Drop Formation in Two-Liquid-Phase Systems C U R T I S B. H A Y W O R T H '
AND
R O B E R T E. T R E Y B A L
NEW YORK UNIVERSITY, NEW YORK 53. N. Y.
MANY
wet, the outer surface. of the problems of D r o p formation in t h e dispersion from simple nozzles of Consequently, all nozzles design of liquid-liquid one liquid into another immiscible liquid was studied used were constructed of extraction equipment reas a function of the physical properties and flow conditions brass tubes, with the deof the system. For a stationary continuous phase, the volve about the phenomena livery end carefully chamof drop formation. In convariables studied were: nozzle diameter (0.155 t o 0.786 fered or beveled a t 45' to a cm.), velocity through the nozzle (0.01 t o 169 cm. per sectinuous contacting apparasharp edge. The sizes used tus such as spray towers, ond), interfacial tension (3.3 t o 32.1 dynes per cm.), visare listed in Table I. Fluid cosity of the dispersed and continuous phases (0.65 t o 21.6 bubbles of one liquid are properties were varied by dispersed into a continuum centipoises), density of both phases (0.879 t o 1.588 grams use of differentliquid pairs, per cc.), and dispersion of both light and heavy phases. of another immiscible liquid, with additions of very small Drop size and formation phenomena were studied with and either rise or fall, deamounts of Alkaterge C , the help of more than 1000 photographs of the systems in pending upon the relative an oil-soluble synthetic web operation. Drop size is uniform and increases with specific gravities. The size ting agent, to the nonvelocity through the nozzle up t o 10 cm. per second, deand uniformity of size of the aqueous phase to cause large creases and becomes less uniform from 10 t o 30 cm. per drops, among other things, variations in interfacial tensecond, and is erratic and nonreproducible a t higher exert a significant influence sion without influencing velocities. Drop size is increased by increased interfacial upon the late of rise or fall other physical properties. tension, decreased difference in density between the and consequently upon the In every case the two phases phases, increased viscosity of the continuous phase, and capacity of the equipment. were mutually saturated increased nozzle diameter. It i s independent of whether The interfacial area between with each other prior to use. light or heavy phase is dispersed, and practically unthe phase6, is dependent Table I1 lists the systems affected by viscosity of the dispersed phase. A semitheoupon the bubble size. A studied, the corresponding retical equation, derived from a consideration of the forces knowledge of the factors inphysical properties, and the acting upon t h e drop during formation, was developed, fluencing bubble size will test conditions. The physiwhich permits prediction of the drop size from system have an important bearing cal properties were in every characteristics within 7.5% in the range 0 t o 30 cm. per upon ability to design and case measured experimensecond velocity through the nozzle. to evaluate the performance tally for the mutually satuof such eauipment. rated ohases at 20" C.. Many &estigations into the nature of drop formation are density by pycnometer, viscosity by Fenske-Cannon-Ostwald described in the literature, most of them concerned with gasviscometer, and interfacial tension hy the Harkins drop-volume liquid systems and consequently not directly applicable to the method (6, 7). The temperature of all runs was within the problem at hand. Rayleigh's early work ( 17) on the instability range 19 ' to 22' C. of liquid jets issuing from nozzles was applied by Smith and Moss (20) to the liquid-liquid system mercury-salt solutions, but drop size was not considered. HaenIein ( 4 ) , in studying the formaTable I . Size of Nozzles tion of drops of liquid issuing from a nozzle into a gas, observed Inside phenomena which closely parallel those observed in the experiOutside Diameter, B.and S. Noazle Diameter, ments described in this report, although a t much greater liquid No. Inch Gage No. Cm. velocities. The time elapsed for a liquid particle to travel from the nozzle to the breakup point of the jet in Haenlein's experiments was studied by Weber (21). Holroyd (9) derived an equation for the size of drops from a liquid jet entering a gas, to which reference is made