THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COTLLEGE OF ENGINEERING Ultrasonic Field Effects on the Rate of Evaporation of Liquid Droplets at Their Terminal Velocity William Mirsky This dissertation was submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan. May, 1956 IP-162

ACKNOWLEDGEMENT We wish to express our appreciation to the author for permission to distribute this thesis under the Industry Program of the College of Engineering.

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS............. ii LIST OF TABLES......................... iv LIST OF FIGURES... vi NOMENCLATURE.......................... INTRODUCTION........................... 1 CHAPTER I. BRIEF SUINTARY OF PREVIOUS WORKS ON DROP EVAPORATION.... 6 A. Previous Works II. ANALYSIS OF TIE DROP EVAPORATION PROCESS... 11 A. Derivation of the Evaporation Equations III. EXPERIMENTAL RESULTS..25. 2........ 23 A. Reduction of Data —Fixed Drops B. Reduction of Data —Free Drops IV. EXPERIMENTAL EQUIPMENT..................43 A. Air Flow System B. Ultrasonic Field Generation System C. Photographic Recording System D. Instrumentation and Accessories V. EXPERIMENTAL TEST PROCEDURE... 66 A. Orifice Calibration B. Drop-Size Measurements C. Experimental Test Procedure VI. DISCUSSION OF RESULTS.................. 75 VII. CONCLUSIONS AND RECOMMENDATIONS.............. 83 A. Conclusions B. Recommendations APPENDIXES A. DERIVATION OF THE EXPRESSION FOR DETERMINING EXPONENT n FROM THE EXPERIMENTAL RESULTS.................. 87 B. EXPERIMENTAL EVAPORATION CURVES AND DATA.......... 90 C. PHYSICAL PROPERTIES AND CONSTANTS...........135 D. CORRELATED RESULTS AND CHECK OF EVAPORATION EQUATION 2.51 FOR FIXED DROPS OF CUMENE, NO ULTRASONIC FIELD.......137 BIBLIOGRAPHY.......................... 140 iii

LIST OF TABLES Table Page I - Experimental Data for Cumene Giving Exponent n as a Function of Relative Air Velocity............... 28 II - Values of the Evaporation Constant X for Fixed Drops of Cumene at Various Combinations of Ultrasonic Field Intensities and Relative Air Velocities............ 30 III - Data Showing the Variation of X with Ultrasonic Frequency at Constant Air Velocity —Cumene Drops......... 32 IV - Data Showing the Variation of Ultrasonic Critical Frequency with Changes in Relative Air Velocity......... 35 V - Values of f for Several Air Velocities....... 38 VI - Evaporation Rates for Free Drops of Some Pure Liquids in a Stationary Ultrasonic Field............... 42 VII - Orifice Pressure Drop Versus Free-Drop Diameter....... 67 VIII - Experimental Data for Hot-Wire Calibration........ 69 IX - Evaporation Data —Fixed Cumene Drops...........117 X - Evaporation Data —Fixed Cumene Drops...........118 XI - Evaporation Data —Fixed Cumene Drops.......... 119 XII - Evaporation Data —Fixed Cumene Drops........... 120 XIII - Evaporation Data —Fixed Cumene Drops...........121 XIV - Evaporation Data —Fixed Cumene Drops.1......122 XV - Evaporation Data —Fixed Cumene Drops...........123 XVI - Evaporation Data —Fixed Cumene Drops.......... I. 124 XVII - Evaporation Data —Fixed Cumene Drops...........125 XVIII - Evaporation Data —Fixed Cumene Drops...........126 XIX - Evaporation Data —Fixed Cumene Drops...........127 XX - Evaporation Data —Fixed Cumene Drops.......... 128 XXI - Evaporation Data —Fixed Cumene Drops........... 129 XXII - Evaporation Data —Fixed Cumene Drops...........130 iv

LIST OF TABLES (cont.) Table Page XXIII - Evaporation Data —Fixed Cumene Drops....... 131 XXIV - Evaporation Data for Some Pure Liquids —Free Drops.... 132 XXV - Evaporation Data for Some Pire Liquids —Free Drops.... 133 XXVI - Evaporation Data for Free Drops of Acetophenone and Kerosene..................... 134 XXVII - Properties of Air (830F)................. 135 XXVIII - Properties of Cumene................135 XXIX - Average Properties of Air-Vapor Mixture (Cumene)..... 136 XXX - Data for Experimental Check of Evaporation Equation 2.51. 137

LIST OF FIGURES Figure Page 1. Sequence Photographs of a Fixed Evaporating Drop of Cumene, Run 5-4, Do = 1112 Microns.......... 24 2. Sequence Photographs of a Free Evaporating Drop of n-Butyl Alcohol. Do = 1178 Microns,......... 25 3. Evaporation Curve —Showing Measurements Used for Finding Exponent n n ~............. * * * 26 4. Variation of Exponent n with Relative Air Velocity.. 29 5. Relationship between Initial Drop Diameter and Total Time of Evaporation as a Function of X and n —Fixed Drops................. ~........ 31 6. Effect of Field Intensity on Evaporation Constant ~ ~ 33 7. Effect of Field Intensity on Evaporation Constant ~ ~ 34 8. Effect of Ultrasonic Frequency on Evaporation Constant at Constant Velocity and Voltage (20 Volts) ~ ~ 36 9. Variation of Critical Frequency with Relative Air Velocity............ 36 10. Evaporation Curves for Some Pure Liquids —Free Drops ~ 39 11. Evaporation Curves for Some Pure Liquids —Free Drops ~ 40 12. Evaporation Curves for Acetophenone and Kerosene — Free Drops. * * * * - * * * * * * 41 13. Photograph of Experimental Equipment ~.. 44 14. Schematic Diagram of Experimental Equipment. 45 15. Sectional View of Vertical Wind Tunnel. * e..47 16. Basic Piezoelectric Ceramic Elements. o - o * * * - o 50 17. Action of the Piezoelectric Ceramic Tube Due to Changes in Polarity of Applied Voltage. * 50 18. Generation of a Standing Sound Wave by the Piezoelectric Tube........ 52 19. Cork Sphere Shown Suspended within the Ceramic Tube.. 53 20. Schematic Diagram of Amplifier............ 56 vi

LIST OF FIGURES (cont.) Figure Page 21. Close-Up Photograph of Vertical Wind Tunnel, Camera, and Lamp....................... 58 22. Sectional View of Lens Extension Tube...... 59 23. Schematic Diagram of Camera Power Supply.... ~...~ 62 24. Drop Terminal Velocity Determined from Drag Coefficient Curve....................... 68 25. Relationship between Drop Diameter and Orifice Pressure Drop............ 68 26. Relationship between Air Velocity and Orifice Pressure Drop..................... 70 27. Relationship between Hot Wire Heating Current and Air Velocity...... ~........... 70 28. Schematic Diagram of Hot Wire Anemometer Circuit.... 71 29. Evaporation Curves for Fixed DroDs of Cumene, v = 0 ft/sec...................... 91 30. Evaporation Curves for Fixed Drops of Cumene, v = 0 92 ft/sec........................ 31. Evaporation Curves for Fixed Drops of Cumene, v = 0 ft/sec......................... 93 32. Evaporation Curves for Fixed Drops of Cumene, v = 0.82 ft/sec......................... 94 33. Evaporation Curves for Fixed Drops of Cumene, v = 0.82 ft/sec.......................... 95 34. Evaporation Curves for Fixed Drops of Cumene, v = 1.16 ft/sec......................... 96 35. Evaporation Curves for Fixed Drops of Cumene, v = 1.16 ft/sec.................. 97 36. Evaporation Curves for Fixed Drops of Cumene, v = 2.01 ft/sec............. ~... 98 37. Evaporation Curves for Fixed Drops of Cumene, v = 2.01 ft/sec.......... 99 38. Evaporation Curves for Fixed Drops of Cumene, v = 2.48 ft/sec... ~.............. ~ 100 vii

LIST OF FIGURES (cont.) Figure Page 39. Evaporation Curves for Fixed Drops of Cumene, v = 2,48 ft/sec.......................... 101 40. Evaporation Curves for Fixed Drops of Cumene, v = 3.51 ft/sec....................... 102 41. Evaporation Curves for Fixed Drops of Cumene, v = 31.51 ft/sec....................... 103 42. Evaporation Curves for Fixed Drops of Cumene, v = 4.29 ft/sec.... 104 43. Evaporation Curves for Fixed Drops of Cumene, v = 4.29 ft/sec. ~.......o.s.... 105 44. Evaporation Curves for Fixed Drops of Cumene, v = 4.96 ft/sec................. io6 45. Evaporation Curves for Fixed Drops of Cumene, v = 4.96 ft/sec......................... 107 46. Evaporation Curves for Fixed Drops of Cumene, v = 6.07 ft/sec................... 108 47. Evaporation Curves for Fixed Drops of Cumene, v = 6.07 ft/sec........................ 109 48. Evaporation Curves for Fixed Drops of Cumene, v = 7.00 ft/sec................ ~.. 110 49. Evaporation Curves for Fixed Drops of Cumene, v = 7.00 ft/sec......................... 111 50. Evaporation Curves for Fixed Drops of Cumene, v = 7.84 ft/sec................ 112 51. Evaporation Curves for Fixed Drops of Cumene, v = 7.84 ft/sec........................ 113 52. Evaporation Curves for Fixed Drops of Cumene, v = 8.59 ft/sec....................... 114 53. Evaporation Curves for Fixed Drops of Cumene, v 8.59 ft/sec....................... 115 viii

LIST OF FIGURES (cont.) Figure Page 54. Evaporation Curves for Fixed Drops of Cumene, v = 8.59 ft/sec...................... 116 55. Heat Transfer Data for Evaporating Fixed-Drop of Cumene —No Ultrasonic Field............... 138 56. Experimental Check of Evaporation Equation 2.51 * 139 ix

NOMENCLATURE.a& diffusion coefficient,?Pt molecular weight, R, gas constant. A surface area of drop, Ar surface area of sphere having radius r, B transfer number due to Spalding,31 C constant, C = 2/f (Pr)1/3 (V/V)1/2, CD drag coefficient, D diameter of drop, Df diameter of outer surface of equivalent thermal boundary layer, DI diameter of outer surface of effective thermal boundary layer, Do initial drop diameter, Dr diameter of sphere having radius r, F factor in Equation (1.16) due to Kinzer and Gunn,17 K = (z - y)/(y - x), K1 2 constants, L latent heat of liquid drop, M mass of drop, T temperature, T temperature of drop surface, Tf temperature at outer surface of thermal boundary layers, Tr temperature at surface of sphere having radius r,

V. volume of drop, X constant. a general exponent, b general exponent, c general exponent, c specific heat at constant pressure, f = 3 sin G/2Cf1, fl proportionality factor, f' wind factor due to Fro'ssling,5 g gravitational acceleration, h film heat-transfer coefficient, i heating current required to maintain a constant hot-wire temperature, io heating current required to maintain hot-wire temperature at zero velocity, k thermal conductivity, n exponent in evaporation equation, n' measured values of n, p pressure, Pv vapor pressure, q heat-transfer rate, r radius of drop, rf radius to outer surface of equivalent thermal boundary layer, ro initial drop radius, rr radius of sphere, xi

t time, tt total time of evaporation, tt arbitrary time such that tt > tt, v relative air velocity of free stream, vl relative air velocity at outer surface of dynamic boundary layer, x =(tt - tX) y = (tt - ty) ' see Figure 3 Z = (tt - tz) J z = (t~ - t )j a L ln [1 + c (Tf - T) ] c (Tf - T) L - = rCk ln [1 + c (Tf- T) ] c L 6 thickness of dynamic boundary layer, St thickness. of equivalent thermal boundary layer, thickness of effective thermal boundary layer, G angle measured from forward stagnation point, X evaporation constant, 4I absolute viscosity, u. microns, v kinematic viscosity, ~ = 3.14159... p density of liquid drop, functional relationship, Nu = hD/k, Nusselt number, Pr = cL/k, Prandtl number Re = Dv/v, Reynolds number, Sc = v/b, Schmidt number. xii

Subscripts a air, s drop surface., v vapor. xiii

INTRODUCTION Interest in the evaporation and combustion processes of liquid fuel drops has increased considerably in recent years, due principally to the demands for increasing jet-engine performance. As a direct result numerous studies have been conducted in this country and abroad to investigate the combustion and associated evaporation processes of liquid drops under a variety of conditions. Because of the extremely complex nature of these processes as they exist in a burning-fuel spray, most investigators chose to study either the burning or evaporation process associated with a single isolated drop. Of these, some suspended drops from fine filaments and photographed the stationary drops as they evaporated or burned,58,10,18,26 while others employed pseudo-drops such as flooded hollow spheres30,31 and flooded porous spheres.l4,15 Still others studied drops falling at their terminal velocityl7,28,32 or injected at various velocities into hot furnace atmospheres.13,29 Relatively few have investigated the evaporation or combustion processes in a spray.l,4 For a thorough study of drop evaporation or combustion, one should consider the effects of the fluid flow pattern around the drop at both the laminar and turbulent boundary layer regions; the internal liquid circulation within the drop and its effects on the boundary layer, drag, and internal heat transfer; conductive, convective, and radiant heat transfer between the drop and its surroundings; and, finally, the

-2 -effects of conductive and convective mass transfer of the liquid vapor, air, and products of combustion on the heat transfer process. Even for the seemingly relatively simple case of a spherical drop evaporating into an air stream having uniform motion, an exact solution to the analytical problem appears to be impossible at this time. When initiating the present program of investigation, the evaporation of a single isolated drop in a moving-air stream was selected as the first step in the study of the more complicated processes involved in a burning-fuel spray. This selection was based on the opinion that combustion is essentially a high temperature evaporation process and that the evaporation study would permit the use of a simpler experimental procedure for investigating some aspects of the heat and mass transfer processes. In addition, better control of many of the variables affecting the process could be realized with the single-isolated evaporating drop. The selection of the technique for conducting the experimental part of the study was based on the following considerations: a. Actual drops would be preferred to pseudo drops, such as flooded-cork balls or hollow spheres, to approximate more closely the true nature of the process, to eliminate possible additional variables, to preserve the internal liquid circulation within the drop, and to obtain data for drops in the size range well below 1,000 microns. b. Filament suspensions should not be used if possible because they distort the drop shape, the air flow pattern around the drop, and the internal liquid circulation within the drop; the actual effect of their presence on the heat

-3 -transfer processes would be difficult to predict accurately, especially if the flow pattern behind the drop were in the form of a turbulent wake; they would limit the minimum drop size to about 300 microns at best. c. The investigation should consider the effect of relative air velocity on the evaporation rate, by studying either drops falling freely at their terminal velocity or drops suspended on filaments in moving-air streams of various constant velocities. The former would be more suitable than a possible third case of drops moving freely along some ballistic curve, as when thrown upward from a-drop-generating device, for in this case the relationship between drop diameter and relative air velocity would be difficult to predict. d. The ability to obtain continuous photographic records of relatively high magnification would be desirable, especially for freely-falling drops. In addition to supplying drop-size data, it would provide a means for detecting variations in drop shape during free fall and, possibly, the flow configuration around the drop. As a result of these considerations, it was decided that an attempt should be made to devise a method by which a drop could be supported at a fixed position in space by means of air drag and other forces. The drop would then be at its terminal velocity with respect to the air stream and, in addition, would be fixed in space relative to the observer. This scheme would offer many obvious advantages with regard to data taking, length of equipment required, and time available for drop evaporation.

-4 -After several efforts, a method was devised by which drops actually could be maintained at a fixed position in space by means of air drag and ultrasonic forces. The development of this technique was primarily the work of Dr. John L. Wighton who, as a graduate student at the University of Michigan, worked with the author on the problem of obtaining "freely" suspended drops. Needless to say, the apparatus appeared extremely promising. However, an inspection of the results obtained with this apparatus soon indicated that the effect of the ultrasonic field on the evaporation process could not be neglected and in some cases would actually be quite appreciable. Therefore, it became necessary to investigate the nature of this effect and to obtain quantitative data for all conditions that might arise in subsequent studies. The investigation was also intended to disclose methods for improving the technique by decreasing the ultrasonic effect, even though it was felt that in some applications the effect might actually be desirable. It is this investigation that forms the basis for this dissertation. The experimental investigation was carried.out in four parts. These are: 1. The study of the evaporation of drops in the absence of an ultrasonic field while suspended on filaments in a moving air stream. These tests are similar to those made by Frossling5 and others but were repeated as a check on the author's apparatus.

-5 -2. The determination of the effect of ultrasonic intensity on evaporation. 3. The determination of the effects on evaporation produced by ultrasonic fields of various frequencies. 4. The determination of the resultant effect by the ultrasonic field on the evaporation process for freely-suspended drops at their terminal velocity. Cumene was used for the greater part of this study because of its suitable rate of evaporation and relatively low cost for the pure grade of liquid used (99 mole percent). Its evaporation rate was slow enough to permit good control of drop position by manual control of the relative air velocity and yet fast enough to avoid excessively long test runs.

CHAPTER I BRIEF SUMMARY OF PREVIOUS WORKS ON DROP EVAPORATION The problem of drop evaporation has been and is still being considered by many research workers from both the theoretical and experimental points of view. Their interest arises through several fields of application. It appears that the earlier workers were primarily interested in the meteorological aspects. Later?, the process was used as an experimental method for finding values of diffusion coefficients. More recently, the problem has gained considerable interest because of its importance in the drying and evaporation processes of the chemical industries and in the combustion processes involved in diesel and turbo-jet engines. The theoretical investigations are based on one of two similar processes, either that of mass transfer or heat transfer. In general, both analyses give similar results. A. Previous Works In 1918 Langmuir,20 using the result he obtained from an investigation of heat transfer from small wires, derived the following expression for drops in still air,~ dM = 4irrvp = Cr, =PMMsr el Cr, (1.1) dt RT showing mass rate of evaporation to be proportional to drop radius.

-7 -Frossling5 extended the theoretical and experimental investigations to include the effects of relative air velocity on the evaporation process. To account for the increased evaporation due to the velocity, the expression obtained by Langmuir was modified by a factor f' which Frossling called the "wind factor," dM = 4- rs7bPv ft (1.2) dt RT A theoretical analysis showed f' to be a function of the Schmidt number times Reynolds number raised to the one-half power, i.e., f' = $ (Sc)(Re)1/ (1.3) However, for Re = O, it was obvious that Equation (1.2) must reduce to Equation (1.1) so that f' was given the form, f' = 1 + * (Sc)(Re)1/2. (1.4) Using his experimental results obtained with 0.1 to 0.9 mm diameter drops suspended on fine glass filaments and thermocouples in a moving air stream at velocities from 0.2 to 7 meters/second, Frossling obtained the final form for the wind factor, f' = 1 + 0.276 (Sc)1/3 (Re)1/2 (1.5) giving the evaporation equation, dM = 4iirbp~v (1 + 0.276 Scl/3 Rel/2). (1.6) dt RT Ranz and Marshall26 performed similar experiments on suspended liquid drops having a range of diameters from 0.06 to 0.11 cm and at Reynolds numbers from 0-200. Variations in air temperature from 0-200~C was introduced as an additional variable.

-8 -The correlation of data was based entirely on FrUssling's result by assuming Nu = 2 + C Pra Reb (1.7) for the heat-transfer process. This result was obtained directly from Frossling's equation for Nusselt's number for mass transfer, Nu = 2 + 0.552 Scl13 Rel/2, (1.8) by simply replacing the Schmidt number with the Prandtl number. The experimental data obtained by Ranz and Marshall was found to be correlated by the expression Nu = 2 + o.60 Prl/3 Rel/2 (1.9) It is evident that the result agrees very well with that obtained by Frossling. Godsave7'8,9 and Kobayasi19 studied the burning rates of stationary liquid-fuel drops. Godsave carried out his experiments at room temperature while Kobayasi did the greater part of his work at elevated furnace temperatures. Both investigators arrived at the same conclusion that the change of drop diameter can be expressed by the relationship, D2= - Xt, (1.10) where, according to Godsave, 8= 8k fDf ln [1 + c (Tf - T)1 (1.11) pc D- L Ingebol4 and Spalding30,31 used a somewhat different experimental approach to the problem in that they used artificial or pseudo-drops rather than actual liquid drops.

