A Hydrodynamic Mechanism for the Coalescence of Liquid Drops. II. Experimental Studies Sidney B. Langl and C, R. Wilke Department of Chemical Engineering and Lawrence Radiation Laboratory, University of Calijornia, Berkeley, Calif.
The coalescence of liquid drops a t planar interfaces was studied experimentally. Coalescence measurements were made in an all-glass thermostated cell. The two-component systems water-benzene, wateranisole, ethylene glycol-benzene, tributyl phosphate-water, and water-Aroclor 1 248 were studied. Artificial sonic disturbances were found to decrease the drop rest times for the tributyl phosphate-water system. Measurement of the natural sonic pattern present in the coalescence cell b y means of a special microphone showed the presence of intense but short-time disturbances. Studies with surfactants showed that concentrations of less than 0.02 mM of surface-active agent in the water-benzene system could increase coalescence times b y a factor of 2. Experimental changes in drop size and system properties agreed with the theory, qualitatively.
A
theory for the coalescence of a single drop a t the planar interface between two immiscible fluids showed that coalescence is composed of a film-thinning step and a film-rupture step, either or both of which may be rate determining (Lang and Rilke, 1971). The effects of drop size aiid the physical properties, density, viscosity, and interfacial tension on the rates of each step were determined (Table I (Lang and Rilke, 1971)). The film-rupture step analysis described the frequency and intensity effects of induced disturbances on the rate of coalescence. The experiments described in this paper were conducted in order to study the phenomenon of coalescence in relation to the theory. Liquid systems were selected t o emphasize extremes in the physical properties. Experiments were conducted to show the effects of sonic and subsonic disturbances in the system. A method was developed for measuring the time-average natural vibration pattern present in the coalescence equipment. Because reproducibility of the data was strongly dependent upon the absence of contaminants in the materials used, a short study of the effects of surfactants on coalescence was included. The analysis of the results showed that coalescence rates are highly dependent upon the natural vibration pattern present in the experimental environment. Because this information is not known, in geneial, it is never possible t o produce a n exact experimental verification of the theory. Experimental Equipment and Techniques
Coalescence Equipment. A three-tank circulating water system \vas used to provide a constant-t'emperature b a t h for the coalescence equipment, physical property measuring equipment, a n d storage for t h e various liquids used. T h e experimental 12 X 12 X 12 in. Plexiglas t a n k was bolted t o a l/*-in. steel plate which in t u r n was bolt'ed a n d grouted t o a reinforced concrete pillar 4 ft high which weighed 2600 lb. This pillar was itself grouted t'o t h e concrete floor of the laboratory which rest'ed on solid earth. The pillar was designed to eliminate accidental movement of the 1 Present address, Department of Chemical Engineering, RlcGill University, Montreal 110, Quebec, Canada. T o whom correspondence should be sent.
coalescence equipment during operation and to damp out the effects of vibration in the building. As described below, some vibration was not eliminated by the mounting method. A removable aluminum rod framework mas bolted to the t a n k to hold the coalescence cell. The temperatures in all tanks lvere corit'rolled a t 25OC. The coalescence cell was designed with several special provisions. A means for flushing out' the interface t o remove contaminants aiid then making the interface planar was provided. The meniscus a t the interface could be eliminated so that observations could be made in the plane of the interface. The cell mas desigiied so that drops of t'he denser phase could be allowed to fall to the interface, or