below. The importance of velocity of dispersed phase, viscosity, and surface tension as determining factors in drop size has been well established by many authors The use of a surface-active agent for bringing about variation (9, 6, 12, 13, 16, I&?), but under conditions pertaining to liquidin interfacial tension without appreciable change in other fluid liquid extraction, little has been done. properties may require justification, for a t least in gas-liquid systems adsorption of the agent a t the interface may result in SCOPE OF THE STUDY AND METHOD variation of tension with time. Recent investigations ( I , 10, The variables governing drop formation were assumed to be: 14, 18) into the problem as it affects liquid-liquid interfacial density of both dispersed and continuous phases; viscosity of tension substantiate early observations (11, 16)that, with a single both phases; interfacial tension; nozzle design, including shape oil-soluble surface-active agent, no interfering adsorption phenomand siae; velocity of the dispersed phase through the nozzle; ena and no appreciable aging of the surface will be encounnature of the motion of the continuous phase; and whether light tered. Any changes in tension are small, within the h i t s of or heavy phase is dispersed. In the present investigation, the precision of the present measurements. They are furthermore continuous phase was kept stationary exceph for eddies induced sufficiently slow that the time required for interfacial tension by the injection of dispersed liquid. Furthermore , experience measurements and the tinlo for drop formation in the experiwith various shapes of nozzles had indicated that reproducible ments reported here can be considered as of the same order of phenomena were most readily obtained with sharp-edged nozzles magnitude, small with respect, to any aging effect. The device so designed that the dispersed phase could not spread over, or used here to control interfacial tension should therefore be satis1 Prasent address, General Chemical Company, 40 Rector St., New York, factory. N. Y. 1174
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
June 1950
The bubbles were formed by introducing them through the nozzles into a tower filled with t8hecontinuous phase. The tower wm square in crow section, so that photograph$ ima es of the bubbles would not be distorted, 9.25 inches on a side a d 4 7 inches high. The sides were of plate glass, cemented with Permanite cement into extruded brass tubin , of the t y e used for shower doors, which formed the corners. %he top anfbottom were brass lates, fitted with 0.25-inch cork gaskets to prevent leakage. %e nozzles were each 6 inches long, soldered into a brass plug which in turn could be screwed into either the bottom or top plate, de ending upon whether the light or heavy phase waa to be dipersel
D LX?.TOWLR L:CO(IIT r( FLOW YLAIURCYKWT
OPOINT
M
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satisfactorily illumiriating the nozzles and dro s. A transparent scale, also illuminated was arranged so tiat its image appeared in the photographs, thus permittin measurement of the drop size. a serial number similarly arrangecffor each run ensured correct identification of the photo raphs. All photogrqphs were taken through a No.plus 3 Proxar fens to make close-ups possible, at a lens opening o f 22 for maximum depth of focus, and at 0.01-second exposure time. The negatives of the photo raphs were studied with the help of a microfilm reader which enfarged the images between two and three times actual size. Dividers were used to compare the dimensions of the drops as they appeared on the screen with the image of the scale. Volumes of the drops were then calculated by assuming them to be spheres if their photographic images were circular, s heroids if the images were elliptical. In the latter caae, the aiameters of spheres of equivalent volumes were calculated and used in subsequent correlations. At low rates of flow, the frequency of bubble formation could be measured by direct observation, and these checked the same fi ures calculated from drop diameter and flow rates excellently. i l t o ether, over 1000 observations and photographs were made, t8e detailed data from which are availahle elsewhere (8). DROP FORMATION CHARACTERISTICS
DROP
A representative series of the photographs taken, shown in
Figure 1.