0~Ingebo carried out evaporation tests with stationary flooded cork spheres, approximately 0.69 cm in diameter. Nine liquids having a range of latent heats from 50 to 500 gram-calories per gram were tested in air from 30 to 500~C. Reynolds number ranged from 1600 to 5700. From an assumed correlation having the form Nu = ( (Re) (S) (1.12) where ka = thermal conductivity of air, kv = thermal conductivity of vapor, Ingebo obtained the expression, k 0.5 0.6 Nu = k() [2 + 0.303 (Re Sc) ]. (1.13) In a later study of the pressure effects on vaporization Ingebo15 modified the above result and obtained the following expression for the Nusselt number, Nu = 2 + 2.58 x 106 (Re Sc g 0.6 (114) where g = gravitational acceleration, 1 = mean-free-molecular path of air, c = root-mean-square molecular velocity of air. Spalding performed his combustion tests with stationary, flooded, hollow metal spheres ranging from 1/2 to 1-1/2 inches in diameter. Fuel was made to pass up through the hollow sphere and spill out over its outside surface through a hole at the top. Any excess fuel that did not burn was collected by a trough at the base of the sphere.

-10 -For a sphere evaporating into a stagnant medium, Spalding gives the result in terms of a dimensionless factor B which he names the transfer number. The result is, D =2 n (1 + B), (1.15) where m = mass rate of evaporation per unit area, B = - h)/L, ha = enthalpy of the surrounding air, hs = enthalpy of the vapor at the drop surface. Kinzer and Gunn17 measured the evaporation rates of freely-suspended water drops by three different techniques: freely-falling electrified drops, drops floated in a tapered tube, and drops supported by a vertical air flow. They were thus able to cover the wide range of drop sizes from 0.0016 to 0.42 cm. The result of their theoretical and experimental study is given by, d -2tkD Tf - T [1 + 0.24F Rel"2], (1.16) dt L where F is an experimentally-determined factor. The values obtained for F were found to be dependent upon the Reynolds number, indicating that the evaporation rate is not a linear function of Rel/2 as found by Frossling. See Equation (1.6).

CHAPTER II ANALYSIS OF THE DROP-EVAPORATION PROCESS The precise analytical solution to any heat-transfer problem in which there is fluid flow around a bluff body becomes very difficult because of the nature-of the flow pattern around the body and its effects on the heat-transfer processes. When mass transfer is also present, as in the case of an evaporating drop, the problem becomes even more complicated. To alleviate the predicament with which the engineer is faced in trying to gain some usable information about this type of process, use is made of an experimentally-determined heat-transfer factor which is used to correlate experimental data obtained for cases that are similar to one another, thus eliminating the need for a critical examination of the processes involved. For the case of an evaporating drop in a moving air stream, the experimental heat-transfer data is well correlated by the Nusselt number as modified by mass transfer and expressed in terms of the Reynolds and Prandtl numbers. This forms the basis for the analysis that follows. A. Derivation of the Evaporation Equations 1. Film Concept of the Nusselt Number An examination of the temperature profile in the laminar airflow region at the surface of an evaporating drop would show that the total change in temperature is confined to a thin thermal-boundary layer or film of thickness 6t' For the solution of heat transfer problems the 11

-12 -conventional procedure is to replace the actual thermal boundary layer with an "effective" layer of thickness St in which the temperature gradient is assumed to be constant and equal to the gradient at the drop surface in the actual film.3 Heat transfer can then be assumed to take place through the effective film by conduction alone under the driving action of the constant-temperature gradient. By equating the heat transfer to the drop given in terms of the heat-transfer coefficient for convection h, q = hA (Tf - T), (2.1) to that given in terms of the effective thermal boundary-layer thickness, q = kA IT) = kA=, (2.2) [drr S bt where heat transferred to the drop is taken as positive, we obtain the result that h = k (2.3) t Since the Nusselt number is defined as Nu = hD (2.4) it becomes equal to Nu = k (2.5) 6' in terms of the effective thermal boundary-layer thickness. It is apparent that the Nusselt number defined in this manner gives the ratio between a characteristic length of the system, in this case the drop diameter, and the effective thermal boundary-layer thickness. The presence of mass transfer in the boundary layer changes the temperature profile near the drop surface and, therefore, the temperature

-13 -gradient at the surface. This causes a change in the thickness of the effective boundary layer and thereby affects the Nusselt number. The Nusselt number is then said to be modified by the mass-transfer rate. 2. Mass Rate of Evaporation Expressed in Terms of the Nusselt Number The heat transferred through the surface of a drop is used as latent heat to evaporate the liquid at the surface temperature and as sensible heat to raise the liquid temperature from the inner drop temperature to the surface temperature. If we let L be equal to the latent plus sensible heats for the liquid drop, the heat balance at the drop surface can be written as, q = -L dM kA dTr = k-D2 (/ dTr\ (2.6) dt drriS \drris where M is the mass of the drop. By introducing the film concept of the Nusselt number as given by (2.5), the above expression becomes, -L dM = ktD k (Tf - T), (2.7) dt 56 or dM = -kTD (Nu) Tf. (2.8) dt L '28 3. Mass Rate of Evaporation Based on Heat Transfer through the Thermal Boundary Layer For the case of a drop evaporating into a moving-air stream the isothermal surfaces surrounding the drop certainly do not form concentric spheres except for those that are extremely close to the drop. At the outer edge of the thermal boundary film there is an isothermal surface whose temperature is very close to that of the surrounding air stream.

For the analysis that follows it is assumed that this outer isothermal surface can be replaced by an "equivalent" spherical one at the same temperature, concentric with the drop, and having radius rf. The temperature gradient at this surface is assumed equal to the average value for the original surface and the radius rf chosen to given an equal area. In this manner the same-rate of total heat transfer to the interior as provided by the original non-spherical surface is maintained. Consider an intermediate sphere of radius rr, where rf > rr > r, concentric with the drop. The heat balance across the surface of this sphere is given by [L + c (Tr - T)] = kAr (2.) rr where c is the specific heat at constant pressure for the vapor. Substituting for the spherical area, separating variables, and writing the equation in integral form between the proper limits, we get, dM Jf drr _ 4rk Tf cdTr f f j (2.10) dt r2 - c T [L+ c (Tr - T)] When integrated, this becomes, dM( ) = n [1+ c (Tf- T) i (2.11) dt rT f c L or dM 4k c (Tf T = c (r- ) In [1 + -T)] (2.12) In this equation rf is the radius to the outer edge of the equivalent thermal boundary layer of thickness St, where the film temperature

-15 -first becomes essentially equal to that of the ambient air stream. In terms of diameters, the above equation becomes, d- =i c 1 -) D/ r in [1 c (Tf -T)] (2.13) dt \ D/Df L where D/Df is the ratio between the diameters of the drop and the outer edge of the equivalent spherical thermal boundary layer. It is interesting to note that Equation (2.11) was obtained by Godsave8 for a single burning drop by the more complicated procedure of first solving for the temperature distribution through the thermal layer. 4. Expressions for Nu in Terms of D/Df Equating the two expressions (2.8) and (2.13) for the mass rate of evaporation, we get, -D (Nu ) (Tf - T) =_kD ( 2 ) In [1+ c (Tf T)] (2.14) L c - D/Df L so that the expression for Nu in the presence of evaporation is given by, Nu = L 2 ) in [1 + c (Tf - T). (2.15) c (Tf - T) 1 - D/Df L From an inspection of Equations (2.8) and (2.15) it is apparent that for given temperatures and liquid, the evaporation will affect Nusselt's number through the factor D/Df. A first-order approximation of Equation (2.15) is obtained by expanding the ln term according to the following rule: X2 X3 4 in (1 + X) = [X - + X X + ] for (-l<X<l) (2.16) 2 3g which gives,

-16 -in [1 + c T] [ AT 1 (c AT)2+ l (C )3 (2.17) L L 2 L 3 L where AT = (Tf - T). Since the series converges very rapidly for the values of c, AT, and L encountered in low temperature evaporation, the series can be approximated to a high degree of accuracy by use of the first term alone. If this is done in Enuation (2.15), we are left with Nu = ( 2 (2.18) 1 - D/Df In the limiting case where Reynolds number approaches zero, the ratio D/Df also approaches zero with the result that, Nu -e2 (2.19) as predicted by others.25 5. Evaporation Equation in Terms of Drop Diameter If p and V are the density and volume of a liquid drop, the mass rate of evaporation can be written as, dM d = t (pV). (2.20) Since V = iD3/6, dM i= p d (D3) = P D2 d (D). (2.21) dt -F at-2 dt Equating this expression for mass rate of evaporation to that given by Equation (2.15), we obtain, it d (1-ir 1kD+ c (Tfk T)-D (222) D2 - (D) in [i B~i.] (2.22) 2 () = c D/Df L

-17 -Separating variables and writing the resulting equation in integral form between the proper limits the equation becomes, D t f (D - d D = 4k in [1 + c (Tf - T)] f dt (2.23) D )Df pc L which, when integrated, gives, 22 8k c (Tf - T)] [D2 -D] -2 ( ) d D = 8kin [1 + c(T )] t. (2.24) D Df pc L It is obvious that for a complete solution we must know the functional dependence of Df upon D. If we follow the assumption made by Godsave that D/Df is constant, the above equation can be written in the integrable form, [I - ] - 2 () Dd D = 8k n [1 + (Tf T)] t (2.25) Df pc L which becomes after the integration, (1 - )[D - D] = 8k in [1 + c (Tf - T)] t (2.26) or D- Do = 8k ( D ) in [1 + c (Tf -T)] t (2.27) pc Df - D L Letting 8k Df) in [1+ + (Tf T)] = (2.28) pc Df LD L then Equations (2.27) and (2.28) are the results obtained by Godsave8 by a different method, where he defines X as the evaporation constant. It must be remembered that these results are based upon the assumption that D/Df is constant throughout the evaporation process of a single

-18 -drop. However, in the next section this ratio is shown to be a function of the Reynolds and Prandtl numbers. 6. Expression for [2/(1 - D/Df)] obtained from Boundary-Layer Theory For the theoretical dynamic boundary layer around a solid sphere in a moving air stream, Goldsteinll gives, V1 3 v sin G (2.29) and for the velocity distribution obtained from pressure distribution measurements at Reynolds numbers just below the critical range, v16 C (vD)1/2 (2.0) where C is a constant depending on the value of 8. The angle G is measured between the drop radii to the forward stagnation point and any other point on the drop surface. If the first of these equations is substituted in the second, the following expression is obtained for the dynamic boundary layer, 2 C V(-D1,/2 3sin e -T- (2.31) Eckert3 shows for a flat plate heated over its entire length that the thermal boundary layer is related to the dynamic boundary layer by the relation bt = (Pr)- 1/3 (2.32) AsSuming that the same form of expression also holds for an evaporating drop, i.e., that the ratio of equivalent thermal boundarylayer thickness to dynamic boundary-layer thickness is proportional to 1/3 we-can write

-19 --t= fl (Pr) 1/3 (2.33) where fl is the proportionality factor. Combining Equations (2.31) and (2.33), the following expression is obtained for the equivalent thermal boundary-layer thickness, 2 C f1/3 (vl1/2 3 sinG ( v Substituting the above expression for 6t in the following, 2 2 D+ D 1 D/Df - 22) 2 [t + ], (2.55) where Df = D + 26t, we obtain the result 2 = 2 + f (Pr)1/3 (Re)1/" (2.36) 1 -DDf where f 1 (2.37) 2 C f 3 sin 9 7. Evaporation Equations Based on the Results of the Boundary Layer Theory Having obtained an expression for [2/(1 - D/Df)] in the more useful form in terms of Re, Pr, and f, we can substitute this expression in the evaporation equations which have been derived in the previous sections. A. If we substitute for [2/(1 - D/Df)] in Equation (2.13) we get, dM - kD [2 + f (Pr)3 (Re)l12] In [1+ ctf (2.38)

-20 -Letting Sk in [1 + c (Tf - T)] =, (2.39) c L the mass rate of evaporation becomes, dM = [2 + f (Pr)"/3 (Re)1/2] (2.40) dt so that 2PD = evaporation rate in stagnant air, f (Pr)' 3 (Re)l/' 2D = increase in rate of evaporation due to forced convection. B. If we substitute for [2/(1 - D/Df)] in Equation (2.15) for the Nusselt number, we obtain Nu = [2 + f (Pr)"/3 (Re)1/2] L in [1 + c (Tf - T)] (2.41) c (Tf - T) L Letting (TL in [1 + c (Tf - T)] = C, (2.42) c (Tf - T) L the expression for Nusselt's number becomes, Nu = a [2 + f (Pr)1/3 (Re)/2]. (2.43) Equation (2.43) shows that Nusselt's number is a function of (Pr)" 3, (Re)1/2, the factor f which must be determined experimentally,and the function a of the fuel properties and temperature difference. 8. Evaporation Equation for Fixed Drops Suspended in a Constant Velocity Air Stream The ratio D/Df, instead of being constant as was assumed for Equation (2.25), was shown by Equation (2o.6) to be a function of Re, Pr, and f. Solution of this equation for D/Df gives,

-21 -D D1/2 -Df2 - = (Pr)2/3Q~~1(2.44) Df [D1 /2 + 2 f (Pr )a/ 3 (-) 1/2 For evaporation at constant air velocity, it is assumed that f (pr)/3 =(V_)/2 _ constant, say (2.45) so that Equation (2.44) becomes D D1/2 Df = D/ 2 + C (2.46) The integral in Equation (2.24) can then be written as, D~ r D2 dD D3/ 2 2 j dD 2 | D, (2.47) 2f D-fdD = f Do Df D- 2 + C D0 Df which can be integrated by the method of substitution. Letting D = y2 dD = 2ydy we obtain the transformed integral D 3/2. D1/2 2J ( dD 2f ( ) y 2y dy (2.48) I ~ y+o where the integrand can be expanded as, 4Y 4 (Y3 C - Cy2 2 - C3 (2.49) Susittngi y+2 C ' Substituting in (2.48) and integrating gives,

-22 -DD_ D d (D2 - D) _4C (D3/2 _DO3/2) Do Df 3 (2.50) 2C2 (D - D) - 4C3 (D1/2 _ DI 2) + 4C4 in o C D0 +C This result, when used in- Equation (2.24.), leads to the equation for drop evaporation at constant relative air velocity. It is given by 73/2 3/2)3 D' +C (DO/ _ D3/2) - C (Do - D) + 3Cn (Do 2 _- 1/2) - 3C3 ln(Dy2C) (2.51) 6k in [1 + c (Tf - T)] t. Cpc L It should be recalled that the equation normally found in the literature for this type of evaporation is given by, D2 - Do = - t (2.52) which differs quite markedly in form from that given by (2.51).

CHAPTER III EXPERIMENTAL RESULTS Experimental data for evaporating drops were obtained from silhouette photographs taken with a 16-mm motion picture camera. In one series of tests the drops were suspended on a fine glass filament, approximately sixty microns in diameter, in constant velocity air streams. Tests were made at several velocities and sound field intensities. A typical sequence of frames from a test run is shown in Figure 1. The second series of tests was made with freely-suspended drops falling at their terminal velocity with respect to the air stream. The drops were actually maintained at a fixed position in space by the combined effects of air drag and ultrasonic forces. A sequence of photographs of a free drop of n-butyl alcohol is shown in Figure 2. The greater reduction in size and lower drop-shape distortion than that obtained with drops on filaments is clearly: illustrated. A. Reduction of Data —Fixed Drops 1. Determination of Exponent n from Experimental Data Because of the reports by many other investigators8,12 18 on similar studies that the total time of life of an evaporating drop could be expressed in the form tt = CDn, (3.1) it was assumed for comparative purposes that the relationship between drop diameter and elapsed time of evaporation could be described by an equation such as,

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-26 -Dn = Do - Xt (3.2) To determine the exponent n from the experimental data for fixed drops, drop diameters computed from measurements of magnified drop images (approx. 14OX)wereplotted against elapsed time of evaporation. In most cases more than ten measurements were made for each drop, and the smoothness of the resulting curves indicated that additional measurements were unnecessary. A typical curve is shown in Figure 3. "I. I I I I I,. -. tx ty tz tt ti ELAPSED TIME FIG. 3 EVAPORATION CURVE - SHOWING MEASUREMENTS USED FOR FINDING EXPONENT n If the assumption given by Equation (3.2) is valid, the curves can be described equally well by the equation, tt - t = K1 + K2 Dn (3.3) where t' is some arbitrarily selected time such that tt > tt, the total time for evaporation, and K1 and K2 are constants. The above equation was solved for three positions on the evaporation curve in terms of three measured quantities x, y, and z, where

-27 -x = tt - tx, y = t 0 ty z t tz. These are illustrated graphically in Figure 3. The complete solution is given in Appendix A and shows that if the diameters Dx, Dy, and Dz are selected so that DX Dt2 (3.4) x x the exponent n will be given by the simple expression n = log K log (Dy/ Dx) ' where K = Z -Y (3.6) y - x For the test data, the following drop diameters were selected: DX = 400 microns Dz = 1000 microns so that from Equation (3.4) Dy = 632.5 microns and n log K. (3.7) 0.199 Using this result, measurements were taken from curves for drops evaporating in air streams of different velocities. The data and resulting exponents n' are given in Table I.

-28 -TABLE I EXPERIMENTAL DATA FOR CUMENE GIVING EXPONENT n AS A FUNCTION OF RELATIVE AIR VELOCITY x y z v Run (sec) (sec) (sec) K log K ni n (ft/sec) 4-2 1.60 5.78 15.67 2.368 0.3744 1.88 1.88 0 4-3 1.78 6.69 17.37 2.176 0.3377 1.70 1.69 0.82 4-4 1.05 5.66 15.48 2.132 0.3288 1.65 1.65 1.16 4-5 1.62 5.71 14.22 2.081 0.3183 1.60 1.63 2.01 4-6 1.07 4.82 12.80 2.127 0.3278 1.65 1.625 2.48 4-7 1.55 4.97 12.15 2.098 0.3218 1.62 1.62 3.51 4-8 1.13 4.32 11.15 2.140 0.3304 1.66 1.60 4.29 4-9 2.20 5.27 11.62 2.067 0.3153 1.58 1.60 4.96 4-10 0.82 3.73 9.70 2.053 0.3124 1.57 1.58 6.07 4-11 0.83 3.57 9.27 2.080 0.3181 1.60 1.57 7.00 4-12 2.45 5.09 10.35 2.000 0.3010 1.51 1.53 7.84 4-13 1.32 4.00 9.27 1.967 0.2938 1.47 1.47 8.59 These data are plotted in Figure 4 giving n' as a function of relative air velocity. The values of the exponent obtained from the smooth curve are given in Table I as n and are the values used in the subsequent analysis for the corresponding relative air velocities. 2. Measurement of the Evaporation Constant X A series of evaporation tests were made with fixed drops at various relative air velocities and ultrasonic field intensities. Twelve velocities from 0 to 8.59 feet per second and six ultrasonic field "intensities" from. 0 to 25 volts were used. The drop diameters measured for each run were then raised to the proper exponential power n determined in the previous section, depending on the velocity at which the

-29 -test was made. The exponent n was assumed to be a function of relative air velocity only. 2.0 z 0 o. 0 I 2 3 4 5 6 7 8 9 RELATIVE AIR VELOCITY, ft/sec FIG.4 VARIATION OF EXPONENT n WITH RELATIVE AIR VELOCITY Data obtained from these runs are given in Tables IX through XXIII in Appendix B. The set of experimental curves for this series of tests, giving Dn as a function of elapsed time of evaporation, are shown in Figures 29 through 54, also in Appendix B. The positive values of the slopes of these' curves, measured in (microns x 10-2)n/second, give the values for the evaporation constant X. Measured values of X for-runs made under several combinations of relative air velocity and ultrasonic field intensity are listed in Table II. To illustrate more clearly the relationship between X and n in determining evaporation rates, log Xtt is plotted in Figure 5 as a function of log (Do/l0)n for several values of the exponent n. The result shows that for a given evaporation constant and initial drop diameter

-30 -TABLE II VALUES OF THE EVAPORATION CONSTANT X FOR FIXED DROPS OF CUMENE AT VARIOUS COMBINATIONS OF ULTRASONIC FIELD INTENSITIES AND RELATIVE AIR VELOCITIES Voltage 0 2.5 5 10 20 25 Velocity Run X* Run j| Run X* Run X* Run X* Run X* 1-3.254 2-9.295 3-3.240 3 -15.249 8-13.310 8-14.365 1-12.221 5-2.238 5-15.237 6-13.226 9-6.366 4-2.222 5-14.231 0 4-14.223 (ft/sec) Avg..230.255.238.237.310.365 1-13.229' 5-3.2 53 3-4,254 3-6 247 8-2.292 8-165 9. - 0.82 2-3.278 2-10.290 4-3.248 Avg..252.271.254.247.292.358 2-4.275 2-11.276.2T1 3-5.51 3-17 24.22 -1 33 1.16 4-4.241 5-4.255 Avg..258.265.251.245.282.28336 4-5.262 2-12.310 3-7.268 6-4.8 -4.298 -17'.343 2.01 5-5.280 3-18.274 Avg..262.295.268.266.298.343 1- 5.292 2-13.320 3-7.2-92 T6-5.275 '7 1..317-.2 2.48 4-6.280 5-6.293 Avg..286.306.292.275. 17.2 1-6.312 2-14.352 3-9.309 6-6.302 8-6.336 B-19 -.344 3.51 4-7.307 5-7.323 Avg..309.337.309.302.336.344 1-7.316 2-15.3-65 3-10.311 6-7.302 8-7.338 -2'0.337 4.29 4-8.306 5-8.327 8-21.363 Avg..511.346.311.302.338.350 4-9.325 2-16.370 3-11.325 6-U.324 8T-.340 8-22.363' 4.96 5-9.331 Avg..325.350.328.324.340.363 1-9.314 5-10.342 3-12.331 6-9.326 t-9.317 8-23.356 6.07 4-10.329 9-2.374 Avg..321.342.331.326.319.365 1-10.341 2-18.595 3-13.340 6- 10.331 -10 42 7-3.374 7.00 4-11.339 5-11.343 Avg..340.370.340.331.342.374 1-11.321 3-2.331 3-14.320 6-11.311 8-11.311 9-4.319 7.84 4-12.325 5-12.328 6-2.326 Avg..323.329.323.311.311.519 5.9 4-13.277 5-13.292 6-13.230 6-12.27 8 —1.272 9-5.255 * = (microns x 10-2)ln/sec.