drops of the lighter phase could be allowed to rise to the interface from below. The cell was constructed from a 2-in. borosilicate glass t'ee containing a plane glass observation window (Figure 1). The bottom of the tee vias sealed and three side arms were attached, one of which vias connected to a female groundglass joint inside t,he cell. K h e n phase 1 was the denser fluid, a glass cup was iiiserted in this joint, and the interface a t which coalescence took place was adjusted to be in the plane of the lip of the cup. If phase 1 wetted the glass better than phase 2 and if the level of the interface out'side t'he cup was below the lip of the cup, no meniscus was present' in the cup. The interface in the cup could be made nearly planar. When phase 2 was the denser phase (drops released upward), the cup was replaced with a glass adapt'er that held a dropping tip. I n this case, the meniscus could not be eliminated and t'he interface was slightly curved. An aluminum bracket attached the cell to the rod framework that supported the cell in the thermostat. The cell t'op was iiiserted into the cell by means of a groundglass joint. Dropping tips, made according t o a method described elsewhere (Lang and Wilke, 1965),were at'tached t o a glass tube which passed through the cell top. Aii enlarged portion of this tube (about 3 nil in volume) provided enough residence time for the drop-forming liquid to come to thermal equilibrium with t,he rest of the liquid. Teflon stopcocks minimized contamination of the liquids, and clamped spherical ground-glass joints (without grease) were used for all connections. A syringe microburet Model Yo. SB2 (11icruInd. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
341
Table 1. Coalescence Runs on Two-Component Systems Reference
System
Charles and Mason (1960a)
Carbon tetrachloridewater
Charles and Mason (1960a) Charles and Mason (1960a) Charles and Mason (1960a) Charles and Mason (1960a) Konnecke (1959) Konnecke (1959) Konnecke (1959) R u n 75a R u n 74. R u n 730. R u n 77. R u n 72a R u n 71. R u n 70. R u n 108a R u n log5 R u n 1125 Run l l l a R u n 110. R u n 79. Run 7% R u n 80. Allan and Rfasori (1961) Allan and Mason (1961) A l a n and Mason (1961) Allan and Mason (1961) Hartland (1967)
Water-nheptane Ethylene glycolbenzene Rater-benzene
Tributyl phosphatewater Water-anisole Ethylene glycolbenzene RaterXroclor 1248 LIercury-84yo glycerol
Temp, O C
P 1, g/cm3
P 2,
P 2,
g/cm3
CP
fJ,
dyn/cm
re, cm
fm,
obsd
h'mb P
15
1.6038
0,9991
1.140
41.1
0.336
3.1
16.8
20
1.5942
0.9982
1.005
40.2
0.335
2.4
18.0
25
1.5751
0.9970
0.894
37.5
0.328
1.5
21.5
30
1.5549
0.9956
0.801
35.6
0.323
1.4
20.9
20
0.9982
0.6838
0.409
3.3
0.464
3.6
11.6
20 40 60 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 20
1.1029 1 ,0984 1.0814 0.9976 0.9976 0.9976 0.9976 0.9763 0.9763 0.9763 0.9975 0.9975 1.1029 1.1029 1.1029 0.9966 0.9966 0.9966 13.6
0.8762 0.8575 0.8451 0.8733 0.8733 0.8733 0.8733 0.9964 0.9964 0.9964 0.9886 0.9986 0.8762 0.8762 0.8762 1.4471 1.4471 1.4471 1.220
0.638 0.485 0.388 0.590 0.590 0.590 0.590 0.973 0.973 0.973 0,957 0.957 0.612 0.612 0.612 203.0 203,O 203.0 99.6
7.4 7.2 7 .O 34.7 34.7 34.7 34.7 9.9 9.9 9.9 25.5 25.5 7.4 7.4 7.4 40.9 40.9 40.9 355.0
0.170 0.170 0.170 0.415 0.340 0.267 0.209 0.508 0.415 0.325 0.772 0.598 0.195 0.159 0.125 0.228 0.180 0.141 0.294
11.6 1.6 5.3 4.7 4.8 4.7 4.9 6.1 5.3 10.1 35.6 12.3 23.5 14.0 20.5 206.0 59.0 42.0 40.8
3.43 8.68 4.35 7.17 4.12 2.20 1.14 18.5 11.5 4.39 5.21 4.59 3.53 2.52 1.07 7.19 7.09 4.43 19.9
20
13.6
1.220
99.6
355.0
0.244
30.3
12.7
20
13.6
1.220
99.6
355.0
0.173
9.1
8.05
370.0
0.248
780.0
6.40
25.0 25.0
0.492 0.288
70 100
184.0 28.4
40.0 40.0
0.492 0.288
150 170
92.3 16.2
1.252 661 . O 13.6 l I e r ~ u r y - 9 6 7 ~ 20 glycerol 170.0 22.5 0.879 1.24 98Yo glycerol1.24 170.0 22.5 0.879 liquid paraffin Hartland (1967) 1.41 170.0 22.5 0.879 Golden syrupHartland (1967) 170.0 1.41 0.879 22.5 liquid paraffin Hartland (1967) a The runs are from this work. Calculated from eq 1 and 3 of Lang and Wilke (1971).