Arrangement of Apparatus
The general arrangement of the ap aratus is shown in Figure 1 . The liquid to be dispersed flowed gravity from tank AI, a 60-gallon stoneware jar, through orifice and manometer B and needle valve C1,into the bottom of tower D at G. Alternatively it could be led by piping not shown to the top of the tower at C. The orifice was used only to indicate constancy of flow, and the available head changed so little during the course of a run that no difficulty was encountered in maintaining constant velocity. The continuous phase was storvd in stoneware jar Az, and umped into the tower rior to operation. Drops of dispersed {ght liquid formed at g r o s e through the tower, collected in a layor a t the top, and overflowed into tank F. Measurement of the rate of flow was made by collectin a meaaured volume at E for B measured period of time. If t%e heavy hase was dispersed, it left the bottom of the tower throu h a g g (not shown) which made sure the tower was filled witt continuous phase, and entered the same piping (I-#) HS before. Every precaution was taken to maintain cleanlii~essof the internal parts of the apparatus, because interfacial tomion particularly is so sensitive to the presence of small amounts of impurities. A 35-mm., f 2.8 camera, H,wltcs uwd to photograph the drops as they formed at the nozzlo. For tohispurpose, the plate lass walls of the tower were covered with black cardboard except for a %inch wide slit down the center of each of two of the walls. Light from flood lamps entered the tower through the dits,
&
Figure 2, exhibits the essentials of the observed phenomena. Although the majority of these are taken from the experiments with carbon tetrachloride and water, they are typical for all the systems, except that the velocity of flow at which the occurrences appear varied slight,ly with the physical properties of the fluids and the nozzle size. At low linear velocities of the dispersed phase through the nozzle, a bubble is formed immediately at the top of the nozzle, where it grows and eventually breaks away as a single distinct drop (Figure 2, a through d). During this stage, bubbles are of uniform and reproducible size a t any velocity. As the velocity is increased, a short jet or stem of dispersed phase extends from the nozzle, the bubbles forming by a “necking-in” at the top of the stem. At certain velocities a very tiny bubble forms below each large bubble, a phenomenon which was also reproducible. The jet length increases with increased velocity to a maximum length, and then decreases (Figure 2, e through j). For the smaller nozzles, the ultimate length may be considerable, aa in Figure 2, k and 1. During this period, drop size increases to a maximum and then decreases; uniformity of bubble size decreases, until ultimately large bubbles of very irregular shape and very small, spherical bubbles are produced simultaneously. Continued increase in dispersed phase velocity does not change the situation greatly until such a high velocity is reached that the stream is “atomized,” producing a cloud of very fine droplets as in Figure 2, m. The effects of the various quantities studied on bubble diameter are shown for typical cases in Figures 3 through 6, where the curves were calculated from an empirical equation described below. In every case, bubble diameter increases with increase in velocity of the dispersed phase through the nozzle, reaching a
Table II. Systems Studied and Operating Conditions Bystem
No. 1
2 3 4
6
0 7 8 9
10 11
12 13 14
Continuous Phase Density, Substance g./co. Water 0 * 9982 Water o.essa Water 0.9982 Water 0 * 9932 Water 0.8982 Water 0.9982 1.1366 Water sucrose 1.1971 Water sucrose 1.2443 Water sucrose 0.9982 Water 0.9982 Water Carbon tetrachloride 1.6831 Benzene 0.8788 0.9982 Water
++ +
Viscosity, CP. 1.01 1.01 1.01 1.01 1.01 1.01 3.31 8.36 19.31 1.01 1.01 0.96 0.66 1.01
Dispersed Phase Density, Substance g./oc. Benzene 0.8788 0.8788 Benaene Alkaterge 0.8788 Benzene Alkaterge Kerosene 0.3002 0,8002 Kerosene Alkaterge 0.8564 Motor oil kerosene 0.8788 Benzene 0.8788 Benzene Benaene 0.8m Benzene 0.8788 Bensene Alkaterge 0 * 8788 0,9982 water 0,9982 Water Carbon tetraohloride 1.5881
++ ++ +
Viscosity, op. 0.65 0.65 0.65 2.40 2.40 21.55 0.65 0.65
0.65 0.66 0.65 1.01 1.01 0.96
Interfacial Tension Dynes/Cii. 25.7 18.2 10.9 32.1 10.3 24.7 22.8 23.3 22.6 24.8 3.3 30.2 26.7 31.0
Nozzle No. Used
Velocity of Dispersed P b e through NOaPle, Cm./Seo. 0.91-26.4 0.14-98.1 0.30-68.2 0.09-63.1 0.01-109 0.01-69.7 0.01-148 0.02-108 0.01-51.2 0.01-146 0.04-61.2 0.01-136 0.02-74.1 0.01-103
INDUSTRIAL AND E N G I N E E R l N G CHEMISTRY
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d
b
i
h
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Vol. 42, No. 6
I
Figure 2.