-31 -i00 80 60 40 30 n-I.88- 1.69 20 1.625 1.57 -1.53 1.47- / 10 8 / I0 z o. _ _- -..-.... - 0 i OA 4, Z~~~~~~~~~~~~~Z/! 0.3 0. ' -C ~ 0.1 0.4 -02 ___. ___ -Fm O... 0.1 0.2 0.3,04 0.6 081 2 34 6 810 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~? INITIAL DROP DIAMETER,Do/100-MICRONS X FIG.5 RELATIONSHIP BETWEEN INITIAL DROP DIAMETER AND TOTAL TIME OF EVAPORATION AS A FUNCTION OF X AND n - FIXED DROPS

-32 -the total time of life will be dependent upon the exponent n, so that X alone does not give a true indication of evaporation rate. 3. Effect of Ultrasonic Field Intensity on the Evaporation Constant The evaporation constants found in the previous section are plotted against ultrasonic field intensity in Figures 6 and 7. Separate curves are used for the different velocities to eliminate the effect of variations in n with velocity. The resulting curves clearly indicate a definite pattern for the effect of ultrasonic field intensity on the evaporation rate. 4. Effect of Ultrasonic Field Frequency on the Evaporation Constant A series of tests were made with fixed drops in constant velocity air streams and at various ultrasonic frequencies. Results at two velocities were measured. These are given in Table III and are plotted in Figure 8. TABLE III DATA SHOWING THE VARIATION OF X WITH ULTRASONIC FREQUENCY AT CONSTANT AIR VELOCITY —CUMENE DROPS v = 2.48 (ft/sec) v = 4.29 (ft/sec) Fre- X Fre- X Fre- X qiuency 1'0 n/ quency 100 quency )n/ec (cps) sec (cps.n/se ps) 100 35,260 0.260 35,329 0.304 35,245 0. 291 35,280 0.258 35,343 0.345 35,266 O.295 35,301 0.271 35,343 0.357 35,286 0.361 35,310 0.289 35,365 0.278 35,307 0.305 35,317 0.291 35,384 0.264 35,326 0.286 35,321 0.301 35,404 0.265 35,347 0.285 35,324 0.304

-33 -0.40 0,30. 0.20,, i: 02O ft/sec 0.40 w o 0. _ 0.30 z 0 0 O2 S10.82 0.:35 0.25 0020...... 0.25APPLIED VOLTAGEV - VOLTS APPLIED VOLTAGE A V - VOLTS FIG. 6 EFFECT OF FIELD INTENSITY ON EVAPORATION CONSTANT

-34 -0.35 J 0.40 07., 0.302 i- 004.29 0510 0........ '0.40 -0.30 0.00. 0 5 16.07 1 o 0VOLTAGE V - VOLTS o I o 0.30m 5 0.35 - 03H..LL.i. 0.20.O 5 10 15 20 25 APPLIED VOLTAGE, V - VOLTS FIG.7 EFFECT OF FIELD INTENSITY ON EVAPORATION CONSTANT

-35 -Values of the evaporation constants obtained for zero ultrasonic field are indicated by broken horizontal lines drawn through the curves. The frequencies at which the maximum evaporation constants occur are designated in the text as the critical frequencies. 5. Variation of Critical Frequency with Relative Air Velocity Drops that evaporate while freely suspended, as shown in Figure 2, would be doing so in an air stream having a velocityequal to the drop terminal velocity. As indicated in Figure 8 the critical frequency was affected by a change in relative velocity, so a series of tests were made to measure the change in critical frequency over the range of velocities likely to be encountered in tests with free drops. Results are given in Table IV and are plotted in Figure 9. The two points obtained from Figure 8 are also shown. TABLE IV DATA SHOWING THE VARIATION OF ULTRASONIC CRITICAL FREQUENCY WITH CHANGES IN RELATIVE AIR VELOCITY Velocity Critical Frequency —(cps) (ft/sec ) Increasing Decreasing Velocity Velocity 0 35,5o4 35,421 0.82 35,655 35,561 1.16 35,633 35,537 2.01 35,535 35,439 2.48 35,475 35,3S98 3.51 35,410 35,351 4.29 35,373 35,328 4.96 35,330 35,298 6.07 35,293 35,282 7.00 35,282 35,257 7.84 35,260 35,256 8.59 35,236 3,244 A large hysteresis effect is clearly illustrated in the figure.

-36 -0.37 --- O~~~~.3~~~~ 0 -2.48 f 'o > ~ -4.29 it Is ) 0.33 — X AT V=O 0 0 C00 0.31 0 _o e J 1 0.29 0.2 7 0.25 - - 35,240 35,280 35320 35,360 35,400 ULTRASONIC FREQUENCY - CYCLE/SEC FIG.8 EFFECT OF ULTRASONIC FREQUENCY ON EVAPORATION CONSTANT AT CONSTANT VELOCITY AND VOLTAGE (20 VOLTS) 35,650 35,600 r I \ u.I _ 3 5,500 ' 35,450: 35,400 L_: IF10 F IG. 8 A530 o35,250 0 I 2 3 4 5 6 7 8 RELATIVE AIR VELOCITY - ft/sec FIG.9 VARIATION OF CRITICAL FREQUENCY WITH RELATIVE AIR VELOCITY

-37 -6. Reduction of Data for Fixed Drops, Based on the Evaporation Equation (2.51) The evaporation equation (2.51) was derived for the case of a single drop evaporating in a constant velocity air stream in the absence of an ultrasonic field. Repeated here for convenience, it was shown to be __a/- +"' 152(-3 '1)-53l Do/2+ C (D8/2 _ D3/2) 3 C (Do - D) + 3C2 (D1/2 D1/2) 3C3 1n (D/2 + C 6k [1 +c (Tf- Tlt (3.8) Cpc L where /(Pr)l/3 (VYl/2 All independent variables are known except for the quantity f which must be determined from the experimental data. Using the values for the physical properties given in Appendix C and the average values of the temperatures measured in the tests, the following expressions were obtained, C = 2.96 (3.10) fv1/2 and 6k pc(Tf T) Cp6k [1+ c (Tf j T)] = 3.29 x 10-7 fv1/2. (3.11) Substituting these in the evaporation equation and modifying the result to express D in microns x 10-2, the evaporation equation for stationary cumene drops in a constant velocity air stream whose temperature is 83%F (the test conditions) becomes

-38 -18.1 44.3 145 fvl (D/2 _ D3/2) 2 (Do - D) + 3 32 (D/2 D2) (3.12) 236 r fv1/2 D6/2 + 1.63 f4 V2 in fv1/2 D1/2 + 1 = t. To solve this equation for f., a point on the evaporation curve is selected and the corresponding values for D and t substituted in the equation. The values for Do and v are the initial drop diameter and relative air velocity for theparticular test run. The values of f computed for several relative air velocities are shown in Table V below. TABILE V VALUES OF f FOR SEVERAL AIR VELOCITIES Air Velocity (fps) f 0.82 2.31 2.01 1.96 4.29 1.74 7.00 1.69 8.59 1.66 B. Reduction of Data —Free Drops Figures 10, 11, and 12, plotted from the experimental data given in Tables XXIV - XXVI in Appendix B, show the results of evaporation tests with freely-suspended drops of fourteen pure liquids and kero.sene. The drops were supported in the air stream at their terminal velocities by means of air drag and ultrasonic forces. A typical sequence of photographs from one of the runs is shown in Figure 2.

-39 -13 O -2,4- DIMETHYLPENTANE X — n - OCTANE 121\- \1 I I 1 I o0 — ETHYL ALCOHOL a -TERT-AMYL ALCOHOL o - PYRIDINE e -- ETHYL n -VALERATE o i- * -n - BUTYL ALCOHOL + - CUMENE 10 z 0 0 0 0 0 20 40 60 80 I00 ELAPSED TIME - SECONDS FIG. 10 EVAPORATION CURVES FOR SOME PURE LIQUIDS -FREE DROPS

-4o13 o - 2-HEPTANONE 12: + - TERT - BUTYLBENZENE * n -DECANE It n -- I -BUTYLBENZENE I I Ie( D ---- METHYLn-HEXYL.KETONE 10 z 89 x co~~~ 0 X 7 cr - 6 w 5 o 0 4 __ 3~~ 0 0 I00 200 300 400' 500 ELAPSED TIME - SECONDS FIG. II EVAPORATION CURVES FOR SOME PURE LIQUIDS - FREE DROPS

10 * - ACETOPHENONE o - KEROSENE 9 10 z 0 7 rx 8 0 3 16 2 '1L I \ ILASE T ME INTE IG. I~ ~ _ __ __ ___e H I I I I~ W5~ _ __ 4 a 0 0 7 0 20 40 60 80 100 120 ELAPSED TIME MINUTES FIG. 1 2 EVAPO RATI ON CU RVES FOR ACETOPHENONE AND KEROSENE~ - FREE DROP~S

When evaporating in this manner, and in a constant frequency field, drop diameter for the pure liquids was found to be a linear function of elapsed time of evaporation. The measured slopes, in microns per second, are listed in Table VI below. TABLE VI EVAPORATION RATES FOR FREE DROPS OF SOME PURE LIQUIDS IN A STATIONARY ULTRASONIC FIELD Liquid Evaporation Rate (microns/sec) 2,4-Dimethylpentane 66.7 n-Octane 22.7 Ethyl Alcohol 17.6 Tert-Amyl Alcohol 17.0 Pyridine 15.2 Ethyl n-Valerate 9.90 n-Butyl Alcohol 8.55 Cumene 8.55 2-Heptanone 6.75 Tert-Butylbenzene 4.80 n-Decane 3.39 n-Butylbenzene 2.39 Methyl n-Hexyl Ketone 2.20 Acetophenone 0.81 For kerosene, the evaporation rate is seen to decrease with an increase in elapsed time of evaporation.

CHAPTER IV EXPERIMENTAL EQUIPMENT The experimental-test equipment is composed of four main functional systems, each being somewhat independent of the others. These are classified as follows: 1) air flow system, 2) ultrasonic field generation system, 3) photographic recording system, 4) instrumentation and accessories. These form the complete apparatus shown in Figure 13. A somewhat clearer understanding of the manner in which these are related can be obtained from the schematic diagram given in Figure 14. The basic operation of the apparatus is as follows. The air system produces a vertical flow of air with little turbulence. This flow is made to pass through a ceramic cylinder of barium titanate, the piezoelectric transducer which produces a standing wave ultrasonic field in the air within the tube. The ultrasonic field, when stationary, i.e., when the sound nodes are fixed, introduces lateral forces on the drop within the tube which hold the drop in a fixed horizontal position. At the same time, the action of the air stream on the drop creates an upward drag force which opposes the downward vertical force of gravity. By varying the velocity of the air stream, the drag force on the drop can be controlled to just balance out the gravitational force, so that the drop is held in a fixed position in space. By adjusting the air velocity 43

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TIME INTERVAL METER ELECTRONIC CAMERA COUNTER POWER CERAMIC 0 0 SUPPLY CAMERA TUBE DROP TIM LAMP 0 0 BY- PASS 110 V SWITCH VERTICAL __ ru,,,IND ----- VACU LBO VCUUM TUBE TUN WINELD~~~ F || IVOLTMETER _o AIR SUPPLY SHUT-OFF ORIFICETAL EQUIPMENT VALVE CONTROL VALVE PRESSURE FILTER REGULATOR SURGE TANK MANOMETER OSCILLATOR AMPLIFIER POWER SUPPLY FIG. 14 SCHEMATIC DIAGRAM OF EXPERIMENTAL EQUIPMENT

it becomes possible to hold the drop in this position as it evaporates. Motion pictures of the drop were taken at known time intervals to get drop diameter as a function of time. A. Air Flow System 1. Vertical Wind Tunnel The low turbulence air stream is formed by a small wind tunnel, approximately six in. in diameter and 7-3/4 in. long. See Figure 15. The body of the wind tunnel is made of six sections of six in. steel tubing. Screens, which reduce the scale of turbulence in the air stream, are soldered to each of the five botton sections. When assembled, the sections are positioned so that the screen mesh sizes decrease as the exit nozzle is approached, except for the 100 mesh bottom screen. A wooden convergent nozzle, used to give the exit air stream a flat velocity profile, provide a smooth approach to the barium titanate tube, and compress the turbulence scale, is fitted into the top section. One-eighth inch pipe couplings provide connections to two small holes in the side of this section and serve as thermocouple holes. Four bolts attach the bottom section to a bottom piate. Air is allowed to enter the wind tunnel through a hole in the center of this plate, while a baffle mounted directly over this hole reduces the velocity of the incoming air and creates a more uniform pressure in the bottom section of the tunnel. Figure 15 clearly shows the individual sections with their turbulence screens, the exit nozzle, and entrance baffle. All sections, properly aligned with each other, are clamped between two plates by four long bolts running along the outside of the

-47 -PIEZOELECTRIC CERAMIC TUBE GLASS WINDOW ELECTRICAL CONNECTIONS TOP PLATE.-TIE BOLT NOZZLE 100 MESH l - -' SCREENS 80 60 __40 -BAFFLE PLATE BOTTOM PLATE AIR INLET FIG. 15 SECTIONAL VIEW OF VERTICAL WIND TUNNEL

tunnel. The top plate serves as a mount for the barium titanate tube and contains spring contactors used to make electrical connection to the transducer. One of the contactors is insulated while the other is grounded to the top plate. Details are shown in Figure 15. The top plate- also carries insulated binding posts for external electrical connections and an adjustable holder for the glass filament used for suspending drops. 2. Air Supply Air is obtained from a building supply header at about 95 psig and 830F and fed to a surge tank through a shutoff valve and small pressure regulator. A hot-water tank rated at 150 psig continuous duty was selected for the surge tank and has served quite well in diminishing the adverse effects due to slight pressure variations in the main line. Leaving the surge tank, the air is made to pass through a filter, control valve, and flow metering orifice before entering the wind tunnel. B. Ultrasonic Field Generation System The ultrasonic field is generated by a cylindrical barium titanate transducer which is excited by a source of high frequency sinusoidal voltage. The transducer and source comprise the field-generating system. 1. Barium Titanate Transducer A transducer is an element that converts energy from one form to another. In the apparatus used in these tests the transducer converts a sinusoidally-varying electrical voltage at a fixed frequency into

acoustic energy at the same frequency. Since a cylindrical transducer is used the acoustic energy is radiated as cylindrical sound waves concentric to the walls of the tube. Only the waves directed toward the center of the tube were of use in these tests. Under certain conditions, the waves within the cylinder combine to form a standing-wave sound field, that is, a sound field having stationary nodes. Different patterns are possible depending on the mode of vibration; however, only the field having concentric cylindrical nodes was used for these tests. When a drop or small solid particle is introduced into the field it is forced to take a position in one of the nodes. The particular transducer used in these experiments is a cylinder cast from a barium titanate which the manufacturer designates as ceramic "A". It has a safe working temperature of 100~C. Dimensions of the cylinder are two in. O.D. x 1-5/8 in. I.D. x four in. long. The corresponding operating frequency is limited to a very narrow frequency band around the resonant frequency of about 35,500 cycles per second. Several basic piezoelectric elements are shown in Figure 16. Very thin layers of silver are plated on both inner and outer surfaces to within 1/16 in. of both the top and bottom of the tube and serve as electrodes for the element. Maximum safe operating voltage specified by the manufacturer is 100 volts rms. However, all tests were made below 45 volts. The voltage is applied between the inner and outer plated surfaces. Before the element could be used, it was necessary to cut holes on diametrically-opposite sides of the tube and install windows forthe purpose of viewing the suspended drops.

FIG. 16 BASIC PIEZOELECTRIC CERAMIC ELEMENTS 0 + ~0 +~~~ A B C FIG. 17 ACTION OF THE PIEZOELECTRIC CERAMIC TUBE DUE TO CHANGES IN POLARITY OF APPLIED VOLTAGE

-51 -The operation of the ceramic element is a result of the piezoelectric effect. The effect is such that if the crystal is strained under an applied stress, electric charges of opposite polarity appear on the two opposite faces of the wall, causing it to become electrically polarized. The opposite effect also occurs. That is, when the two plated surfaces are connected to a source of voltage, so that the ceramic lies in an electric field, it will suffer a strain and either expand or contract. When an alternating voltage is applied to the ceramic such that the frequency is equal to the resonant frequency of the element, the amplitude of mechanical deformation of the tube wall becomes quite large and results in the generation of an ultrasonic sound wave. This action is illustrated in Figure 17. One polarity causes the wall to increase in thickness and decrease in length, thereby generating a radial compression wave within the tube. The opposite polarity causes the opposite effect and generates a radial rarefaction wave. As the wall alternately increases and decreases in thickness it generates a sound field in the radial direction. The action of two waves originating at diametrically opposite sides of the tube is illustrated in Figure 18 to show how they combine to form a standing-wave sound field in the form of concentric cylindrical nodes. The pattern is easily made visible with lycopodium powder sprinkled on a flat horizontal sheet held within the tube. Figure 19 shows a small cork sphere suspended in air in one of the nodes of the ultrasonic field.

-52 -DROPLET, / fN ~ / WAVE GENERATED AT THE RIGHT SURFACE WAVE GENERATED AT THE LEFT SURFACE RESULTANT PRESSURE WAVE FIG.18 GENERATION OF A STANDING SOUND WAVE BY THE PIEZOELECTRIC TUBE

t-9) 2 Ultrasonic;_.,;;_Field,;;;;;;;;.......... etc ion..;-..:'...i'..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...r..!El-,0000;EEi~iEiE~EEiVE:: f:;0:SiES000000000200000000'0...........,'::::f A~~~~~~~~~~ s. spse and00 covnin deiefrdtcig h rsneo st~inry fi eld is$ a needl ie a~ttach-e~d to th~e ~end of a. fi-ne thedTe nelis -sulspenlded Lin th~e tLube whil }e thle freqetfncy i8s vari.edaonth fi~~~~~~{- "ga 8d by *%1 %9 the fiel andK held in a8{5'{} ) fixed Ww pos1iti ono in oneo h plied to the tub. This voltage, when measured by a vacuum tube volt................. meter, also nerves '.s an indication of the relative field intens i~~~~~~~~~~~~~~........ty. This method x ~~~~~~~~~~~~~~~~~~~~ - u 'eci~~......... th.oghu.th.tstfo te.n.i.1.fr. cluency setting and will detect "tuned" fi~~~~~~~~~~~~~~~~~el~~d adequate enough to.........su pend drops.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...............

-54 -When a drop has been suspended, a more critical indication of the tuning is obtained by observing the motion of light reflected from the surface of the drop and appearing on the inside surface of the tube. The change in angle at which the light is reflected is due to distortion in drop shape. The distortion occurs as a result of field forces acting on the drop, and at high field intensities the drop sphere is considerably flattened, depending on the value of the applied voltage and the tuning of the tube. At the resonant frequency, which will be referred to as the critical frequency, the strongest field action occurs and creates the maximum drop distortion. Therefore, when tuning for the critical frequency, the deflection of the reflected light beam increases as the critical frequency is approached from either direction and reaches a maximum at this frequency. The drop distortion was also viewed with a pocket microscope. A small light was.placed inside the wind tunnel to provide backlighting as the drop was viewed from above. At high field intensity and critical frequency the distortion was quite pronounced, giving the drop the appearance of a rounded, well-flattened disk. An alternate method used for detecting and exploring the sound field was the hot wire technique. Although not as convenient to use for field detection, it is capable of providing more information and was used to a limited extent for this purpose. 3. Ultrasonic Frequency Voltage Supply The high frequency voltage supply consists of a voltage stepdown transformer, oscillator, power supply and amplifier. These are shown in the schematic diagram, Figure 14.