Metric Instrument Co., Cleveland, Ohio) used to form drops was attached to a small laboratory jack mounted liest to t'he experimental tank. Operation of Coalesence Equipment. X primary cleaning procedure, involving a hot' chromic acid treatment', and a simpler secondary cleaning procedure were devised. Details of the cleaning procedure and of all ot'her items discussed in t,his paper are given elsewhere (Lang, 1962a, 1962b). The primary procedure was performed between major sets of esperimental runs a n d a t a minimum frequency of once every 4 days. The secondary procedure mas used after each day's operations. The coalescence equipment could be assembled so that either the phase-1 liquid was the denser phase (drops were allovied to descend to the interface) or the phase-2 liquid was the denser one (drops were allowed to rise upward to the interface). The assemblage of the equipment and t'he method of operation of the two modes were similar. The complete assembly for the mode in which phase 1 was the denser 342 Ind. Eng. C h e m . Fundom., Vol. 10, No. 3, 1971
liquid is shown in Figure 1. Funnels F1, F2, and F3 contained, respectively, phase-1 liquid used to fill the cell, phase-2 liquid used to fill the cell, and phase-1 liquid used to fill the tube connected to the dropping tip. The interface in t,he coalescence cup could be flushed and t'he excess fluid removed with hypodermic syringe H1. The int'erface in the cup could be made planar by adjustment of the plunger in syringe H2. The procedure used in an experimental run was standardized as much as possible, so t h a t direct comparisons could be made between runs. An experimental run consisted of 50 coalescence measurements, a number sufficient to enable the coalescence distribution curve to be dravm accurately (Charles and Mason, 1960a, 1960b; Cockbain and AleRoberts, 1953). Each run of 50 measurements was divided into 4 groups of 12 or 13. Between these groups, the interface in the coalescence cup was flushed and made planar. Each drop was rapidly formed almost to full size with the microburet. The drop then was allowed to hang from the dropping tip
Figure 1 . Schematic diagram of coalescence equipment for operation when phase 1 is denser than phase 2. The legend is explained in the text
for 1 niiii in order t,o come to thermal and chemical equilibrium n i t h the surrounding fluid. The drop was very don-ly forced off the dropping tip by a n additional movement of the microburet. The technique of drop formation was the came as the oiie recommended in the drop-volume method for measuring surface or iiiterfacial tension (hdamson, 1960). ‘The coalescence rest time was measured with a stopwatch from the time at nhich the drop reached t,he interface until the firPt-stage coalescence process occurred. Suhdivisioii of a run into four groupi provided a useful 5tatictic:il test for the coiisistency of the dat’a in a run. Ench of the four groups was considered to be a separate treatment n i t h 12 or 13 replicatioiis. anall wras made on each run t o determine if the difference between groups or treatments ( L e , , the group average) was statisticnlly sigiiificant (Cochran aiid Cos, 1957). Snedecor’s F-distribution (l’earsoii and Hartley, 1954) was used to check for statistical +yiificance of the differences b e t ~ e e n groups. .ilthough n large number of runs showed significance even a t the 1% level, it was not felt that this \vas sufficient n priori reason for discarding the data. However, each run dizcarded because of accidental contamination of the test fluids showed very strong significance a t the lYc level. -111 of the esperimeiital data taken in the study and a numerical exainple of the statistical calculations are given elselThere (Lang, 19628, 1962b). Sonic Equipment. It \vas desired t o produce and detect soiiic i r c q u e r q disturbances within t h e coalescence cell which !vas submerged i n the thermostat. Several types of loudspeakers aiid microlihones were coiistructed or purchased before sntisfactory results ivere obtained. T h e
most successful loudspeaker was a swimming-pool speaker (Universal Xodel XJI-2FUTY flush mounting underwater loudspeaker made by Universal Loudspeakers, Iiic., K h i t e Plains, 7S. Y.) which was mounted on the side of the experimental tank. Microphones were made by soldering the perforated back of the sensing disk of a Turner Model 9X microphone (Turner Microphone Co., Cedar Rapids, Iowa) t o a small brass case which \vas then filled with transformer oil. -1photograph of the coalescence cell and loudspeaker is shown in Figure 2 . Sounds of various frequencies were produced by coniiecting a n R-C oscillator and audio amplifier to the loudspeaker. The beat frequency experiments were performed using two R-C oscillators in parallel, and white noise was produced by a random noise generator. The voltages imposed on the loudspeaker and the sound pressures detected by the microphones rvere measured with an oscilloscope having a sensitivity of 1 mVjcm. Random noise measurements were made with a harmonic wave analyzer. Impedance measurements were made with a n impedance bridge which could be used either as a modified Wheatstone bridge or as a Maxwell bridge. I n order that sound pressures in the coalescence cell could be related to power dissipation in the loudspeaker, it was necessary to measure the impedance of the swimming pool speaker, perform a n absolute calibration on the microphones, and measure the microphone response t’o various speaker power inputs. These calibrations were performed over a frequency range extending from 50 to 10,000 Hz. The microphone calibration technique was given by Beranek (1949). The voltage produced by the sound pressure field Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
343