Bubble Formation
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Le., light phase bubbled upward or heavy phase bubbled down ward-had no influence on drop formation other than through the effects described above. 1.0
INTERPRETATION OF EXPERIMENTAL DATA
i 0 a
Dimensional analysis is frequently used to assist in the interpretation of complex phenomena involving many variables. In the present instance, such an analysis led to the following dimensionless groupings of the variakles:
W
0.0
g 0
0.1
Figure 3.
Effect of Nozzle Diameter on Drop Size, System 3
T
e
1.0
Figure
VELOCITY,
cwacc.
10
Effect of Interfacial Tension on Drop Size Systems I,2, 3, 11; nozzle 3
maximum a t a velocity of about 10 cm. per second, usually before maximum length of the liquid jet from the nozzle is reached. Drop size and uniformity then fall rapidly with increased velocity up to approximately 30 cm. per second. At higher velocities, drop size is very nonuniform, and measurements are made with difficulty. Above velocities of about 10 cm. per second, where nonuniformity begins, the plotted data are for the largest bubbles only in a given run. Below velocities of 30 cm. per second, drop size increases with increased nozzle diameter (Figure 3) and increased interfacial tension (Figure 4). Viscosity and density could not be varied independently, but the range of viscosities studied was the greater. Figures 5 and 6 indicate the relatively small effect on drop size caused by relatively large changes in viscosity of the continuous and dispersed phases, respectively. Figure 6 shows some effect of interfacial tension 88 well as density difference. Choice of dispersed phase-
f
=
f
[(F),
The symbols are defined below. Many attempts to determine the nature of the undefined function were made, largely by graphical treatment of the data, but none was successful. The “static’J drop diameter, Ds, produced with essentially zero velocity of flow of dispersed phase, such as that which is observed during the measurement of interfacial tension and which may be calculated from the system constants by the method of IIarkins (6, 7), was also introduced into these attempts as the ratio Dp/Ds without useful result. Attempts were made to determine the functions in the Holroyd equation (9),
without success. When none of these attacks proved fruitful, it was thought that a clue to the relationship among the variables could be found by a study of the mechanics of drop formation in an attempt to relate the forces acting on the bubble, or the energy required to form a bubble, to the time of drop formation and drop size. Of several approaches tried, the greatly simplified treatment described below led to the most useful result.
Figure 7 shows a dro being formed at a nozzle and the several forces actin6 upon it. ft is assumed that the drop will be stablethat is, it m11not separate from the nozzle or the jet from which it is formed as long as: 1. The rising velocity, V R , of the drop is smaller or e ual to the velocity, v, of the dispersed hase through the nozzle. %he risin velocity is the velocity which the drop would rise (or fall7 freely through the continuous phase due to the buoyant force acting u on it. 2. T i e buoyant force, FB, acting on the drop is smaller or equal to the force of interfacial tension, Fo. The drop will break away when both VR>V and FB>Fu. All forces acting on the drop can be expressed in t e r m of equivalent drop volumesl inasmuch as the volume of the drop submerged in another liquid represents a buoyant force. A balance of the various forces can then be made in terms of their equivalent drop volumes.
wd
I n this simplified approach, the forces acting on the drop are congidered to be Fv due to interfacial tension, FB, the buoyant
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Vol. 42, No. 6
The volume, 1’8, of the tttlling drop under “static” conditions, or zero velocity of dispersed phase, will be der.
where $
(2)
is Harkins’ corrwt ion.