A voltage step-down transformer was used to decrease the building 220 volt, 60 cycle supply to 110 volts, since the 110 volt building supply was heavily loaded at times by other equipment in the building. The resulting large voltage surges caused erratic operation of the equipment and loss of stabilizing action on freely-suspended droplets. After the change to the 220-volt supply, no further difficulties of this nature were experienced. The high frequency voltage signal is obtained with a HewlettPackard Model 200 AB variable frequency oscillator. The output signal is fed directly to the input of a 45-watt amplifier which serves to amplify the voltage, provide sufficient power to drive the ceramic tube, and to improve the impedance match between the voltage supply and ceramic tube. A separate B+ supply is used to provide some of the power to the amplifier. Schematic diagrams for both the amplifier and B+ supply are given in Figure 20. C. Photographic Recording System Photographic records of evaporating drops were taken at fixed time intervals to get drop diameter as a function of elapsed time of evaporation. Enlarged drop images were obtained with a modified 16 mm motion picture camera. The timing device was calibrated with a stop watch during each run. 1. Motion Picture Camera A 16 mm U.S. Army Air Force Type N-6 gun camera, with speeds of 16, 32, and 64 frames per second, was used to photograph the

330V O.C. + L 0C' Tl7 OUTPUTL URN RC R 5K 30W TCl = OUTPT MRANFT3 R700,10W 3800 OH PRIMR Y T 115V 3C- -- 6011j- R, C R4 3V 6F6 CI Otmfd. MICA T3 POWER TRANSFORMER 375- 375 VOLTS AT 61-6 38 150 D.C00 OHM SEONARYT V=6L6 C,,C5 =25mfd2250, 25V. 150mo. D.C. V =U4G 20 SCHEMATIC DIAGRAM OF AMPLIF400V. RI =0. SMEG., 1/2W LI I 4H AT I0:)mo.,100 Ohms R. a 1700, 1/2W Ti I DRIVER TRANSFORMER, TURNS RATIO, PRI-1/2 SEC.=4:I R.3 - 5.1K, 30W T2 = OUTPUT TRANSFORMER:l800 OHM PRIMARY TO 500 OHM SECONDARY RS =2250, 25W FIG. 20 SCHEMATIC DIAGRAM OF AMPLIFIER

evaporating drops. Before the camera could be used, it was necessary to provide the camera with a sliding mount for rough focusing, a combination lens extension tube and reflex viewer, and a focusing screen adaptor. Figure 21 gives a close-up of the modified camera mounted in position. The sliding mount is nothing more than a pair of slotted pieces of thin metal plate, each attached to a wooden support b-y means of soft rubber grommets. The camera mounting bolts fit into the slots, allowing the camera limited motion in one direction only. Adjustments for rough focusing are made with a focusing screw. The lens extension tube and reflex viewer unit consists of five sections. These are the threaded aluminum lens mount, three extension tube sections, and the reflex viewer housing. Various factors of magnification can be obtained by varying both the number of sections used and the focal length of the lens. Figure 22 shows the assembled unit mounted to the camera. Most of the results were obtained with the original camera lens, a 35 mm, f/3.5 Wollensak, providing a magnification factor of about 7X when used with all extension tube sections. To increase image sharpness, the lens was mounted backwards in the lens mount, i.e., the front lens element faced the film instead of the drop. The inside of the extension tube is lined with black velvetine and a black paper diaphragm was inserted in the tube to cut down light reflections from the tube wall. At the camera end of the tube, an imagesplitting block reflects part of the incoming light and forms a second image on a ground glass viewing screen directly above the block, while the

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I I I-I I I 11 1.I.........I. I - -- I -..........._ - FIG. 21 CLOSE-UP PHOTOGRAPH OF VERTIOAL WIND TUNNEL, CAMERA,

VIEWING MIRROR IMAGE SPLITTERVIEWING SCREEN BLOCK VIEWING SCREEN EXTENSION TUBE CAMERA DIAPHRAGM a LENS FOCUSING. ~ SCREW MOUNTING. BOARD -' -> -- IMAGE PATH FIG. 22 SECTIONAL VIEW OF LENS EXTENSION TUBE- SHOWN MOUNTED TO CAMERA

-60 -transmitted image appears on the 16-im film. Transparent Scotch Tape is used to frame the field of view of the camera on the viewing screen. Two right-angle prisms were used to make the image splitter. The hypotenuse of one was half-silvered, then cemented to the hypotenuse of the other, forming a rectangular block. Images produced by the block are much cleaner than those from a simple half-silvered mirror since ghost reflections from the non-silvered surface of the plane mirror are eliminated. With this arrangement, the drop can be observed in the reflex viewer as it is being photographed, making it possible to control drop position during evaporation. For critical focusing, a piece of fine ground glass was placed at the plane of focus in a discarded film magazine. The drop image appearing on the ground surface is inspected with a pocket microscope for best focus while turning the lens in its screw mount. When the camera was first operated, considerable camera vibration developed. It was especially severe during starting periods. Because of the high image magnification used, even slight vibrations resulted in badly-blurred images, making accurate measurements impossible. The problem was solved to a satisfactory degree by altering the camera mount by the addition of soft rubber grommets and loading the camera and extension tube with steel blocks. This lowered the resonant frequency of the system to a point well below the vibration frequency. The decrease in vibration amplitude resulted in satisfactory operation.

-61 -2. Photographic Accessories These include the camera control and power supply box, timer, and background lamp. A circuit diagram for the camera control box is shown in Figure 23. The control box is used to convert 115-volt, 60 cycle building supply to 25-volts D.C. for camera operation. This is accomplished with a 115:26 step-down transformer and full-wave rectifier. Various switches are used to control the power to the camera, timer, and background lamp. The timer is an Air Force Camera Intervalometer, type B-5A. This unit can be adjusted to give repetitive time intervals of from zero to 60 seconds in 1/2 second intervals. At the end of each time interval, a short pulse of D.C. power is allowed to pass to the camera, causing it to operate for the duration of the pulse. At a camera speed of 16 frames per second, about eleven frames were exposed during the pulse. Therefore, the timing operation is semi-automatic in that it must be started and stopped. A timer by-pass switch is provided so that the camera can be operated manually, if desired. Background illumination for the drop is provided by the lamphouse of an Argus 35 mm projector. A 100-watt projection lamp provides more than enough illumination so that good control of light intensity is obtained with a 5-ampere Variac. A piece of heat absorbent glass placed in front of the lamp reduces the radiant heat passing to the ceramic tube. This was felt necessary to protect the tube from overheating. In addition, a red "A" filter placed between the lamp and ceramic tube further reduces the light intensity and decreases the effect of chromatic aberration in the camera lens.

-62 -oS2 0 2 o G 23S 1D5:26 O 115 V I TO _ -. 604 ~ 1 [ TIMER FIG. 115 V 604 OUTLETS FIG. 23 SCHEMATIC DIAGRAM OF CAMERA POWER SUPPLY

-63 -D. Instrumentation and Accessories The instrumentation and accessories comprise the equipment for measuring ultrasonic frequency, air velocity, and temperature, and the miscellaneous small accessories. Accurate frequency measurements were made with a HewlettPackard electronic counter, Model 521-A, used in conjunction with a Berkley time-interval-meter, Model 5120. The output signal of the variable frequency oscillator, used for driving the barium titanate tube, was also applied to the input of the electronic counter. This instrument counts the events, in this case the voltage oscillations, in a given time interval. However, the time interval used in the counter is based on 60-cycle line frequency and was not accurate enough for use in this case. Therefore, the pulses of both the first and six-thousandth oscillations were fed from the counter to the start and stop connections respectively of the Berkley time-interval-meter. This instrument measures the time interval between two events to within one one-millionth of a second, the timing being based on an accurately-controlled crystal oscillator. The time required for the 5999 oscillations was easily converted to ultrasonic frequency in cycles per second. Air-flow measurements made with a sharp-edged orifice were used to compute relative air velocities. Orifice and inside pipe diameters are 0.150 in. and 0.375 in. respectively. The pressure drop across the orifice was measured with one of two U-tube manometers, a mercuryfilled manometer for large flow rates and one filled with acetylene tetrabromide, s.g. = 2.964, for low flow rates. The latter was used only for

-64 -steady-state operations because of the adhesion of the fluid to the tube walls. Calibration of the orifice by means of suspended drops is described in the next chapter. A hot-wire anemometer probe, made from a length of ceramic thermocouple-wire shielding, two steel sewing needles, and 0.0005 in. platinum wire, was used for checking the shape of the velocity calibration curve. When used in the bridge circuit shown in Figure 28 the probe provided data for determining velocity variations in accordance with the following equation derived by King,l6 i2 = i2 + K (P v)l/2 (4.1) Air and drop temperature measurements were madewith an ordinary copperconstantan thermocouple-and precision-type potentiometer. For air measurements, the unshielded thermocouple wias placed in the air stream at the exit of the ceramic tube. Drop temperature measurements were made by suspending the drops on a fine thermocouple in air streams of known velocities. The filament for suspending drops was made by drawing a 7/32 in. glass rod into a fine thread, breaking the thread at a convenient length, and reheating the end to form a slightly bulbous tip. This slight enlargement provided better support for the large drops. A rubber stopper pressed on the rod end of the filament was used to store the unit in a glass tube when not in use, providing protection against breakage. When in use, the glass filament was supported in the adjustable holder shown in Figure 21. Besides giving lateral and vertical adjustments for drop position, it also provides a rapid means for withdrawing the filament from the tube for cleaning or drop reloading, and repositioning within the tube. The structure also serves as a mount for the thermocouple and filter holders.

A Heathkit vacuum-tube-voltmeter, used for measuring the voltage impressed across the ceramic tube, and an ordinary pocket stopwatch, used for checking the timing of the camera intervalometer, complete the accessories.

CHAPTER V EXPERIMENTAL TEST PROCEDURE A. Orifice Calibration Calibration of the air-metering orifice was based entirely on drag-coefficient data for solid spheres. The method for computing terminal velocities for spheres of given diameter and specific weight is outlined in Reference 2. It is based on the fact that the drag equation log CD = log g (p - Pa) D3 2 log Re (5.1) - 512 which is derived from the equation of motion for spheres subjected to gravitational, buoyancy, and drag forces, plots as a straight line with slope of -2 on log CD vs. log Re coordinates. This equation can be solved when either Re or CD is set equal to unity since all quantities but CD and Re are known. To obtain the terminal velocity for a given drop size, Equation (5.1) is solved for Re by setting CD = 1 and substituting the proper values for D and the other known physical constants. The corresponding straight line, having a negative slope of 2 and passing through the point whose coordinates are the computed Reynolds number and CD = 1, is drawn on a log-plot showing the experimental drag coefficient curve for solid spheres as a function of Reynolds number. Such a plot is shown on page 16 of Reference 11. The intersection of the straight line with the drag coefficient curve locates the only solution which satisfies both the equation and the experimental drag coefficient curve. The terminal velocity is computed from the value of Re at the point of intersection. 66

Results for cumene drops are shown plotted in Figure 24, giving terminal velocity as a function of drop diameter. To relate this information to orifice pressure measurements, test results were obtained giving the diameter of freely-suspended drops as a function of orifice pressure drop. Test data, given in Table VII are plotted in Figure 25. TABLE VII ORIFICE PRESSURE DROP VERSUS FREE-DROP DIAMETER Ap D Ap D in. Hg microns in. Hg microns 25..3 757 11.9 525 23.8 739 9.9 472 21,9 698 7.9 436 19.9 682 5 9 379 17.9 631 3.95 325 15o9 595 1.95 240 13.9 568 1.24 212 For this test, n-butyl benzene was used in place of cumene because of its identical specific gravity (sp. gr. = 0.866) but much slower rate of evaporation. (See Table VI.) The latter was intended to reduce the possible effects of evaporation on drag. By cross-plotting the information in Figures 24 and 25, the desired result was obtained giving air velocity as a function of orifice pressure drop. This result and the corresponding empirical equation are shown in Figure 26,

-68 -D v 200 2.02 o 'I 300 3.28 Xo 400 4.53 F 6 500 5.70,_ 600 6.90.- l 700 8.13 o 0 _1 w >4 z W 0l.. _ 0 0 1 2 3 4 5 6 7 DROP DIAMETER, MICRONS X 10o FIG. 24 DROP TERMINAL VELOCITY DETERMINED FROM DRAG COEFFICIENT CURVE, REF. x < o z 0 w 0 4 8 12 16 20 24 28 ORIFICE PRESSURE DROP, IN.H8. FIG. 25 RELATIONSHIP BETWEEN DROP DIAMETER AND ORIFICE PRESSURE DROP

-69 -In addition to providing relative air velocity data, the velocity information was also used for calibrating a hot wire probe. The probe was used for some preliminary velocity measurements and velocity profile explorations. The calibration was based on King's equation (4.1) which states that the square of the hot wire heating current is a linear function of the square-root of the air velocity. Figure 27 shows the linear calibration curve obtained from the experimental data tabulated in Table VIII. The schematic diagram of the hot wire anemometer circuit is given by Figure 28. TABLE VIII EXPERIMENTAL DATA FOR HOT-WIRE CALIBRATION i2 Ap v vA/2 (ma)2 in. Hg ft/sec (ft/sec)1/2 1.44 x 104 0 0 0 1.56 o.o4 0.37 O.61 1.62 0.09 o 0. 52 0.72 1.69 0.18 0.74 0.86 1.73 0.26 0. 90 0. ~5 1.80 0.44 1.16 1.08 1.88 0.88 1.64 1.28 1.96 1.32 2.02 1.42 2.00 1.76 2.32 1.52 2.03 2.20 2.60 1.61 2.10 3.08 3.08 1.71 2.20 3.96 3.50 1.87 2.25 6.o 4.30 2.07 2.31 8.0 4.96.2.23 2.40 10.0 5.55 2.36 2,50 14.0 6.56 2.56 2.60 20.0 7.85 2.80 B o Drop-Size Measurements Because of the distortion of drop shape caused by the filament suspensions used in the fixed-drop evaporation tests, it was necessary to

-70 -/ 7. 04 ORIFICE PRESSURE DROP, IN. HG. FIG. 26 RELATIONSHIP BETWEEN AIR VELOCITY AND ORIFICE PRESSURE DROP It 2.6 0 3 12. O mm m 0 4 8 12 16 20 24 28 F1G. 27 RELATIONSHIP BETWEEN HOT WIRVELOCITY AND HEAORING CURET AND AIR VELOPCITY ING,."~ CURREN AN IEOCITY

-71 -3250t,O 6500SI 3GALVANOMETER HOT WIRE VARIABLE ON-OFF 0-200 M A D C SUPPLY SWITCH AMMETER FIG. 28 SCHEMATIC DIAGRAM OF HOT WIRE ANEMOMETER CIRCUIT

-72 -determine which of the many possible drop-size measurements would lead to the best approximation of drop volume. By tracing on fine coordinate paper the outlines of several enlarged drop images, covering the range of sizes encountered in these tests, it was possible to determine the volume of each size by graphical integration. These values were compared to the volumes obtained from diameters measured at various positions and inclinations on the image and it was found that the average diameter obtained from the two measurements made at 45 degrees from the horizontal position gave the best results for all sizes. Therefore, all drop-size measurements in this investigation were obtained in this manner. Magnification factors for each evaporation run were obtained by comparing the photographic image and actual sizes of a fine wire. Since variations in film shrinkage, time of exposure, and film development affect film image size, photographs of the wire were taken at the beginning of every run. C. Experimental Test Procedure The equipment, set up and connected as shown in Figure 13 and 14, is ready for a test run. About forty-five minutes before the run is to be made, the amplifier, oscillator, and variable D.C. supply are turned on and allowed to warm up. During this time the camera lens is opened, set to about f/4.5, and the focusing screen inserted into the film magazine compartment. The background light for the drop, after being turned on, is positioned to give the best field of illumination when viewed on the viewing screen in the lens extension tube. With the air turned on at a relatively low velocity and the ultrasonic supply warmed up, the oscillator is tuned to the approximate

resonant frequency of the transducer tube, approximately 35,000 cps, and the voltage across the tube adjusted to about 20 volts by varying the D.C. supply. A small diameter wire, glued to the end of a fine thread, is lowered into the tube and the oscillator frequency varied until the wire is suddenly "grasped" by the sound field and held in a fixed position. The voltage is again adjusted to about 20 volts and a fine frequency adjustment is made to increase the grasp if possible. When the adjustment is correct the ultrasonic field will hold the wire in position against moderate shifts of the thread suspension. A glass eye-dropper, drawn to a fine tip, is then filled with a liquid of relatively low volatility, such as kerosene, and the drops are shaken from the dropper into the tube directly above the node previously occupied by the wire. If the majority of the drops fall, the air velocity is increased; if they rise, the velocity is decreased. It will be found that eventually some drops become suspended in the air stream. The air velocity is further adjusted until the drop occupies a position between the two windows in the tube and becomes visible on the viewing and focusing screens. Viewing the image on the focusing screen with a pencil-type microscope, about 20X, the lens is adjusted to bring the image into sharp focus. The filament suspension, mounted in its holder, is then located in the tube so that it is centered in the field of view of the camera and properly focused. Before each run is made, the following readings and settings are checked: air temperature, critical frequency setting, air velocity setting,

voltage (sound field intensity), camera focus, camera speed, lens opening, lamp control (variac) setting, intervalometer setting. Photographs are then taken of the test number, wire for size determination, and the evaporating drop suspended on the filament, in that order. For taking the drop pictures, the drop is attached to the filament by means of a fine eye-dropper. The filament is immediately lowered into the tube and the camera and stop-watch started simultaneously. Under the control of the intervalometer, the camera photographs the evaporating drop at fixed time intervals. At the start of the last series of photographs, the stop-watch is stopped, providing a check on the timing of the intervaIometer. The drop temperature for cumene was assumed to be 4.50F lower than the temperature of the air stream. The value was based on experimental results obtained in this investigation and was found to hold for the small range of air temperatures encountered in these tests. After development, the film was projected in a microfilm reader where the drop-size measurements were made. These data, together with the corresponding time measurements, are tabulated in Appendix B. The procedure used for the free-drop tests was similar to the one just described for fixed-drops. However, in the test with free drops no filament suspension is required to support the drop, and the free drops are "falling" at their terminal velocity with respect to the air stream throughout the evaporation process.

CHAPITER VI DISCUSSION OF RESULTS The expression for Nu, based upon the heat-transfer processes occurring across an assumed equivalent thermal boundary-layer, was modified by boundary-layer considerations to give, Nu = a [2 + f (Pr)1/3 (Re)1/2]. (2.43) In general, the form of this result is in agreement with the expressions for Nu obtained by others, notably Friossling,S Equation (1.5); Ranz and Marshall,26 Equation (1.9); Ingebo,l4 Equation (1.13); and Kinzer and Gunn,17 Equation (1.16). However, the Equation (2.43) does contain an additional factor a not found in the other expressions. An inspection of Equations (2.42) and (2.17), defining a and the expansion for the in term in the evaporation equation, shows that the value for a is very nearly equal to unity for low temperature evaporation, i.e., when the expansion given by Equation (2.17) is very closely approximated by the first term alone. In fact, if only the first term of the expansion is considered, a becomes equal to unity and Equation (2.43) reduced to Nu = [2 + f (Pr)l/3 (Re)l/2]. (6.1) With an increase in (Tf - T), as for high temperature evaporation or combustion, the other terms of the expansion cannot be neglected, and a becomes an important factor in the expression for Nu. For these cases, instead of using the expansion, it becomes more convenient to use Equation (2.42), giving a in terms of in [1 + c (Tf - T)/L] directly. 75

-76 -The term a arises because of the effect of mass transfer on the heat-transfer process. Consider the case of a drop evaporating under the influence of a fixed-temperature difference. If in some manner the evaporated vapor could be collected right at the drop surface, the maximum amount of heat would reach the surface. However, if the vapor were allowed to diffuse away from the drop, the heat reaching the surface would be reduced by the amount required to heat the vapor to the ambient temperature. This heat loss should be indicated by a decrease in the Nusselt number for the process, and it seems quite appropriate that the loss would be goverened by the -latent heat of the liquid, the specific heat of the vapor, and the temperature difference between the drop surface and ambient air stream, as given by the factor a. The term f in the expression for Nu is the only empirical factor appearing in the evaporation equations derived in Chapter II. Therefore, it was necessary to evaluate f from experimental results. Since its appearance was based on a simplified boundary layer, it would be difficult to reduce the factor to more fundamental quantities of the physical system —unless a more thorough and certainly more involved study were made of the actual dynamic and thermal boundary layers. The simplified spherical boundary layers would quite probably have to be discarded in such a study. In the evaluation of f from the experimental results for evaporation at constant velocity, it was assumed that f was a function of velocity only. This was necessary for solving the integral in Equation (2.24). The assumption can hardly be considered drastic in view of the fact that all of the investigators mentioned above except Kinzer and Gunn indicate that f is a fixed constant for all cases.

