-2.5 2.5-3.0 3.0-3.5 3.5-4.0 0.- 1.- 2.- 3.- 4,- 5.- 6.- 7.- 8.- 9.1. 2. 3. 4 5. 6. 7. 8. 9. 10. 67 149 45 25 11 5 10 1 2 1 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0 0 0 1 2 0 0 0 0 0 0 0 1 2 5 0 8 0 1 4 0 0 3 3 2 0 7 0 5 3 0 0 0 1 2 0 2 0 3 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0

w Z z w 0 z 0) 0 o Q. Oe 98 95 -/_ 90 -- 80, — j 70 60 - 50 40 30 20 10 5 -- y ------- -- / _ _ -,/_ J______ __ _ _ _ _ Iw Z IL -r z w z I Ibi -I () () a0 IL O'e o~ 95 90 80 70 60 50 40 30 20 I0 5 99 98 CA,CA) 0 (O z- M- < C;l 0) = C ~ I - 5XId 2 126 10' 1d DROP DIAMETER, Cm Figure 75. Distribution Plot for Run 17, DROP DIAMETER, Cm Figure 76. Distribution Plot for Run 18.