A drop of given size and shape will rise or fall through the continuous pliase, depending upon the viscosities and demities of the fluids, a t a certain velocity, the rising velocity, WR. If UR is smaller than the velocity of the liquid through the nozzle, the drop will not separate but will instead ride upon the jet of liquid issuing from the nozzle (assumption 1 above). Bond ( 3 ) determined the rising velocity as Figure 5.
Effect of Continuous Phase Viscosity on Drop Si Systems 7, 8, 9; nozzle 3
Solving Equation 6 for DR and’&stituting u for V R results in
DR = [apg]”’ 180Kp,
i 0. e
(7)
from which
w
W c
V R = 0.5236
L 4,
[-i\,gI3‘* 18vKpc
(8)
0 L 0
The liquid stream forming the drop enters it with a velocity u, as a result of which, and the mass of the stream, a certain amount of kinetic energy is supplied to the drop acting in the direction of flow-Le., away from the nozzle. The kinetic energy can he expressed as
o
w
O0.l
Figure 6.
Effect of Dispersed Phase Viscosity on Drop Size Systems 1,
d, 6;
nozzle 3
force, and FR,the force due to the kinetic energy of the stream entering the drop. The force due to interfacial tension is given by F s = TDNU (3 ) and the volume of drop with sufficient buoyant force to overcome Fo will be
Harkins (6, 7) observed that at zero velocity through the nozzle not all of the drop will separate and move away, hut a certain fraction will remain behind a t the nozzle. He determined this fraction remaining behind, and expressed it pphically as a function of the volume of the drop formed and nozzle diam-
tFBeFK
F i g u r e 7 . Buoyant, Interfacial Tension, and Kinetic Energy Forces in Drop Formation
STABLE
UNSTA8LE
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June 1950
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rL(t,CR
Figure 8.
K VI. Nozzle Diameter, p, Conatant
WL
VPDV’
2s
2s
Figure 9.
or
The total volume, VF,of the falling drop may then be considered to be made up sf the following partial volumes: (1) the volume V S necessary to overcome interfacial tension, (2) the additional volume, VR, necessary to produce a rising velocity at least equal to the velocity of the dispersed phase through the nozzle, and (3) the negative volume equivalent, V K ,of the kinetic energy supplied by the incoming stream: v.9
f V R - VK
(12)
Substituting Equations 5, 8, and 11, and letting (o&)1’8, there is obtained
K
W M inapplicable here. It was therefore evaluated from the experimental data in the following manner. Equation 13 was solved for K , and values were calculated from the data of 185 experimental runs covering the entire range of variables, but with nozzle velocities not exceeding 30 cm. per second. Inspection of the results indicated that interfacial tension and dispersed phase viscosity had little if any influence on the value of K. For constant viscosity of the continuous phase, a log-log plot of K against DN resulted in straight parallel lines such as those in Figure 8, whose equations are
The total kinetic energy supplied to the drop then becomes
VF
Effect of p, on
Dp
=
e)
Equation 13 can be solved for VP by trial and error. To simplify the solution it has been found that $ can be replaced by the constant 0.655 without introduction of appreciable error in the range of density difference and interfacial tension covered in this study. Should this not be desirable, 0.665 may be used as a hst approximation, and a trial vdue of VFobtained 1 to be corrected by recourse to Harkins’ data [& E 2.nF where F is the correction factor given by Harkins (6,7)]. The constant K in Equation 13 remains to be determined. Bond’s value ($), found to apply for very small spherical droplets,
(2) -
K0Q.W
A plot of 4.05 DN0.r47 against pLleon logarithmic coordinates (Figure 9) then established the viscosity function:
Substitution of Equation 15 and 13 then resulta in
J,
= 0.655 in Equation
which can be used to calculate VFand hence D p . To simplify the use of this equation, Figure 10 was prepared, eliminating the neceasity of trial-and-error computations for DF. Equation 16 has been plotted on Figures 3 through 6, where it is seen to describe the data up to velocities of 30 cm. per second well within the experimental precision. Furthermore, it should be noted that Equation 13 reduces to Harkins’ equation for ‘$tatic” conditions at zero nozzle velocity exactly, and Equation 16 will do so within the limits of applicability of the approximation tegarding $ Inasmuchasthe development of these equations ignores the complicating features introduced by eddy currents within the continuous phase, and other factors affecting the
e).