-77 -The results of this investigation are listed in Table V and show f varying with velocity, the variation being quite small for velocities greater than 4 ft/sec. The general shape of the curve obtained from these data is quite similar in some respects to the one given by Kinzer and Gunn for their factor F in Equation (1.16). Their curve continues to rise for smaller velocities, then quite suddenly drops to almost zero at very low velocities. (Their result is actually plotted as a function of drop diameter for freely-falling drops.) No sound theoretical reason can be given at this time for the behavior of f. Since f is associated with the formation of the boundary film, the explanation will no doubt come from a closer examination of the theory describing the flow around drops. A correlation of the evaporation data for fixed drops of cumene evaporating into air streams of constant velocity and no ultrasonic field is given by Figure 55 in Appendix D. The fact that f is not a. fixed constant for all cases gives rise to the separate curves for each of the test velocities. The values for Nu shown in Figure 55 are considerably higher than those reported in the literature. This is also apparent when comparing the expressions for Nu and noting that the minimum value obtained for f in this investigation is almost three times the value reported by Ranz and Marshall.26 It is quite probable that the agreement would have been closer if some other method of air velocity calibration had been used. By assuming equal drag coefficients for both solid and liquid spheres the resulting calibration no doubt gives velocity measurements that are somewhat low. Any correction would increase the value of the velocity, increase the Reynolds number, decrease f, and shift the curves in Figure 55 to the right.

-78 -This would bring the results closer to the values for Nu given in the literature. When the evaporation process is described in terms of drop diameter and elapsed time of evaporation, the theoretical equation for the process is given by D2D d(D) = 8k n [1c (Tf - T) t, (2.24) D0 Df pc L Do Df PC where the dependence of Df upon D is required for a complete solution. If D/Df is assumed constant throughout the evaporation process for a single drop, the above equation becomes identically equal to the result obtained by Godsave,8 that is, D = D - Xt, (1.10) where X is given by Equation (2.28). The experimental results obtained in this investigation indicate that the value of the exponent in the above equation is not constant for all conditions and certainly not equal to two except, possibly, for evaporation into stagnant air. This is also indicated by Ingebol4 who shows that for Nu > 10, which would correspond to large values of Re, the total vaporization time is given by tt = CD1'4 (6.2) The result predicts the value n = 1.4 for the exponent in Equation (1.10) and corresponds to the value n = 1.47 found in this investigation for maximum velocity. Therefore, the assumption that D/Df = constant for all cases appears to be incorrect or only an approximation at best. By basing the relationship between Df and D upon boundary layer considerations for the evaporation of fixed drops in a constant velocity

-79 -air stream, a second solution to Equation (2.24) was obtained and is given by, (DI3/2 - 3/2) 3 C (D D) + 3C2 (Dl/2 - Dl/2)- 3 in 2 + C 2 D1"2 + C0 (2.51) 6k c~~ (Tf - '~) 6k In [1+ c.(TfT) t. Cpc L where = = 2 C (6.2) f (Pr)/ (V/v)1/2* ' The equation shows good agreement with experimental results as indicated in Table XXX and illustrated in Figure 56 in Appendix D. It should be pointed out that the experimental checks were made for those runs from which the values of f were evaluated, demonstrating that the equation accurately predicts the "shape" of the evaporation curves. The same degree of accuracy could not be expected to hold for the other tests at similar conditions because of the spread in experimental results for fixed conditions, as shown in Table II. The effects on evaporation of the various factors involved in the heat transfer and evaporation processes are easily determined from an inspection of Equations (2.8) and (2.43). It is apparent that the variation in f becomes an important factor in establishing the value for Nusselt's number. Also, as the temperature difference between the drop and its surroundings increases, the factor a becomes increasingly more important in evaluating Nusselt's number and should not be neglected for these cases.

-80 -The introduction of ultrasonic energy into the evaporation process greatly increased the complexity of the problem by both direct and indirect means. Figures 6 and 7-show the effect on evaporation of increasing field intensity. In general, as the intensity increased the rate of evaporation also increased. However, the opposite effect was also found at low intensities. While no satisfactory explanation can be found for this effect, it is believed that the increase in evaporation with an increase in field intensity is due to the turbulent-like character of the ultrasonic field. This characteristic causes a break-up of the laminar boundary layer surrounding the drop and increases both the temperature and vapor-concentration gradients next to the drop, thereby increasing the rates of both the heat and mass transfer processes. A change in ultrasonic frequency appears to have an indirect effect on evaporation through its effect on the "tuning" of the ceramic tube. For a given impressed voltage, the tube will generate its field of maximum intensity at its resonant frequency. As the frequency shifts from this critical value the amplitude of vibration of the tube will diminish, lowering the field intensity and drop evaporation rate. However, Figure 8 shows that for a large shift from the critical frequency the evaporation rate drops below the value given for evaporation at zero field intensity —an effect that certainly was not expected and is hard to explain. The same effect was obtained for the two series of tests taken at different relative air velocities and shown in Figure 8. An additional indirect effect on evaporation is due to the shift in critical frequency with a change in relative air velocity. Results of

experimental tests are shown in Figure 9. Over the range of velocities used in the evaporation tests, the critical frequency decreases with increasing velocity. This behavior appears to be due to the cooling effect of the air stream on the tube. A large part of the heat generated within the tube wall by internal friction is given up to the air stream, the rate of heat transfer increasing with increasing velocity. Since resonance of the tube is established when the mean circumference is equal to one wavelength of sound within the ceramic, and since sonic velocity increases with temperature, the resonant frequency must increase with an increase in temperature, i.e., a decrease in relative air velocity. The evaporation rate of a free-drop evaporating in an ultrasonic field such as used in this investigation would be influenced by all of the factors mentioned above. With reference to Figure 9, consider an evaporating free-drop initially at the critical frequency corresponding to the existing initial velocity. Since the frequency is not changed during the test, the evaporation process takes place from right to left along a horizontal line on Figure 9. In moving from right to left during evaporation, the effect of the ultrasonic field will decrease as the critical frequency gets higher and higher with respect to the set frequency. However, the normal rate of change of diameter increases as the drop size decreases, as shown in Figure 3. The two effects appear to cancel one another, giving the linear evaporation curves shown in Figures 10 and 11. The results giving the effects of ultrasonic energy on drop evaporation must be considered as preliminary at this time, since it

-82 -appears that no other investigation of this topic has been made. The experimental equipment and test procedure were exploratory in nature. Many improvements in both are contemplated. Many of the difficulties encountered in taking test data arose from the extreme sensitivity of the evaporation process to slight changes in some of the variables associated with the ultrasonic system. The results appear to be especially sensitive to: (a) Location of the drop with respect to the sound node, (b) Variations of impressed frequency. The effect of slight variations around the critical value is quite evident in Figure 8. (c) Variations in ceramic tube temperature. No control was imposed during these tests.

CHAPTER VII CONCLUSIONS AND RECOMMENDATIONS A. Conclusions Experimental results for drops suspended on a fine glass filament in a moving air stream indicate that elapsed time of evaporation is a linear function of D2 -only when evaporation takes place into stagnant air. For evaporation into a moving air stream the experimental results are closely approximated by a linear function of Dn versus elapsed time. The value of n was found to decrease with an increase of relative air velocity and approached a limiting value between 1.45 and 1.5 for high velocities. The evaporation process is closely approximated by the equation Dn = Do - Xt (3.2) where n is a function of relative air velocity. The analysis of the heat transfer process during drop evaporation, modified by boundary-layer considerations, led to the following expression for Nusselt's number: Nu = a [2 + f (Pr)3(Re)1/2], (2.43) where a is a function of the temperature difference between the drop surface and the surroundings, latent heat of the liquid, and specific heat of the vapor; f is a semi-empirical factor to be determined experimentally. When expressed in terms of drop diameter, the evaporation equation obtained from the analysis of the heat transfer process is given by D [D2 - D] -2 fl2 = _8k in [1 + c (Tf- T)] t. (2.24) [D D(-2 - (_) d Do Df pc L 83

-84 -For the assumption (D/Df) = constant, Equation (2.24) becomes equal to the result obtained by Godsave,8 i.e., D2 D2= -t (2.27) where X 8k Df in +1 c (Tf -T) t (2.28) PC Df - D L When the expression for (D/Df) is obtained from boundary layer considerations for evaporation at constant relative air velocity, Equation (2.24) becomes (D3/2 - D3/2) C (D - D) + 3C2 (D1/2 - D1/2) - C3 in + C 0 - o \ D/2 + C (2.51) = 6k in [1 + c (Tf - T)] t Cpc L where C is given by Equation (6.2). The agreement between Equation (2.51) and the experimental results is good, as indicated in Figure 56. The factor a must be considered when evaluating Nusselt's number for drops evaporating in high temperature atmospheres. The use of equal drag coefficients for liquid and solid spheres in the calibration of relative air velocity apparently has resulted in low values for relative air velocity. Results obtained with drops evaporating in an ultrasonic field show that the evaporation rate is affected by the field, the effect being dependent on both field intensity and frequency. The combined action of the ultrasonic field and relative air velocity on the evaporation of freely suspended drops is such as to make drop diameter a linear function of elapsed time of evaporation.

A correlation between normal evaporation and evaporation within the ultrasonic field has not yet been established because of the complex nature by which the field effects are dependent upon such parameters as relative air velocity, field frequency and intensity, temperature of the barium titanate tube and location of the drop with respect to the sound node. The investigation of the effects of ultrasonic energy on evaporation cannot be considered more than exploratory in nature. Only a start has been made on a new technique for studying and possibly controlling evaporation and combustion of liquid fuel drops. Further developments are required to gather additional information on the exact mechanism by which the ultrasonic field affects the evaporation process. B. Recommendations i. The equipment described in this dissertation can be used to obtain accurate drag coefficient data for evaporating liquid drops or solid particles. An accurate measure of relative air velocity is required. 2. High intensity ultrasonic energy is capable of breaking up large drops. This phenomenon should be investigated as a possible aid to fuel atomization and evaporation. 3. It appears that high-frequency, high-intensity ultrasonic energy may provide a relatively simple means for obtaining greatly improved mixing in a fuel spray, thereby leading to higher combustion rates. This possibility should be investigated.

4. An investigation should be made concerning the possibility of building similar equipment for operation at high temperatures. Application to single drop combustion studies would, no doubt, lead to many interesting results. 5. A complete check of the evaporation Equation (2.51) is required for a wide range of conditions, either with original data, or with existing data obtained by other investigators and recorded in the literature. Its application to combustion should be checked. 6. The manner in which the evaporation rate is made to fall below the normal rate at certain frequencies was quite unexpected and should be investigated.

APPENDIXES

APPENDIX A DERIVATION OF THE EXPRESSION FOR DETERMINING EXPONENT n FROM THE EXPERIMENTAL RESULTS The equation (tt - t) = K1 + K2 Dn (A-i) in three unknowns K1, K2, and n is applied to the experimental curves of drop diameter versus elapsed time of evaporation. Three positions on the curves are required to solve for the three unknowns; these positions are designated by the drop diameters Dx, Dy, and Dz. With reference to Figure 3, the equations for the three positions are given by tt tx = x = K1 + K2 Dn (A-2) t,- ty = y = K1 + K2 Dy (A-3) t' t = z = K1 + K2 Dn (A-4) t Z Z From Equation (A-4) we obtain n K1 = z - K2 Dz. (A-5) This result is substituted in Equations (A-2) and (A-3) to give x = z - K2 (Dz - Dn) (A-6) and y = z - K2 (Dn - D). (A-7) Solving for K2 in both of these equations gives K = z -x z- y K2 = XDn (A-8) z Dn ny which reduces to (y x) D- (z x)y + (z -y) = 0. (A-9) Upon dividing by (y - x), 87

-88 -n z x n z - y n Dz - x Dy + Y Dx = o. (A.10) If we let Z -X -= 1 + K (A.11) y - x then z -x Y + Y - z z Y +x - Y + _- Y + 1, (A.12) y-x y- x y-x y- x y-x y-x so that z Y + 1= 1 + K, y x or K = Z- (A.14) y - x By substituting Equations (A.11) and (A.14) into Equation (A.10) and dividing through by Dhn, Equation (A.10) becomes n n (DZ) - (1 + K) () + K =. (A.l5) This expression is solved for K, giving K in terms of the drop diameters at the three positions and n, (Dz/Dx)n (D/Dx)n (A.16) (I~y)n _ 1 If the diameter ratios are selected so that D ()2 (A.17) Dx D then substitution gives K= (PDDx) - (D /D ) (A.18) (Dy/D)n - 1 so that upon factoring we obtain

-89 -K - (Dy/DX) [(DV/DX) - 1] (A.19) (Dy/Dx)n -1 or K = (Y). (A.20) This is solved for n by taking the log1o of both sides, giving the result n = Log K (A.21) Log (Dy/Dx) If we select Dx = 400 microns, Dz = 1000 microns, then Z = 2.5 (A.22) and E= (DZ)-/2 = 1.581. (A.23) The diameter at y is then computed to be, Dy = 1.581 Dx = 632.5 microns. (A.24) Substitution in Equation (A.21) finally leads to the result n = Log K = Log K (A.25) Log (1.581) 0.199 where K is given in terms of the measured quantities x, y, and z by Equation (A. 14). Tabulated results from the experimental part of the study are given in Table I.

APPENDIX B EXPERIMENTAL EVAPORATION CURVES ALND DATA On Figures 29 through 54, the following dimensions apply to the various quantities: velocity (v) f/sec, voltage (V) volts A.C. (rms), temperature (T) OF, x (measured at 400t) constant x seconds, y (measured at 700b1) constant x seconds, z (measured at 1000 ) constant x seconds, evaporation constant (X) (microns x 10-2)n/sec. 90

II -I - I - - - - RUN 1-3 1-12 4-2 4-14 5-2 VELOCITY 0 0 0 0 0 100 JO VOLTAGE 0 0 0 0 2.5 ' TEMPERATURE 83 83 83 83 86 ~..~ ~~~ ~~~~~~ ~ ~~~~~~~~~~~~~~~~ "-1x ---.6o0 - o 90 -~~.. y 7.30 Q9O oS l~- - z -1.601 -- =T ~ ~ ~ ~b~~~ ~Z -- 15.67- - ___,0. 0 x.221 0.20.22 O.23 ~, 80 8- -- o 0 2 " so 70: 0 ~ 0 60, i40 4 2W _ 4-14 4 I01,-t CI 1o I 1-3 1 I I 1s-2 4-z 0 40 80 120 160 200 240 260 320 ELAPSED TIME - SECONDS ' FIG.29 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v= 0 f.t/sec)

110 RUN 2 -9 5-14 3-3 5-15 VELOCITY 0 0 0 0 10oI0 VOLTAGE 2.5 2.5 5 5 TEMPERATURE 88 85- 86 86 X.... 90 -- -- - ca ~ ~ ~ ~ ~ __o __X 0.295 0.231 0.2400.237 -8 80 0 5 0' 460,I _o _ _ _~hti y~ I i 30 0 40 3-3,,5-14 5-15 i~~~~~~~~~~~~~~~~~ 0 0 40 80 120 160 200 240 280 320 ELAPSED TIME - SECONDS FIG.30 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v =0 ft/sec)

RUN 3-15 6-13 8-13 8-14 9-6 VELOCITY 0 0 0 0 0 100 VOLTAGE 10 10 20 25 25 TEMPERATURE 86 84 82 82 80 90 y - _ - - 0 (1.70.. 0 C, co _o 50 iO 3 0,. 20 z 10 9- Y 8-14 8-13 3 —15 0 40 so 1_ 160 200 240 280 _ ELAPSED TIME - SECONDS FIG. 31 EVAPORATION CURVES FOR FIXED DROPS —CUMENE (v =OOft/ sec ) I-l 0. o. 20_ _._ _ _ _ _ _ _ _ 10'' 0 4 0 80 120 160 200 ~~~~~~240 280 320 ELAPSED TIME - SECONDS FIG. 31 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v: 0 ft/sec)

RUN 1-13 2-3 4-3 2-10 5-3 VELOCITY 0.82 0.82 0.82 0.82 0.82 -5 Vo VOLTAGE 0 0 0 2.5 2.5 - TEMPERATURE 83 83 83 88 86 u)_ _ X -- 1.78 --- on o~ ~~ Y 8.-I —1839 '" — 117.371 f~i,,,l ~_ Xl 0-~ "c- r ~i~fi~~n I I I I Ixo290o.280.048229 0.29G0; 9_ 2, - 40) 0 t z 30 2 6,I f55 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*,. WS Q ~ 5-3 o r — ~ 44 0.1012 0 0~0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.32 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v=0.82ft/sec)

RUN 3-4 3-16 8-2 8-15 VELOCITY 0.82 0.820.82 0.82 501 I VOLTAGE 5 1 0O 20 25 -' T\~~~ 6 I I.TEMPERATURE 86 86 83 8!_____ _ _0.247 0.29 0..40 _I___I.. 0 20 ': 0 m~.r ~ z IL L L L IIIII 0 0 I-. 2~~~~~~~~~~~~~~~~~~~~o 8-2~~~~~~~~~~~~~~~~~~~~~~~0 0 20 40 60 80 100 120 140 160 ELAPSED TIME- SECONDS FIG.33 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v= 0.82 ft/sec)

RUN 4-4;3-5 3-17 8-16 VELOCITY 1.16 1.16 1.16 1.16 50...10_. __ _ VOLTAGE 0 5 1 0 25 WJ I G 9 t I I I TEMPERATURE 83 8 6 86 81 ____ ~L I I I I I I~ __ _ _ JX 1.05 - - - Y 7.24- - - Z 15.48 - - - 0. '0 " 40 oa X 0.241 0.251 0.245 0.336 o 0o.. - 0 40 E rz 2l 2 o "E ~20 54 W ~~~~~~~~~~~~~ 0 ~~~~4-4 a 0 0. 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.34 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v= 1.16 ft/sec)

RUN 2-4 2-Il 5-4 - VELOCITY 1.16 1. 16 1.1616 50 ___VOLTAGE 0 2.5 2.5 2 TEMPERATURE 84 87 86E 8 X 0-7 027 -. - 0 z 0 30 20 I- ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~IL 10 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 20 40 60 80 100 120 14016 ELAPSED TIME - SECONDS FIG.35 EVAPORATION CURVES FOR FIXED DROPS- CUMENE Cv =1.16 ft/sec)

RUN 4-5 2-12 5-5 6-4 VELODCITY 201 2.01 2.01 2.01 __0 10 _ _ _ VOLTAGE 0 2.5 2. 10 TEMPERATURE 83 87 86 84 x_ X 9.62 cn ~9 Y 7.09 T IZ 194.22 -CO _ 0.262 0.310 0280 0.258 40 8m m o 7 X z o 0 30 2 _ (L W _ 10 o ~ 4 0.10 2 0' 0 20 40 60 80 900 120 140 160 ELAPSED TIME - SECONDS FIG.36 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v:2.01 ft/sec)

RUN 3-7 3-18 8-4 8-17 VELOCITY 2.01 2.01 2.01 2.01 50 l l l l I. VOLTAGE 5 1 20 25 TEMPERATURE 86 86 83 81 En I I I I I Z...: 40 X - 0.268 0.274 0.298 0.343 0 0 CI) 30 0 20 w Io: L1 X=8-4 3-18 Q I I I I I I I I I I I 1 8-17 3-7 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.37 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v=2.01 ft/sec)

RUN 4-6 5-6 3-8 6-5 VELOCITY 248 2.48 2.48 2.48 50 10 VOLTAGE 0 2.5 5 10 TEMPERATURE 83 86 86 84 o _ _ _ _ _ _ _ _ _ _ _ _ X 1.07 co V 6.11 10 ( Z 12.80 - - 40? 8 ____ ____ ____ 0.280 0.293 0.292 0.275 E,40 8g o 0 O~~ 2 -) o c 30 S2 6 55 i _ _ _ _ _ 0. 0 1 -w 0 ir d~~ IL 10 O S3-8 6-5 4-6 5-6 0 0O 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.38 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (V;=2.48 ft/sec)

RUN 1-5 2-13 8-5 8-18 VELOCITY 2.48 2.48 2.48 2.48 501 _ _ VOLTAGE 0 2.5 20 25 TEMPERATURE 83 87 83 81 inj I Fs\ I I I I I - - -1= - 40 ____ _ _ \_X_ 0.292 0.320 0.317 0.329 4o l <e~oX h I N. i 0 z 0 o 0 220 W ~~~~I-~~~~~~~~~~~~ ~8-5 0 0 I I I 0 I00 1 20 1I0 11601 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.39 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (V = 2.48 ft/ sec)