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 10. J = 0.00411
(!!:);
Vol. 42, No. 6
Graphical Solution of Equation 16
H = 0.0021
(3
stability of the liquid jet fro1n ivhich the drops form as discussed by Fbyleigh (17)and others (WO),only the maximum bubble size is predicted by the equations in the region of nonuniformity, u = 10 to 30 om. per second. Figure 11 shows the comparison between actual and calculated drop size for approximately one third of the measurements at velocities up to 30 cm. per second. The remainder, not plotted because of crowding, appear much the same. The average deviation for the 639 measurements a t velocities up to 30 cm. per second is 7.5%.
.
f 0 01069
("
9 ~ ~ 4 7 ~ ~ ~ ~ , i C ~ * ~ ~ ~ ) 8 / :
pirical equation which predicts all drop sizes a t velocities below 10 cm. per second, and maximum drop size in the range 10 to 30 cm. per second within 7.5%. ACKNOW LEDGY ENT
The authors wish to thank Maurice A. Knight for providing the Permanite cement, and the Commercial Solvents Corporation for the Alkaterge C.
SUMMARY
B
The effect of nozzle diameter, velocity, interfacial tension, viscosity, and density on drop size in liquid-liquid systems was investigated for one nozzle design and a stationary continuous phase, Representative photographs are exhibited. Below a velocity of dispersed phase through the nozzle of approximately 10 cm. per second, drop size is uniform for a given velocity, increasing with increased velocity. From 10 to approximately 30 cm. per second, drops are less uniform at a given velocity, and decrease with increasing velocity. At higher velocities, shes of the drops are so nonuniform that conclusions regarding them could not be drawn. Below velocities of 30 cm. per second, increased drop size results from increased nozzle diameter, increased interfacial tension, decreased difference in density between the phttses, and to a lesser extent increased viscosity of the continuous phase. Viscosity of the dispersed phase seems to have negligible inBuence. Drop size was not influenced by choice of dispersed phase, except through the effects already described. A much simpliied explanation of the action of the forces on a drop during its formation hm been drawn, resulting in an em-
ACTUAL DIAMETER,CY.
Figure 11. Comparison of Actual and Calculated Drop Diameters
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
June lSs0
-
NOMENCLATURE
D = diameter,cm. F force, dynes I,$ = functions g = acceleration due to gravity, cm./sec.* K = a correction to Stokes’ law V = volume, cc. u = velocity, om. per second. Without subscript, velocity of dispersed phase through the nozzle W = maa,grama p viscosity, centipoise8 r = 3.1416 = density, grams per cc. p 4p = difference in density between dispersed and continuow phases ama per cc. u = interfadaytension, dynes per cm. $ = function 6 function 9
Subscripts
R
= buoyant = continuow hase = dispersed pgase
-
c
D F
fallm~(or rising) drop K = kinetic energy N = nozzle R freely rising (or falling) Refers to velocity of dispersed pb though the norzle u interfacial tension
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LITERATURE CITED
(1)Alexander, A. E.,Trans. Faraday Soc., 37, 15 (1941). (2)Bond, W.N., Phil. Mag., (7)4,889 (1927). (3)Guyer, A., and Peterhaus, E., Helv. Chim. Acta, 26, 1099 (1943). (4) Haenlein, A,, Forsch. U&te Ingenbrw., 2, 139 (1931). (5)Halberstadt, S., and Prsuanits, P. H., Z. angew. Chem., 43,970 (isao). (6) Harkins, W. D., in “Physical Methods of Organic Chemistry,”
Vol. 1, A. Weissberger, ed., New York, Interscience Publilera, 1945. (7)Harkins, W. D.,and Brown, F. E., J . Am. Chem. Soc., 41,499 (1919). (8) Hayworth, C. B., dissertation, New York University, 1949. (9)Holroyd, C.B.,J . Franklin Znet., 215, 93 (1933).
(10)Hutchinson, E.,J . Colloid Sci. 3,219 (1948). (11)Lewis, C. M.,Phil. Mag., 15, 499 (1908); 16, 466 (1909). (12) Merrington, A. C.,and Richardson, E. G., Proe. Phys. Soc., 59,1 (1947). (la) Neumann, E.,and Seeliger, R.,Z . Phyuik, 114, 571 (1939). (14)Powney, J., and Addison, C. C., Trans. Paradug Soc., 33,1248 (1937). (16) Prausnitz, P.H., Kolloid-Z., 76,227 (1936). (16) Rayleigh, Lord, Phil. Mag.,(6)48,321 (1899). (17)Rayleigh, Lord, Proc. London Math. Sac., 10, 4 (1878);Proc. Roy. Soc., 29,71 (1879);Phil. Mag., (5)34,177 (1892). (18) Reed, R. M., and Tartar, H. V., J. Am. Chem. Soc., 58, 322 (ieae). (19)Schnurmann, R., Xolloid-Z., 80, 148 (1937). (20) Smith, 8. J., and M O W , H., Proc. ROY.SOC.,A93, 373 (1817). (21)Weber, C., 2. awew. Math. u. Mech., 2, 136 (1931). Rocmvm November 30, 1049.
Mass Transfer of Pure liquids from a Plane, Free Surface L. J. O’BRIEN’AND L. F. STUTZMAN NORTHWESTERN TKCHNOLOdlCAL INSTITUTE. LVANSTON. ILL.
I n this study of m a r transfer a turbulent air stream was passed over a pan of liquid suspended from the bottom of an air duct of square cross section. The liquid level was maintained constant and level with the floor of the duct throughout the interval in which data were recorded. Values of the effective fllm thickness and the fllm transfer o d c i e n t concerned have been calculated from the data obtained for air m a r velocities which cover the range between 8.6 and 70 pound moles per hour per square foot with corresponding Reynolds number (based upon effective diamoter of duct) of approximately 2600 to 22,000. A total of sixty-six runs were made, using flve Iiquidc;i.e., acetone, benzene, 1-propanol, toluene, and water. Them
data are expressed with an average deviation of less than 6% by the following empirical equations:
T
X in Equation 1, k considered as the resistance to ma88 transfer acroea which the driving force, Ap, exists. Gilliland and Sherwood (8) conducted experiments on evaporation with a wettedwall column, and presented values for the effective film thickness involved in the evaporation of nine liquids. By dimensional analysis they confirmed that the effective film thickness can be expreased by a combination of dimensionless group, such that
HE theory of diffusion in gases waa developed primarily by Maxwell (IO), and simplifigd by Stefan (N), as a part of the kinetic theory. For steady-stste diffusion of one gaa through a second stagnant gas, it can be shown that the above theory can be used to yield the following equation:
DP Ne=--
Ap
RTx Pnnr
The use of the doublafilm concept developed by Whitman (36) in the design of gas absorption equipment is well known. However, in the awe of evaporation of a chemically pure liquid only the gaa film exists, and thia regktance waa investigated in this study. Because the boundary of this film on the gas side cannot be fixed, a pseudo or effective film thicknnas, defined by the term 1
Prsssnt address, The Pure Oil Company, Chioago, Ill.
= 0.20 (se)-1O*(Re)b whereb = 0.63(SOp’,and k,XP,, p. 0.041D1~~Gb, where h = 0.64/m.’. The data were further correlated with an average deviation of 4.6% by the equation:
in which JD was found to be:
JD = 0.11 (Re)-O.M
McCarter and Stutzman (16) obtained a similar equation, with the exception that the Reynolds number waa corrected for liquid velocity. Most investigators of evaporation and those concerned with gas absorption usually have presented correlations of their data in terms of the film transfer coefficient. The