RUN 4-7 -2-14 5-7 8-19 VELOCITY 3.51 3.51 3.51 3.51 50 10 VOLTAGE 0 2.5 2.5 25 O w TEMPERATURE 83 87 86 8 o C _ X.55 0U)~~~~~~,~ X 1.55~Y 6.13- - - 7N I Z, I ~ Z 12.15 - - - 40 eI _______,_ __, X __0.307 0.352 0.323 0.344 40 8 o o 2o - z o - _ 30 47 "' I 'o,. 5Ow o %%0 4 10~~~~~~~~~~~~~~~~~~~~~~~` 0. %,t;5-' 4-7 I030 4 P~~ C~ o (E o I I I I I I I I I I I `hbS~~~~~~~,~-?,,oc~4-? 8- 19 0 20 40 60 80 I00 120 140 160 ELAPSED TIME - SECONDS FIG.40 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v =:3.51 ft / sec)

RUN I-6 3-9 6-6 8-6 VELOCITY 3,51 3.51 3.51 3.51 5ol 0 VOLTAGE 0 5 10 20 TEMPERATURE 83 86 84 83 el4 1 F T I.... - z4O X ~_ _ _ _ 0.312 0.309 0.302 I0.336 U) z 0 3J I 20 a. 10.- 9%-s6 6s1-6 0 0 20 40 60 80 00 120 140 160 ELAPSED TIME - SECONDS FIG.41 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v=3.51ft/sec)

RUN 1-7 4-8 2-155-8 6-7 VELOCITY 4.2914.29 4.29 4.294.29 ~50 -'~- r I I I 1 I 1 I 1 VOLTAGE 0 0 2.5 2.5 10.. o. 0TEMPERATURE 83 83 87 86 84 W 0 X __ ___ x -1.13 --- Y -5.42 0 -- 11.15 -- -- I ____ ____ _ 0.316. 0.3065 0.3B27 0.02 0 o_ - X z z 0. 0 % = o s om W 30 2 6 20~~~~~~ 4 b'l' o N, 04 at 0. 10 2 21 6-7 0' O0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.42 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v= 4.29ft/sec)

RUN 3-10 8-7 8-20 8-21 VELOCITY 4.29 4.29 4.29 4.29 50 VOLTAGE 5 20 25 25 TEMPERATURE 86 84 81 81 ) ~~~Y -. -.. ~0__ ___>4 -0.311 0.338 0.3370.363 40 '0 2 z 0 0__30_ ol 20 w w hia. I0 0 0 0 20 40 60 80 100 120 140 160 ELAPSED TIME- SECONDS FIG.43 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v=4.29 ft/sec)

II --- RUN 4-9 2-16 3-Il 6-8 VELOCITY 4.96 4.96 4.96 4.96 50 O -0. VOLTAGE 0 2.5 5 10 0 U: TEMPERATURE 83 87 86 e 84 o _ _ X 220- - - I 1 ' I s% Y 6.32 - - 0 I z 11.62 - - - 40 __ ____ _ _ - 0.325 0.370 0.328 0.324 40 8 o0 0 X a) a7 ~. 0I z. ~ 0 30 2 r r~~~~~~~~~~~~~~~~~~~~~~ 01 _ _ _ _ _ _ _ _ _ _ _ _ o oON 2~~ ~~~~~~~~ _ _ 20 54 a.05~~~~ P, ~ ~ ~ ~ ~4-9 w I3 a0 0 2-16 w4-9 C 0 C 0 20 40 60 80 100 120 140 160 ELAPSED TIME- SECONDS FIG.44 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v=4.96ft/sec)

RUN 5-9 8-8 8-22 VELOCITY 4.96 4.96 4.96 50 VOLTAGE' 2.5 20 25 TEMPERATURE 86 84 81 X - -- 0~~~~~~~~~~~~ Z — - -- -- O z __ - - 4(0 ___ __ __ _ _ X 0.331 0.340 0.363 0 0 U) _o 1 z 0 8 228- ~-2 Ix 0 2 30_ _ _ 20 w~~~~~~~~~~~~~~~~~~~~~~ 0 ~20 ' QS W I-5-9 0. 10 0 0 20 40 60 80 100 120 140 160 ELAPSED TIME- SECONDS FIG.45 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v=4.96ft/sec)

RUN 1-9 4-10 3-12 6-9 9-2 VELOCITY 6.07 6.07 6.07 6.07 6.07 50_ 10 _ __ _ VOLTAGE 0 0 5 1025 TEMPERATURE 83 83 86 84 80 __ __ __ x -0.82 - Y -4.70- - - Z - 9.7 0 --- o-40 'rs ___ ___ 0.314 10.32910.3310.3260.374 40 2 - x z I co 0~~~~~~~~~~~~~~~~~~~~, 30 2 6 L i o~~~ ~IJ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Ik 24 o. 10 2 w a ~ ~ ~~~~~~~~~~~~- - 4-10 0 a a a I ~I ________________ 1 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.46 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v=6.07 ft/sec)

RUN 5-10 8-9 8-23 VELOCITY 6.07 6.07 6.07 50 VOLTAGE 2.5 20 25 TEMPERATURE 86 81 8 z -- ____ ____ __0~X_ 0.342 0.319 0.356 -.. 40 l 30 -o 30 __ bJO~~~~~~~~~~~~~~~~~~~~~-I 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.47 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v:6.07ft/sec)

RUN 4-11 2-18 5-11 3-13 N~aL.~~~~~~ ~VELOCITY 7.00 7.00 7.00 7.00 50 10. - VOLTAGE 0 2.5 2.5 5.~ w ' TEMPERATURE 83 87 86 86 o __I _X 0.83 '~, Y 4.50- - - Z 9.27 - - -.440 8f I ___ N ___ ___ ___ __ I0.339 0.398 0410.34 0 0 0 2~~ X__0 __ N _ _ c' 0 0O ' 6 a o o ~' I 0' Isa~~~~~~~~~~! I — 4-11 Q 0I0 2 at a 2-18 i'.______ __,S —II 4 —11 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.48 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v=7.oo00ft/sec)

RUN 1-10 6-10 8-10 9-3 VELOCITY 7.00 7.00 7 501 I VOLTAGE 0 10 20 25 TEMPERATURE 83 84 81 80 0 4c~90III X 0.341 0.331 0.342 0.374 z 0 ~_30 20 II 0 -0 610 8-10 O 20 40 60 80 100 120 140 0 ELAPSED TIME - SECONDS FIG.49 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (V=7.00ft/sec)

RUN 1-11- 4-12 3-14 6-11 9-4 VELOCITY 847.84 7.84 7.84 7.84 50 10 VOLTAGE 0 0 5 10 25 - N TEMPERATURE 83 83 86 83 80 IaJw o N ''X -2.46 - -- 9 cZ __ _ _Y - 5.97 -- I N mN -- - i 10.35 -- ___"I _ __x 10.321 (032510.3200.11 0.319 o - X N 3o 2 6 z o C 30 6 IL o.20 ~4 __ W 0 4-12 OE 4 a. 10 2 0 a, I- I I I I 111 e1 3-14 4-i2 0' O~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 0 C i- -- 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.50 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v 7.84 ft/sec)

RUN 3-2 5-12 6-2 8-11 VELOCITY 7.84 7.84 84 7. 84 50 VOLTAGE 2.5 2.5 5 20 TEMPERATURE 86 85 84 81 fl~ Z..-. -. m. __X 0.331 0.328 0.326 0.311 40 0 -0 co z 0 W. 0 20 W~~~~~~~~~~~~~~~~~~~~~~~ W~~~~~~~~~~~~~~~~~~~~~~~ I-' In) 0 bJ a 10 0 S ~~~~ ~ ~ ~ ~~~~~~~6-2 _ __ __ _ 8-11 0 20 40 60 80 100 120 140 160 ELAPSED TIME - SECONDS FIG.51 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v= 7.84ft/sec)

"~. I I I I I I I I I I~RUN 4-13 5-13 8-12 =,, I. I I I I I I Iv~cVELOCITY 8.59 8.59 8.59 50,II 1 '9~1 I I T I I I I"" IV IL~IL 50 10 VOLTAGE 0 2.5 20 C f~~~~~~~~~~~~~TEMPERATURE 83 85 81 O __ _ \ x 1.32 - - N~ _ _ _ _ __9 4.89. 7,. Iz 9.27 40'8 - - x 0.277 0.292 0.282 0 0 X Co 7 t Z~~~~~~~~~~~~~~~~% z = 2 30 26 _ _ _ __ ii~ ~ ~~~~~~~~, I H Q.~~~~~~~~~~~~~~~~~~~o 0 0, 0 0- - 0 2604 w ~ t O~~ a~~~~~~~~~. 1\ 2 o es~ 20' ~. o \ 4-13 5-d' 0 0 0 20 40 60 80 I00 1.20 140 160 ELAPSED TIME - SECONDS FIG.52 EVAPORATION CURVES FOR FIXED DROPS- CUMENE (v=8.59ft/sec)

RUN 6-12 9-5 VELOCITY 8.59 8.59 50 VOLTAGE 10 25 TEMPERATURE 83 80 0__ 20 40 60 80 10x 0.278 0.255 0 O_ __ 20ELAPSED TIME - SECONDS... IFIG53 EVAPORATION CURVES FOR FIXED DROPS 0 O 20 40 60 80 O00 120 140 160 ELAPSED TIME - SECONDS FIG.53 EVAPORATtON CURVES FOR FIXED DROPS- CUMENE (v =8.59 ft/sec)

RUN 6-13 VELODCITY 8.59 100 _ _ VOLTAGE b TEMPERATURE 84 x 90 0~~~~~~~~~~~~~~~~~~~ z~~~~~~~~~~~~~~~~~~~ 80~~~~ 0.230 0 70 8 C, _ _ _ 60 50 40 Iw x 30 4 IL 20 0 0~~~~~~~~~~~~~~~~~~~~~~~ 6- 13 10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I0 0 40 80 120 160 200 240 280 320 ELAPSED TIME - SECONDS FIG.54 EVAPORATION CURVES FOR FIXED DROPS-CUMENE (v=8.59ft/seC)

-117 -TABLE IX EVAPORATION DATA - FIXED CUMENE DROPS Field voltage = 0 volts D = Drop diameter (microns) t - Elapsed time (seconds) Run 1-3 Run 1-12 Run 4-2 Run 4-14 v 0.00 fps v - 0.00 fps v _ 0.00 fps v = 0.00 fps T 830F30 T = 83 F. T - 830 F. t D D 100 D D t D (1T0) t D (iOO) t D (10U D (iU) 0.0 836 54.0 0.0 978 72.*5 0.0 1008 77.2 0.0 1117 93.2 15.3 805 50.5 15.3 953 69 1 3 981 73.3 20.4 1079 87.2 30.6 767 46.o 30.6 928 65.9 36.6 950 68.8 40.8 1051 83.3 45.9 729 41.9 45.9 904 62.8 54.9 924 65.5 61.3 1022 79.4 61.2 695 38.3 61.2 877 59.0 73.2 887 60.3 81.7 993 74.7 76.5 658 34.4 76.5 846 55.3 9i.5 852 56.1 102.1 960 70.0 91.8 616 30.7 91.8 821 52.4 109.7 824 52.7 122.5 926 65.5 107.1 575 26.9 107.1 790 48.7 128.0 794 49.1 142.9 890 60o.8 122.4 531 23.1 122.4 760 45.4 146.3 757 44.9 163.4 852 56.i 137.7 479 19.0 137.7 733 42.4 164.6 722 41.1 183.8 820 52.2 153.0 425 15.1 153.0 704 39.2 182.9 681 36.9 204.2 776 47.0 168.3 356 10.9 168.3 665 35.2 201.2 638 32.6 224.6 739 42.9 183.6 288 7.3 183.6 628 31.5 219.5 598 28.8 245.0 696 38 3 198.9 596 28.7 237.8 549 24.5 265.5 6)52 34.0 214.2 562 25.7 256.1 508 21.2 229.5 522 22.4 274.4 445 16.5 244.8 479 19.0 292.7 371 11.8 260.1 432 15.6 310.9 311 8.4 275.4 384 12.5 290.7 330 9.4 Run 1-13Run Run Run 4-3 Run 2-4 v _ 0.82 fps v: 0.82 fps v _ 0.82 fps v- 1.16 fps T = 83~ F. T = 840 F. T 83 F. T 840 F. t) D (D1t )l t D ( ) t D (1U0)' 0.0 871 38.8 0.0 872 38.9 0.0 982 47.6 0.0 916 38.7 15.3 819 35.0 12.3 823 35.2 14.2 946 44.5 12.3 868 35.2 30.6 769 31.2 24.5 782 32.4 28.5 897 40.8 24.5 814 31.8 45.9 714 27.7 36.8 730 28.7 42.7 851 37.3 36.8 765 28.7 61.2 659 24.2 49.o 674 25.2 57.0 804 34.0 49.0 710 25.4 76.5 600 20.7 61.3 626 22.1 71.2 756 30.5 61.3 650 22.0 91.8 536 17.1 73.5 563 18.5 85.4 703 27.0 73.5 583 18.4 1073.2 858 499.1 132 858 49 51 99.7 -350 23.6 85.8 20 15.1 98.0 428 11.7 113.9 59' 20.3 98.0 446 1.1. t8 128.2 525 16.5 142.4 455 12.9 156.6 371 9.2..........__!_170.9 280 5.7 _... _... _-_

TABLE X EVAPORATION DATA - FIXED CUMENE DROPS Field Voltage = 0 volts D = Drop diameter (mitcrons) t = Elapsed time (seconds) Run 4-4 Run 4-4 Run 1-5 Run 4-6 v = 1.16 fps v - 2.01 fps v 2.48 fps v: 2.48 fps T = 830F. T = 83 F. T: 830 F. T 83 F. t D (l~)1:6 t D (1-.63 t D ( D 825 t D ( D 1.625 0.0 945 40.7 0.0 1066 47.4 0.0 837 31.5 0.0 1123 51.1 11.2 909 38.0o 10.2 1031 4.8 10.2 08785 28.5 1 0.2 O85 48,2 22.5 871 35.7 20.4 988 41.8 20.4 731 25.4 20.5 1047 45.6 33.7 826 32.6 30.7 953 39.4 30.6 681 22.6 30.7 1007 42.8 44.9 787 30.0 40.9 910 36.5 40.8 623 19.5 40.9 964 39.8 56.2 746 27.5 51.1 866 33.8 51.0 565 16.6 51.2 922 37.0 67.4 704 25.1 61.3 827 31.2 61.2 504 13.8 61.4 876 34.0 78.6 653 22.1 71.5 782 28.6 71.4 435 10.9 71.6 830 31.1 89.8 603 19.4 81.8 731 25.6 81.6 351 7.7 81.8 785 28.5 101.1 554 16.8 92.0 689 23.2 91.8 280 5.3 92.1 735 25.6 112.3 497 14.1 102.2 635 20.4 102.3 683 22.8.123.5 432 11.2 112.4 589 18.0 112.5 626 19.7 134.8 369 8.6 122.6 531 15.2 122.8 571 317.0 132.9 476 12.7 133.0 515 14.3 143.1 401 9.6 143.2 443 11 2 153.3 323 6.8 153.5 369 8,3 Run 1-6 Run 4-7 Run 1-7 Run 4 -v 3.51 fps v 3.51 fps v = 4.29 fps v 4 29 fps T = 830 F. T 830 F. T83 F T - 8'3 F. D 1.6 D 1.62 D i eDo t D (T0D) ' t D () D ). t D (:)6 0.0 919 36.3 0.0 1084 47.4 0.0 968 37.8 0.0 1130 48.3 10.2 871 33.3 10.2 1039 44.3 9.2 925 35. 1 9.2 1091 4.8 20.4 817 30.0 20.5 994 41.3 18.4 871 32.0 18.5 1051 43.0 30.6 763 26.9 30.7 946 38.1 27.6 819 28.9 27.7 1004 40.1 40.8 712 24.0 41.0 901 35.2 36.8 768 26.0 36.9 961 37.2 51.0 639 20.1 51.2 848 32.0 46.0 714 23.2 46.2 922 35.0 61.2 584 17.5 61.4 790 28.5 55.2 656 20.2 55.4 868 31.8 71.4 518 14.4 71.7 735 25.3 64.4 598 17.5 64.6 817 28.8 81.6 441 11.0 81.9 682 22.5 73.6 532 14.5 73.8 767 26.0 91.8 356 7.8 92.2 620 19.2 82.8 464 11.7 83.1 710 23.0 102.0 276 5.2 102.4 559 16.2 92.0 386 8.7 92.3 658 20.4 112.6 491 13.2 101.2 301 5.8 101.5 601 17.6 122.9 412 9.9 110.8 542 14.9 133.1 329 6.9 120.0 467 11.8 129.2 393 8.9 ________ ___ __ __ __ 1 138.5 311 6.1

-119 -TABLE XI EVAPORATION DATA - FIXED CUMENE DROPS Field Voltage 0 O volts D - Drop diameter (microns) t = Elapsed time (seconds) Run 4-9 Run 1-9 Run 4-10 Run l-10 v _ 4.26 fps v - 6.O7 fps v = _6.O7 fps v _ 7.00 fps T 83 F. T 830 F T - 83 F, T. 83~ F. (DD )1. 57 t D (TD ) t D ( t D (D )15 t D (l1OO 0.0 1015 40.8 0.0 925 33.6 0o.o0 1121 45.6 0.0 956 34.6 9.2 971 38.0 8.2 874 30.7 8.2 1081 43.0 8.2 906 31.9 18.4 922 35.0 16.4 825 28.0 16.4 1037 40.0 16.4 855 29.1 27.7 873 32.1 24.6 791 26.2 24.7 993 37.6 24.6 798 26.1 36.9 818 28.8 32.8 737 23.5 32.9 950 35.0 32.8 726 22.5 46.1 767 26.0 41.0 685 20.9 41.1 897 32.0 41.0 686 20.5 55.3 710 23.0 49.2 622 18.0 49.3 852 29.6 49.2 626 17.8 64.5 651 20.0 57.4 569 15.6 157.5 800 26.7 57.4 560 15.0 73.8 593 17.2 65.6 499 12.7 65.8 748 24.0 65.6 490 12.1 83.0 522 14.1 73.8 441 10.4 74.0 697 21.5 73.8 423 9.6 92.2 452 11.2 82.0 379 8.2 82.2 635 18.6 82.0 345 7.0 101.4 369 8.1 90.2 341 6.9 90.4 584 16.2 90.2 280 5.0 98.6 511 13.2 106.9 445 10.3 115, 369.7. Run 4-11 Run 1-11 Run 4-12 un 4-1 v = 7.00 fps v 7.84 fps v: 7.84 fps v 8.59 fps T - 830 F. T 830 F. T -8= 830 F t. ' t P ()5ilj. t PD (D)1.5 t D )1. 47 0.0 1102 43.3 0.0 843 26.1 0.0 1042 36.1 0,0 1108 34.2 8.2 1052 40.1 8.2 788 23.5 7.2 994 33.6 6.2 1067 32.6 16.4 1008 37.6 16.4 728 20.8 1 14.4 951 31.3 12.4 1033 31.0 24.6 958 34.7 24.6 673 18 5 21.6 905 29.1 18.6 994 29.3 32.8 910 32.1 32.8 603 15.6 28.8 853 26.6 24.8 954 27.5 41.0 859 29.2 41.0 538 13.1 36.0 804 24.3 31.0 910 25.7 49.2 808 26.5 49.2 465 10.5 43.1 754 22.0 37.1 869 24.0 57.4 751 23.7 57.4 380 7.7 50 3 702 19.7 43.3 831 22. 6 65.6 697 21.1 57.5 643 17.2 49.5 787 20.7 73.8 636 18.2 64.7 589 15.1 555 7 742 19.0 82.0 568 15.2 71.9 527 12.7 61.9 699 17.4 90.2 509 12.9 79.1 466 10.5 68.1 650 15.6 98.4 428 9.8 86.3 389 8.0 74.3 596 13.8 106.6 350 7.1 93.5 312 5.7 80.5 549i 12.2 86.7 496 10,5 92.9 432 8.6 99.0 369 6.8 105.2 312 5,3

-120 -TABLE XII EVAPORATION DATA - FIXED CTJMENE DROPS Field voltage - 2.5 volts D Drop diameter (microns) t - Elapsed time (seconds) Run 2-9 Run 5-2 Run 5-14 v = 0.00 fps v = 0.00 fps v= 0.00 fps?T= 870 F T,- 860~ F. T 85~0 F. D1.88 D 1.8s t D ( D )1.8 | t 5) | t D (iD65).tD 0. 0 1200 106.5 0.0 979 72.8 0.0 968 71.3 15.3 -- - 18.4 9L7 68.1 20.4 942' 68.o0 30.7 1155 99-2 36.8 916 6 41 40.9 904 62.8 46.0 1124 95.0 55.1 877 59,2 61.3 868 58.0 61.3 1094 89.8 73.5 844t 55.2 1.7 828 53.1 76.7 1060 84,6 1 91.9 805 50.4 1 102.2 788 48.4 92.0 1021 79.0 110.3 769 L6, 2 122.6 748 43.9 107.3 993 74.8 128.7 725 41.4 143.0 704 39.2 122.7 965 70.8 147.0 689 37.4 163.4 655 34.2 138.0 924 65.14 165.4 645 33.2 183.9 605 29.5 153.3 898 62. 0 183.8 602 29.2 204.3 555 25.1 168.7 861 57.2 202 2 547 24.5 224.7 492 20.0 184.0 827 52.9 220.6 493 20.1 245.2 430 15.5 199.3 787 48.2 238.9 434 15.8 265,.6 357 10.9 214.7 745 43. 7 257.3 370 11.7 286.0 272 6.6 230.0 708 39.5 275.7 288 7.3 245.3 662 35 0 260.7 618 30.7 276.0 566 26.0 291.3 507 21.1 306.7 449 16.8 322.0 387 12.8

-121 -TABLE XIII EVAPORATION DATA - FIXED CUMENE DROPS Field Voltage -2.5 volts D = Drop diameter (microns) t - Elapsed time (seconds) Run 5-3 Run 2-10 Run 2-11 Run 5-4 v = 0.82 fps v = 0.82 fps v = 1.16 fps v- 1.16 fps T - 860~ F. T = 880~ F. T = 87~ F. T = 860~ F. O.9 D.O t D (-1o t O| (i-6) t D (i-)) t D ( )10 0.0 1055 53.6 0.0 932 43.6 0.0 1015 45.8 0.0 1112 53.0 14.3 1010 49.9 15.3 875 39.1 15.3 954 41.3 13.3 1075 50.1 28.5 967 46.2 30.7 814 34.7 30.7 894 37.1 26.5 1028 46.9 42.8 919 42.4 46.0 751 30.2 46.o 834 33.1 39.8 982 43.4 57.1 874 39.0 61.3 687 25.9 61.3 767 28.8 53.1 934 40.o 71.4 828 35.5 76.7 613 21.4 76.7 697 24.6 66.4 886 36.7 85.6 775 31.9 92.0 536 17.1 92.0 615 20.0 79.6 833 33.0 99.9 721 28.2 107.3 447 12.6 107.3 536 16.0 92.9 785 30.0 114.2 665 24.5 122.7 341 7.9 122.7 447 11.8 106.2 728 26.5 128.4 603 20.9 138.0 346 7.8 119.4 671 23.1 142.7 542 17.4 132.7 606 19.5 156.9 471 13.8 146.0 544 16.4 171.2 395 10.2 159.2 473 13.0 185.5 312 6.9 172.5 388 9.3 185.8 303 6.2 Run 2-12 Run 5-5 Run 2-13 Run 5-6 v = 2.01 fps v= 2.01 fps v = 2.48 fps v - 2.48 fps T = 870 F. T 860 F. T = 870 F. T 86~0 F. (i60 t 1'63 D. t 0D ( D )*63 t ( t D - ( D.625 ~10-0 100 l 10 0.0 820 30.8 0.0 989 41.9 0.0 924 37.1 0.0 987 41.2 13.3 750 26.6 12.3 942 38.8 12.3 872 33.9 11.2 942 38.3 26.5 680 22.8 24.5 889 35.2 24.5 808 29.8 22.5 883 34.14 39.8 600 18.5 36.8 834 31.8 36.8 741 25.9 33.7 838 31.6 53.0 513 14A4 49.1 777 28.3 49.0 667 21.8 45.0 780 28.2 66.3 417 10.2 61.4 717 24.7 61.3 591 18.0 56.2 721 24.8 79.5 311 6.3 73.6 659 21.5 73-5 510 14.1 67.4 661 21.6 85.9 590 18.1 85.8 417 10.2 78.7 601 18.5 98.2 520 14.7 89.9 534 15.2 110.4 439 11.1 101.2 458 11.8 122.7 350 7.7 112.4 373 8.5 123.6 277 5.2

-122 -TABLE XIV EVAPORATION DATA - FIXED CUMENE DROPS -Field Voltage - 2.5 volts D - Drop diameter (microns) t = Elapsed time (seconds) Run 2-14 Run 5-7 Run 2- Run 5-8 v = 3.51 fps v: 3.51 fps v 4.29 fps v 4.29 fps T 87 F. T - 860 F. T 870~ F. T - 860 F. D 2 D L D )1.60 D 1.60 D(t D t D t D (D-) 100 100. 1.... 0.0 972 39.9 0.0 1023 43.3 0.0 1062 44.0 0.0 966 37.7 10.2 922 36.7 10.2 974 40.0 10.2 1013 40o.6 10.2 909 34.1 20.4 868 33.0 20.4 921 36.5 20.4 954 36.9 20.4 858 31.0 30.6 808 29.5 30.7 866 33.0 30.6 891 33.1 30.7 799 27.7 40.9 810 29.6 40.8 829 29.5 40.9 732 24.1 51.1 759 26.6 51.0 764 25.9 51.1 673 21.1 61.3 701 23.5 61.2 690 22.0 61.3 602 17.7 71.5 633 19.9 71.4 617 18.4 71.5 532 14.5 81.8 572 16.9 81.6 536 14.7 81.8 453 11.2 92.0 500 13.6 91.8 )-447 11.0 92.0 360 7.7 102.2 418 10.2 102. 0 350 7.4 112.4 331 6.9 _ Run 2-16 Run 5-9 Run 5-10 Run 2-18 v: 4.96 fP; v = 4.96 fps v = 6.07 fps v = 7.00 fps T = 87~ F. T = 860~ F. T: 86 F. T = 870 F. 10)t10 D ( t D ( ) 1t -100 100 100 100 0.0 1006 40.2 0.0 964 37.5 0.0 1075 42.5 0.0 1021 38.3 8.2 957 37.0 9.2 920 34.8 9.2 1023 39.5 7.2 979 35.9 16.4 910 34.2 18.4 863 31.4 18.4 974 36.5 14.3 924 32.9 24.6 861 31.3 27.6 812 28.5 27.6 916 33.0 215 87f 330.1 32.8 803 28.1 36.8 758 25.5 36.8 858 29.8 28 6 823 27.4 41.0 747 24.9 46.1 700 22.5 46.1 803 26.8 35.8 770 24.6 49.2 691 22.1 55.3 635 19.3 55.3 743 23.8 42.9 710 21.6 57.4 631 19.1 64.5 573 16.3 64.5 674 20.4 50.1 649 18.8 65.6 565 15.9 73.7 504 13.3 73.7 605 17.2 57.2 584 16.0 73.8 498 13.0 82.9 422 10.0 82.9 535 14.1 64.4 519 13.2 82.0 419 9.9 92.1 338 7.0 92.1 455 11.0 71.5 443 10.3 101.3 373 8.0 78.7 359 7.4

-123 -TABLE XV EVAPORATION DATA - FIXED CUIMENE DROPS Field voltage - 2.5 volts D = Drop diameter (microns) t = Elapsed time (seconds) Run 5-11 Run 3-2 Run 5-12 Run 5-13 v = 7.00 fps v - 7.84 fps v 7.84fps = 8.59 ps T = 860~ F. T - 860 F. T - 85~ F. T 850 F. D 1.53 1. 47 t D (1-) t D (t D (s3 t D (lOO.100 100 100 100 0.0 941 33.8 0.0 877 27.6 0.0 1070 37.6 0.0 1076 32.8 9.2 885 30.7 7.1 835 25.7 8.2 1032 35.4 8.2 1030 30.9 18.4 828 27.6 14.2 787 23.5 16.4 982 33.0 16.4 977 28.5 27.7 762 24.3 21.4 735 21.1 24.6 926 30.1 24.6 922 26.1 36.9 694 21.0 28.5 680 18.8 32.8 871 27.5 32.8 861 23.7 46.1 621 17.6 35.6 625 16.5 41.1 813 24.7 41.0 803 21.4 55.3 552 14.6 42.7 564 14.1 49.3 748 21.7 49.2 745 19.1 64.5 472 11.4 49.8 501 11.8 57.5 689 19.1 57.4 676 16.6 73.8 381 8.2 57.0 433 9.4 65.7 628 16.6 65.6 610 14.2 83.0 288 5.3 64.1 354 6.9 73.9 560 13.9 73.8 537 11.8 82.1 487 11.2 82. 0 459 9.4 90.3 401 8.4 90.2 373 6.9 98.5 315 5.8 98.4 290 4.8

-124 -TABLE XVI EVAPORATION DATA - FIXED C4ENE:: DROPS Field voltage = 5 volts D Drop diameter (microns) t = Elapsed time (seconds) Run 3-3 Run 5-15 Run 3-4 Run 3-5 vy 000 fps v 000 fps v = 0,82 fps v l 116 fps 86_ F. T -.86. T 86~ F, T- 86~0 F... ):l. L2 t D (1- t D (6t D0) (l )5 0o0 933 66~,4 oo 1048 82,8 0o 0 951 44,9 o, 0 890 36.9 18.3 903 62.6 18.4 1017 78.0 15.3 901 41*1 15.3 833 33.0 36.6 867 58&1 36.8 989 74,0 30.5 851 37.2 30.5 774 29,3 54.9 833 53*9 55*3 954 69.5 45.8 798 33.4 450.8 715 25,6 73.2 794 49.1 73*7 921 65.0 61.0 740 29.5 61,0 645 21,6 91*5 752 44.4 92.1 889 6o.7 76.3 681 25,6 76,3 578 181. o109.8 716 40o5 110*5 855 56o4 91.5 619 21,7 91.5 498 14.2 128.1 673 36.1 128.9 818 52.0 106, 8 552 17*9 106,8 407 10. 2 146.4 625 31.3 147.4 - -- 122*0 476 14.0 122,0 304 6,2 164.7 578 27o0 165.8 744 43*7 137.3 392 10.1 183.0 529 22,9 184.2 702 391 152*5 304 6.5 201,3 473 18.6 202*6 659 3407 219.6 415 14.5 221*0 615 30.4 237.9 341 10.0 239*5 563 25.7 257*9 511 21.5 276.3 456 17.4 294.7 392 13.0 313*1 329 9.4 331.6 269 -604 Run 3-7 Run 3-8 Run 3-9 Run 3-10 v.. 2.01 fps v 2.48 fps v = 3.51 fps v = 4.29 fps T 860 F T 86~0 F T - 86 F T - 860 F, t.D.(... D D- D (~2D)1 D D(10-0 t D (l -- t D..60 0o lo84 40 o0 1014 43.0 00.0 962 39 1 0o.0 o52 36'.9 153 1 15.3 0952 39*0 153 891 3.7 15.3 4 32.1 30.5 970 40.7 30o5 882 34.3 30.5 810 29.6 30.5 790 27.3 458 908 36,3 45*8 813 30o1 45.8 731 250o 45.8 699 22.5 61.0 844 32*3 61.0 736 25o6 61. o 632 19.9 61. 0 609 18.0 76.3 775 28*1 76.3 653 21.1 76.3 548 15.8 76.3 503 13.2 91. 5 704 24.1 91.5 566 16.7 91.5 443 llo2 91.5 386 8.7 lo6.8 627 19.9 o106.8 473 12.4 106.8 333 700 122.0 551 16.1 122. 0 367 8.3 137.3 462 12.-1 152.5 373 8,6 167.8 323 6.7

-125 -TABLE XVII EVAPORATION DATA - FIXED CUMENE DROPS Field voltage _ 5 volts D = Drop diameter (microns) t = Elapsed time (seconds) Run 3-11 Run 3-12 Run 3-13 Run 3-14 v = 4,96 fps v 6.o7fps v7.00 fps v7.84ps T = 860 F. T T 860 F. T = 860 F. T 860 F, Dt t D (D15D3a5 D 5 ).s D ( t D ( ( 5 O t D (yD f.57 100 100 100 10 0.0 906 34.0 0.0 975 36.6 0.0 872 30.0 0.0 1081 38.2 15.3 823 29,2 13.3 901 32.2 12.3 805 26.5 10.2 1023 35.1 30.5 731 24,2 26,5 816 27.5 24.5 717 22.0 20.4 958 31.8 45.8 632 19.1 39.8 733 23,3 36,8 623 17.7 30.6 899 28.8 61.0 525 14.1 53.1 639 18.7 49.0 527 13.6 40,8 830 25.5 76.3 408 9.5 66.4 543 14,5 61.3 416 9,4 51.1 755 22.0 79.6 434 10i2 73.5 291 5.4 61.3 683 18.9 92.9 332 6.6 71.5 601 15.6 81.7 519 12.4 91.9 423 9.1 102.1 332 6.3 Run 6-2 Run 6-3 v 7.84 fps v = 8.59 fps T 840 F, T - 840 F, t D ('D t D L)47 o.o 1041 36.0 0.0 1051 31.8 9.2 984 33.1 8.2 1003 29.6 18.3 926 30,1 16.3 946 27.2 27.5 863 27..0 24.5 895 25.1 36.6 800 24.1 32.6 836 22.6 45.8 734 21.1 40.8 778 20.4 55.0 666 18.1 48.9 715 18.0 64,1 592 15'2 57.1 650 15.6 73.3 513 12.2 65,2 584 13*4 82.4 428 9.2 73,4 514 11.1 91.6 339 6*5 81.5 435 8,7 89.7 351 6.3

-126 -TABLE XVIII EVAPORATION DATA - FIXED CUMENE DROPS Field voltage 10 volts D = Drop diameter (microns) t = Elapsed time (seconds) Run 3-15 Run 3 Run 3-16 Run 3-17 v -.- 0.00 fps v 0.00 fps v 082 fps v - 1.16 fps T - 860~ F. T - 84~ F. T 860 F, T: 860 F tD -.8 D DB0 D.$- D 1. 5 t D ( 1-0_ t O (0)S t D ( ) t D (I) '5 0.0 987 73.9 0.0 1027 80.0 0,0 1049 53.1 0. 0 970 42,3 20,4 956 69.7 20.5 998 75.11 15.3 loll 49~9 17.4 913 38.4 40.8 916 64.1 4o0.9 962 70.7 30,6 959 45.5 34.7 849 34.o 61.3 869 58,1 61.4 926 65,7 45,9 912 41 9 52.1 781 29.7 81.7 830 53*3 81.8 891 61.2 61.2 857 37.7 69.4 716 25.6 102.1 783 48.0 102.3 855 56.5 76.6 809 341o 86.8 635 21.1 122.5 739 43.0 122.7 816 51,9 91.9 752 30.2 104ol1 556 17.0 142.9 693 38,2 143.2 779 47.2 107.2 696 26.5 12105 469 12.8 163.4 642 33*1 163.6 734 142,5 122.5 639 22,9 138.8 366 8.5 183 8 587 27.9 184.1 691 37 9 137.8 573 19.1 204.2 530 23,0 204.5 647 33.4 153,1 505 15.5 224.6 467 18.1 225.0 598 28.8 168.4 429 1107 245.0 389 12.8 245,4 547 24.5 183.7 350 8.3 265.5 307 8,2 265.9 495 20.2 286.3 443 16.4 306.8 386 12,.7 327.2 352 10.7 Run 6.4 Run 3-18 Run 6-5 Run 6.6 v - 2.01 fps v 2.01 fps v 2.48 fps v = 3.51 fps T - 840 F. 860 F, T 86~i F. T - 840 F. o0.0o 1041 457 o.0 1067 47.4 0,0 1036 44,6 0o0 1027 143.5 12.2 1005 43.0 17.4 1002 42.9 11.2 995 41.9 10.2 989 l4,8 24.24 9g 39.8 34.7 ^?9 37.8 22,4 950 38.8 204 938 375 36.6 9 36,3 52,1 851 32.9 33.7 901 35.7 30.6 9 34-3 48.8 863 33.7 69,4 776 28.2 44.9 855 32.8 4o.8 842 3107 61.1 811 30.3 86*8 696 23.6 56,1 801 29.5 51.1 786 28.2 73.3 755 27.0 104.1 609 19.0 67.3 748 26~3 61.3 733 25,2 85.5 696 23.6 121.5 512 14,3 78.5 690 23.0 71,5 677 22.1 97.7 639 20,5 138.8 402 9.7 89.8 633 20.1 81.7 618 19.1 109.o9 579 17.5 101.0 571 17.0 91.9 551 16,0 122.1 513 14,4 112,2 5C06 14.0 102.1 488 13.0 134113 443 11.3 123.4 437 11, 0 112.3 412 9,9 146.5 367 8. 3 134.6 361 8.0 122.5 3210 7.3 158.7 303 6.1 145.9 298 5,9 132.7 282 5.4

-127 -TABLE XIX EVAPORATION DATA - FIXED CUMENE DROPS Field voltage - 10 volts D - Drop diameter (microns) t - Elapsed time (seconds) Run 6-7 Run 6-8 Run 6-9 Run 6-10 v 4.29 fps v 4.96 ps v - 6.7 fps v 7.00 fps T 840 F. T - 840 F. T 840 F. T 840 F. D I 6 c D 1.so D )D.ss D )1.57 (100' t 1D 00) t D 00 t D 57 0.0 1023 414 1 0 1040 42.3 0.0 986 37.1 0.0 1057 40,4 10.2 977 38.2 9.2 994 39.4 9.2 946 34.8 9.2 993 36.8 20.4 924 351 18,4 944 36.2 18o4 886 31.3 18,4 938 33.5 30.6 874 32.1 27.6 894 33*2 27.6 832 28.5 27.6 883 30.6 40,8 820 29,1 36.8 843 30,3 36.8 775 25.5 36,8 823 27.4 51*0 762 25,8 46,o 791 27.4 46.0 712 22*3 46.,1 -763 24.4 61.2 707 22,9 55,1 735 24*3 55,2 655 19.5 55o3 700 21.1 71.4 645 19.7 164.3 683 21,6 64.4 592 16,.6 64.5 635 18o2 81,6 579 16*6 73.5 621 18.6 73o6 519 13.5 73,7 567 15.2 91.8 506 13.4 82.7 559 15*7 82.8 443 lO5 82.9 495 12,4 102.0 436 10, 5 91,9 495 12,9 92,0 361 7.6 92.1 417 9,4 112.2 356 7.6 101.1 424 10,1 1012 292 5.5 101.3 343 6;.9 122.4 298 5.7 110.3 353 7.5 * 110,5 305 5 8 _________:119.5:9 5.7 Run 6-11 Run 6-12 v/= 7.84 fps v - 8.59 fps T = 83 F. T - 830 F. t D (D ) t D (D 4 100 10) 0.0 1021 35,0 0*0 1037 31.0 8.2 973 32.6 8*2 989 29,0 16,4 919 29*7 16.4 938 26.8 24.6 867 27.2 24*6 883 24.6 32.8 812 24.7 32*8 828 22.4 41.0 758 22.1 41.0 767 19.9 49.1 698 19.6 49.2 707 17.7 57.3 639 17.0 57.4 645 15.5 65.5 578 14.6 65.6 577 13a2 73.7 511 12.1 73.8 506 10.8 81.9 439 9.6 82.0 431 8,6 90.1 369 7,4 90.2 355 6,4 98.3 323 6.o 98.4 305 5.1

-128 -TABLE XX EVAPORATION DATA - FIXED CUtENE DROPS Field voltage - 20 volts D = Drop diameter (microns) t = Elapsed time (seconds) Run 8-13 Run 8-2 Run 8-3 Run 8-4 v = 0.00 fps v = 0.82 fps v = 1.16 fps v = 2.01 fps T _ 82~ F. T - 830 F. T = 830 F. T 830 F. t D ( D (169 t D ()1.6 t D (D16) 100,1... 10, 100 0.0 1075 87.0 0.0 956 45.3 0.0 978 43.0 0,0 1040 45,3 25.5 1022 79.1 20,3 878 39.2 18.3 909 38,1 15o3 971 40,8 51.0 966 70.8 40.6 795 33.2 3607 831 33.0 30.6 902 36.0 76,4 906 62.7 60.9 709 27.4 55.0 750 27.7 45.9 831 31.7 101.9 848 55.6 81.2 613 21,4 73.4 663 22,6. 61.2 753 26,9 127.4 781 47.8 101.5 508 15.6 91.7 568 17.5 76,5 674 22,5 152,9 709 39.7 121*8 394 101 110.0 459 12.4 91,7 588 17.9 178.4 630 31.7 142,1 323 7.3 128,4 356 8.1 10700 493 13 5 203*8 548 24,4 146.7 319 6.8 122.3 395 9.4 229.3 455 17.2 13706 338 7.3 254,8 348 10.4 Run 8-5 Run 8-6 Run 8-7 Run 8-8 v = 2.48 fps v 3.51 fps v = 4.29 fps v 4,96 ips T = 830 F T = 830 F. T = 840 F, T = 830 F. t D 1.62 ( 6D D (60O 0t D ( t | t 100) t D 100 0.0 1006 42.8 0.0 1028 43.7 0.0oo 1043 42.7 0O0 1034 42.0 14.3 941 38*3 14.3 959 38.9 13.3 969 3708 13,3 967 37.7 28,5 870 33.5 28.6 879 33.8 26.5 898 33e4 26.5 894 33,2 42,8 799 29.3 42.9 806 29.4 39.8 819 2809 39.8 809 28.3 57.1 718 24,5 57*2 717 24.3 53*1 739 24.5 53.1 725 23.8 71.4 633 20,1 71.5 628 19.5 66*4 649 19.9 66.4 638 19.4 8506 543 15.6 85,7 534 15.1 79,6 556 15,5 79.6 540 14.8 99.9 445 113 100,0 428 10.5 92.9 456 11.4 92.9 438 10o,6 114.2 348 7.6 114.3 327 6.8 106.2 343 7.2 128.4 308 6.2 119.4 315 6.3

-129 -TABLE XXI EVAPORATION DATA - FIXED CMENE DROPS Field voltage = 20 volts D = Drop diameter (microns) t. Elapsed time (seconds) Run 8-9 Run 8-10 Run 8-11 Run 8-12 v 6. c7 fps v - 7.00 fps v 7.84 tps v 8.59 fps T = 810 F. T - 81~ F. T = 810 F. T = 81~ F. t D ( t D (i 1D 5 t D (Y 15 t D (D 3100 7 oo0 988 37.1 0.0 1013 37.8 0.0 980 32.9 0.0 o1044 31.6 12.2 926 33.7 12.2 938 33.6 11,2 915 29.6 9, 2 988 29.1 24.4 853 29.5 24.4 862 29.5 22.5 846 26.2 18.4 931 26.6 36.5 781 25.8 36.6 783 25.3 33.7 767 22.5 27.6 869 23.9 48,7 704 21.9 48.8 701 21.4 45.0 688 19.1 36.8 803 21.4 60.9 619 17.8 61.1 619 1795 56.2 602 15.6 46.o 738 18 9 73.1 532 14.0 73.3 513 13.0 67.4 513 12.2 55.1 669 16.3 85.3 422 9.7 85.5 - 78*7 394 8.1 64.3 598 13.9 97.4 314 6.1 97.7 283 5.1 89.9 286 5.0 73.5 524 11.4 82.7 433 8.6 91.9 342 6.1

-130 -TABLE XXII EVAPORATION DATA - FIXED CUMENE DROPS Field Voltage 25 volts D s Drop diameter (microns) t = Elapsed time (seconds) Run 8-14 Run 9-6 Run 8-15 Run 8-16 v 0.0 fps v 0,00 fps v 0.82 ps vr 116 fps T = 82 F, T 800 F. T 820~ F. T 810 F. t D (t D ( D '- t D -)t D OO) 0.0 1009 77.2 0.0 983 42,9 0.0 988 47.9 0.0 1059 49,0 25.5 956 69.7 30.5 921 65.0 20.4 882 39.7 16.3 985 43.6 51.1 909 63.4 61.1 826 52,8 40.9 774 31.8 32.6 909 38.1 76*6 821 52.5 91.6 716 40.3 48,9 828 32.7 102.2 730 41,9 122.2 612 30.3 65.2 738 27,0 127*7 639 32.5 152.7 475 18.8 81.6 644 21.6 153.2 538 23.6 183.2 316 8.7 97,9 543 15.3 178.8 406 14.0 213.8 261 6. 1 1142 431 11 2 204.3 278 6*8 i 130.5 303 6.2 Run 8-17 Run 8-18 Run 8-19 Run 8-20 v 2.01 fps v 2.48 fps v = 3.51 fps v = 4.29 fps T - 810 F. T = 810 F. T = 810 F. T-:810 F. i L o u r —, _. 0 t D ( ' ' t D D ) L6 5 t D (D —.6 t D (L-)0.0 1063 47.1 0, o 1071.47.o 0.0 993 41.2 0.0 1025 41.3 14.3 991 42.o 14.3 997 41.9 13.3 955 38,7 11. 2 966 37.7 28.5 915 36s9 28*5 915 36.4 26.6 874 33o5 22.4 899 33 6 42.8 838 32.0 42.8 838 31.6 39.9 796 28.8 33e7 831 29.6 57l1 754 27o0 57.1 756 26.8 53.2 713 24,1 44.9 763 25.9 71.4 669 22.1 71.4 671 22.1 66.5 631 1908 56,1 688 21.9 85,6 581 17.6 85.6 584 17,6 79-8 534 1501 6703 616 18 4 99.9 481 12.9 99.9 483 12.9 93o1 423 10.3 78,5 535 14.6 114.2 374 8.6 114*2 374 8.5 106.4 313 6,3 89.8 449 11 101.0 356 7.6

-131 -TABLE XXIII EVAPORATION DATA - FIXED CUMENE DROPS Field voltage -25 volts D = Drop diameter (microns) t = Elapsed time (seconds) Run 8-21 Run 8-22 Run 8-23 Run 9-2 v = 4.29fps v = 4.96 fps v -= 6.~ fps v = 6.07' fps T = 81~ F, T = 810 F. T - 810 F. T = 80~ F, D Lec D i1D-60l.sE D 'i. s t D ( D(D-6O t D t D (D)1.5 _ __ k100 100 l00 0.0 1072 44,4 0.0 1066 44.1 0.0 991 37.6 0..0 992 37.6 11.2 1006 40.1 10.2 1008 40,4 10,2 928 33.8 10,2 929 33.8 22~5 936 35.8 20,4 943 36.2 204 860 29,9 20.3 856 29.7 33.7 866 31.6 30.6 882 32.7 30.6 794 26.5 30,5 783 25.8 45.0 797 27.6 40o8 816 28.7 40o8 724 22.9 40,7 705 21.9 56.2 722 23.6 51.0 753 25,3 51.0 653 19.4 50.9 625 18,1 67.4 644 19.7 61.2 684 21.7 61.2 576 15.9 61.0 548 14.7 78.7 566 16.0 71-4 613 18.2 71,4 490 12.3 71-2 439 10o3 89.9 476 12.1 81.6 538 14.8 81.4 368 7o8 101.2 383 8 6 91.8 450 11.1 91,-5 274 4 9 112 4 272 5.0 102,0 369 80 1 112.2 275 5.0 Run 9-3 Run 9-4 Run 9-5 v 700 fps v 7848,59 fps T - 800 F, T 800 F. T - 800 F 1.5 1.53 1.4 t D (10D. t D (1-0) t D ( D-) 0o0 996 37.0 030 987 33.1 0o0 995 29.3 10,2 929 33.0 9,2 926 30,1 9.2 947 27.2 20.4 856 29.1 18.4 864 27,1 18.4 894 25*0 30.6 779 25.0 27.5 798 24.0 27.6 831 22.5 40.8 705 21.5 36,7 736 21.2 36.8 772 20,2 51,1 625 17.8 45.9 667 18.1 46.1 710 1709 61.3 535 13.9 55.1 594 15.3 55.3 650 15.7 71.5 434 10.0 64.3 519 12.4 64,5 577 13.2 81.7 341 6.9 73.4 433 9,4 73.7 502 10.7 82.6 347 6.7 82.9 415 8,1 91 8 269 4.5 92.1 344 6.1 101o3 293 4,9

-132 -TABLE XXIV EVAPORATION DATA FOR SOME PURE LIQUIDS —FREE DROPS 2,4-Dimethylpentane Ethyl n-Valerate Ethyl Alcohol Time Diameter Time Diameter Time Diameter Sec. p Sec. | Sec. O 704 0 1280 0 988 4.25 431 28.5 985 9 851 4.69 410 57.5 740 23 588 7.31 231 87.5 426 32 431 n-Octane Pyridine -Cumene Time Diameter Time Diameter Time Diameter Sec. Sec.. Sec. 0 1050 0 1050 0 1220 9 862 7.5 945 13 1080 19 630 17.0 798 28 977 29 410 27.2 640 42 840 37 210 37.5 493 57 725 47.0 315 72 588 47.5 294 89 461 102 325 118 168 Tert-Amyl Alcohol n-Butyl Alcohol Time Diameter Time Diameter Time Diameter Sec. Sec. p Sec 0 1000 0 1178 61.3 654 3.18 986 3.4 1167 64.4 622 6.43 938 6,8 1145 67.6 589 11.80 861 9.1 1135 71.7 567 15.43 787 12.2 1080 73.6 534 19.06 722 15.8 1058 87.2 425 22.68 659 22.2 980 90.1o 392 26.30 606 24.9 948 93.4 371 29.95 529 27.8 926 104.6 283 33.74 468 37.8 840 106.1 261 37.49 417 40.9 818 107.3 240 41.24 356 44.0 774 45.18 270 47.2 764 47.37 240 48.3 752

-133 -TABLE XXV EVAPORATION DATA FOR SOME PURE LIQUIDS —FREE DROPS Methyl n-Decane Tert-Butylbenzene Time Diameter Time Diameter Time Diameter Sec Sec Sec 0 1143 0 1010 0 1196 57.7 970 67 910 35.4 1040 146.5 637 245 495 65.4 882 207.5 445 306 344 95.4 745 266.5 253 366 239 125.4 640 155.4 462 185.4 304 n-Butylbenzene 2- Heptanone Time Diameter Time Diameter Sec Sec 0 1174 0 1210 45.3 1052 12 1120 10503 942 28 1010 165.9 800 42 936 226.3 648 58 820 287.3 517 73 693 346.0 365 88 609 406.3 223 103 514 408.5 202 118 410 133 273

-134 -TABLE XXVI EVAPORATION DATA FOR FREE DROPS OF ACETOPHENONE AND KEROSENE Acetophenone Time Diameter Time | Diameter Min-Sec.. |. Min-Sec | B 0-0 987 14-44.3 317 0-45.0 932 15-45.2 264 1-46.5 901 16-45.2 214 4-46.4 794 17-45.0 155 6-45.6 708 18-15.1 138 8-46.2 611 19-47.5 103 10-53.2 517 20-16.1 94 12-46.1 409 20-46.0 91 Kerosene Time Diameter Time Diameter Min-Sec p Min-Sec p 0-0 862 43-20 490 2-20 795 46-20 480 4-20 745 49-20 480 6-20 730 52-20 480 8-20 700 55-20 485 10-20 675 58-20 468 13-20 633 63-20 446 16-20 630 68-20 440 19-20 610 73-20 425 22-20 590 78-20 414 25-20 560 85-20 403 28-20 545 93-20 382 31-20 540 98-20 370 34-20 530 103-20 360 37-20 512 108-20 360 40-20 495 113-20 327

APPENDIX C PHYSICAL PROPERTIES AND CONSTANTS TABLE XXVII PROPERTIES OF AIR (83~F) Property Symbol Value Units Thermal Conductivity ka 4.28 x 10-6 B/sec ft F Specific Heat Ca 0.24 B/lb F Specific Density Pa 0.073 lb/ft Absolute Viscosity I[la 125 x 10-7 lb/ft sec Kinematic Viscosity v a 17.1 x 10-5 ft2/sec TABLE XXVIII PROPERTIES OF CUMENE Property State Symbol Value Units ~F Thermal Conductivity Vapor kv 2.22 x 10-6 B/sec ft F 81 Specific Heat Vapor c 0.30 B/lb F 81 Specific Density Liquid P 55.2 lb/ft3 60 Absolute Viscosity Vapor ~v 40.3 x 10-7 lb/ft sec 80 Latent Heat --- L 160 B/lb 78.5....~~15

-136 -TABLE XXIX AVERAGE PROPERTIES OF AIR-VAPOR MIXTURE (Cumene) Property Symbol Value Unit s Thermal Conductivity k 3.25 x 10-6 B/sec ft F Specific Heat Cm 0.27 B/lb F Absolute Viscosity m 82.6 x 10-7 lb/ft sec Prandtl Number Pr 0. 69 -- EVAPORATION EQUATION CONSTANTS 1. = L ln [1+ cv (Tf - T)] cV (Tf- T) L 160 ln [1 + 0.3 (83 - 78.5) 1 0.3 (83 - 78.5) 160 cx = 0.9956 (dimensionless) 2.: lkk ln [1 c (Tf - T)] c. L (3.25 x 106) [1 0.3 (8 78.5) 0.3 160 = 2.86 x 10-7 (lb/ft sec) 2 2 3. C = 2 f (Pr)'/3 (V)l// f (o.69)/3 ( v ) v 17.1 x 10-5 2.958 fvl/2

APPENDIX D CORRELATED RESULTS AND CHECK OF EVAPORATION EQUATION 2.51 FOR FIXED DROPS OF CUMENE, NO ULTRASONIC FIELD TABLE XXX DATA FOR EXPERIMENTAL CHECK OF EVAPORATION EQUATION 2.51 Diaam. Run V (fps) l Do 1000 800 600 400 4-3 0.82 (ec) (sc 0 -- 58.6 111.5 154.4 (sec) tm (sec) 0 17.8 67.0 109,8 143.9 (sec) 4-5 2.01 |tc 0 18.2 67.3 109.5 144.1 (sec) tm 0 28.5 67.8 101.8 128.7 (sec) 4-8 4.29 || c 0 28.5 67.8 101.8 129.7 (sec) t (sm 0 17.3 50.1 78.4 101.7 (sec) 4-11 7.00 tc) 0 17.7 50.2 78.4 101.7 (sec) tm 0 17.3 47.2 74.2 96.8 (sec) 4-13 8.59 tc 0 17.9 48.o 74.2 95.9 (sec) tm = measured elapsed time of evaporation, experimental results. tc = computed elapsed time of evaporation Equation 3.12. 137

30mm-m- - -im — m —m 20 101 1 I I I I I I I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I I~ ~ ~~1 r I I. I I I I I I I \- F = 1.69~~~f 1.6 61 1 I I_ I I I ~~~~~~-ff 1. 96 - 2.31 4 0 CO) co Cs, 3 - - - _ _ Nu O(2 f (Pr'3 (Re) - OC = 0.996 Pr = 0.69 I 2 3 4 6 8 10 20 30 40 60 80 100 200 REYNOLDS NUMBER, (Dv/V) FIG.55 HEAT TRANSFER DATA FOR EVAPORATING FIXED-DROPS OF CUMENE - NO ULTRASONIC FIELD

I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l RUN 4-3 4-5 4-8 4-1, 4-13 VELOCITY 0.82 2.01 4.29700 8.59 O____10 __ __ VOLTAGE 0 0 0 0 0 TEMPERATURE 83 83 83 83 83 x~ - - - - ~ Z -----— Y' --- — - -- X 0 IL 91~~~ 1? II a.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 0 cr - CURVES PLOTTED FROM EXPERIMENTAL RESULTS 0 POINTS COMPUTED FROM EQUATION 2.51 0 0 20 40 60 80 00 120 140 160 ELAPSED TIME - SECONDS FIG. 56 EXPERIMENTAL CHECK OF EVAPORATION EQUATION 2.51

BIBLIOGRAPHY 1. Bolt, J. A., and Mirsky, W., Some Aspects of the Evaporation Rates of Liquid-Fuel Drops in a Standing Wave Ultrasonic Field, Univ. of Miah. Eng. Res. Inst., Project 2253-3, July, 1955. 2. Brown, G. G., et al. Unit Operations., New York: John Wiley and Sons, Inc., 1950. 3. Eckert, E. R. G., Introduction to the Transfer of Heat and Mass., New York: McGraw-Hill, 1950., 4. Fledderman, R. G., and Hanson, A. R., The Effects of Turbulence and Wind Speed on the Rate of Evaporation of a Fuel Spray, U.S. Navy, Bureau of Ordnance, Report CM667, 1951. 5. Fro'ssling, N., "Uber die Verdunstung fallender Tropfen." Gerlands Beitrage d. Geophysik, 52, 170 (1938). 6. Fuchs, N., Concerning the Velocity of Evaporation of Small Droplets in a Gas Atmosphere, NACA TM-1160 (1947). 7. Godsave, G. A. E., The Combustion of Drops in a Fuel Spray, NGTE (England), Memorandum M95, 1950. 8. Godsave, G. A. E., The Burning of Single Drops of Fuel, NGTE (England): Part I, "The Temperature Distribution and Heat Transfer in the Pre-Flame Region," Report R66 (1950); Part II, "Experimental Results," Report R87 (1951); Part III, "Comparison of Experimental and Theoretical Burning Rates and Discussion of the Mechanism of the Combustion Process," Report R88 (1952); Part IV, "The Flow of Heat and Carbon Residue Formation in Drops of Fuel," Report R125 (1952). 9. Godsave, G. A. E., "Studies of the Combustion of Drops in a Fuel Spray —the Burning of Single Drops of Fuel." Fourth International Symposium on Combustion, Baltimore: Williams and Wilkins, 1953. 10. Gohrbandt, W., The Evaporation of Spheres in a Hot Air Stream, NGTE (England), Memorandum M110 (1951). 11. Goldstein, S., Modern Developments in Fluid Dynamics, 2 vols., England: Oxford University Press, 193-. 12. Graves, C. C., Burning Rates of Single Fuel Drqps and their Application to Turbojet Combustion Processes, NACA RM-E53E22, 1953. 140

-141 -13. Hall, A. R., and Diedericksen, J., "An Experimental Study of the Burning of Single Drops of Fuel in Air at Pressures up to Twenty Atmospheres." Fourth International Symposium on Combustion, Baltimore: Williams and Wilkins, 1953. 14. Ingebo, R. D., Vaporization Rates and Heat-Transfer Coefficients for Pure Liquid Drops. NACA TN-2-368 (1951). 15. Ingebo, R. D., Study of Pressure Effects on Vaporization Rate of Drops in Gas Streams. NACA TN-2850 (1953). 16. King, L. V., "On the Convection of Heat from Small Cylinders in a Stream of Fluid: Determination of the Convection Constants of Small Platinum Wires with Applications to Hot-Wire Anemometry." Phil. Trans. Roy. Soc. A, 214, 373 (1914). 17. Kinzer, G. D., and Gunn, R., "The Evaporation, Temperature and Thermal Relaxation-Time of Freely-Falling Waterdrops." Journal of Meteorology, 8, 71 (1951). 18. Kobayasi, K., "The Evaporation Velocity of Single Droplets of Liquids." The Engineer's Digest, 15, 463 (1954). 19. Kobayasi, K., "The Combustion of Single Droplets of Fuel." The Engineer's Digest, 16, 17 (1955). 20. Langmuir, I., "The Evaporation of Small Spheres." Phys. Rev. 2, 12, 368 (1918). 21. Langstroth, G. 0., et al., "The Evaporation of Droplets in Still Air." Canadian Journal of Research, A 28, 580 (1950). 22. Maisel, D. S., and Sherwood, T. K., "Evaporation of Liquids into Turbulent Gas Streams." Chem. Eng. Prog., 46, 131 (1950). 23. Maxwell, J. B., Data Book on Hydrocarbons, New York: D. Van Nostrand Co., Inc., 1950. 24. Maxwell, J. C., "Diffusion," Scientific Papers, Vol. II, Cambridge University Press, 1890. 25. McAdams, W. H., Heat Transmission. 2nd Edition, New York: McGraw-Hill Book Company., Inc., 1942. 26. Ranz, W. E., and Marshall, W. R., "Evaporation from Drops, Part I," Chem. Eng. Prog., 48, 141 (1952); Part II, ibid., p. 173. 27. Rossini, F. D., Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds. Pittsburgh: Carnegie Press, 1953.

-142 -28. Saad, M. A., "Evaporation and Combustion of Single Fuel Droplets in a Hot Atmosphere," Ph.D. Dissertation, Mech. and Ind. Eng. Dept., Univ. of Mich., 1956. 29. Simpson, H. C., "Combustion of Droplets of Heavy Liquid Fuels," Sc.D. Dissertation, Chem. Eng. Dept., M.I.T., 1954. 30. Spalding, D. B., "Combustion of Liquid Fuel in a Gas Stream, Part I" Fuel, 29, 2 (1950); Part II, ibid., p. 25. 31. Spalding, D. B., "The Combustion of Liquid Fuels" Fourth International Symposium on Combustion, Baltimore: Williams and Wilkins, 1953. 32. Topps, J.E.C., An Experimental Study of the Evaporation and Combustion of Falling Droplets. NGTE (England), Memorandum M105 (1951).