Atlas Powder Co., Wilmington, Del.); and sodium oleate (J. T. Baker Chemical Co., Phillipsburg, N. J.). (Sorbitan is a n inner ether produced from sorbitol.) It was necessary that the phase 1 and 2 materials be mutually saturated at 25OC. The saturation was accomplished by vigorously stirring together several hundred milliliters of each of the two phases for a minimum of 24 hr. Flasks of saturated materials were stored at 25OC until used. The densities and viscosities of the saturated phases and the interfacial tension between the phases were measured, respectively, by the pycnometer technique, Cannon-Fenske viscometers, and a ring tensiometer. Results of the physical property measurements are given in Table I. Experimental Results heliminarv Results. The effects of surface renewal, distance between t h e d ropping tip and the int.erface, mild external vibrations, the method of purification of materials, a n a arop aging were srudied in a number of experiments. T h e experiments described in t.he section were all made with the water-benzene system, b u t the conclusions are probably applicable to most other systems. Picknett found that, if the interface were not renewed for a long period of time before coalescence measurements were made, the drop rest times were excessively long (Picknett, 1957). A run, prior t o which the surface in the coalescence cup had not been renewed for a 10-hr period, was compared with runs with surface renewal after every 12 or 13 coalescence measurements. No effect of lack of surface renewal was observed indicating that some contamination may have been present in Picknett's equ ipment whereas contamination was eliminated in this experimient. .-Le> : ..":.IA "&..A_. "+&.-& I n all the experiments condutiuau U L YULD SUUUJ, L\U ~ U V ~ U L ~ U was made t o minimize the distance a drop would fall between the dropping tip and the interface. However, some variation in this distance from run t o run was impossible t o avoid hecause of the difficulty of adjusting the distance precisely. Experiments with drops having a n equivalent spherical radius (TJ of 0.267 cm showed no discernible effect when the distance between the lower end of the drop just prior t o release and the interface was changed from 1 to 10 mm. With large:r drops (r. = 0.415 em), both shorter and longer rest times were observed with the 10-mm distance. ThirI effect was due to the greater kinetic energy carried by the :~~~.. 2 L.. larger drops. nnorrer rem Iurms w e w pruuu~cu uy w a v e s causing premature film rupture (Lang and Wilke, 1971); longer rest times were produced by large interfacial waves which caused the drop t o move Up and down in a largeamplitude oscillation. No oscillations of the drop itself were observed in these or in the other experiments. The effect of mild external disturbances was investigated. No discernible difference w m ohserved h e h e e n runs in which a pump was operating5 in the thermostat or was turned off, or in runs during dayti me working hours and at night. As a precaution, however, the pump circulating water t o the thermostat was alwajis turned off during a run. 1 :~~-~..-:-.L., The effect of purity 01 m e reagenxs usea was m v e ~ w g a ~ a u . Studies were madl: with fractionally distilled, fractionally J . : l , . L . ~ . .-J cryya~rt~imau, tmu Lesearch grade (99.93 mole % minimum 1 purity) benzene, and with deionized and filtered, and distilled and unfiltered, water. Mass spectrographic analyses of some of the materials are reported by Lang (1962a, 1962h). An analysis of the results of the runs showed the effects of the different methods of purification t o he statistically significant at the 2.5% level. The difficulty of reproducing
,.
, . .
Figure 2. Photograph of coalescence equipment for operation when phase 2 is denser than phase 1. The glars adapter and the dropping tip can b e seen in the coales cence cell. The swimming-pool loudspeaker i s located at the left side of the tank and the laboratory iack holdingI the microburet is an the right
that would exist a t the microphone location if the micro phone were not there was determined. The technique iS based on the electrical reciprocity principle and does not require a n y absolute standards. The sensitivity of the micro phone at 1000 He was -77 dh (ref I V/(dyn/cmz)). AI measurements were made with the coalescence cell in plae in the thermostat t o duplicate actual operating condition as nearly as possible. Details of the calibration technique and calibration data are given by Lang (1962a, 1962h). Materials. To minimize the effects of contamination special techniques were devised to remove small quan tities of both soluble and suspended impurities from thc liquids used in this study. T h e water used bot,h as ar experimental fluid and as a final rinse in cleaning was p r e pared by passing distilled water through two ion-exchange columns and a 0.45-fi pore filter t o remove suspendec materials. Reagent grade benzene was purified by i triple fractional crystallization followed by filtration This method was found t o he more effective in the remova L1 of thiophene and carbon disulfide than fractional distillatior Tri-n-butyl phosphate was purified by a single vacuur n distillation over sodium bicarbonate using a n 18%. colum n packed with glass Raschig rings. Anisole was purified b Y >. ,... , . . , , a . ,1 ~ 1 ~ . , ~. . . A~ > ~ amiiiauon m a awm. column. rnl I ne emyiene giycui an" iiruciur 1248 (a tetrachlorinated diphenyl from Monsanto Chemical Co., St. Louis, Mo.) were not purified further. Three surfaceactive agents, which were not further purified, were also used: Span 80, sorbitan monooleate; Tween 81, sorbitan monooleate plus 5 molecules of ethylene oxide (both from
.
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344 Ind. Eng. Chem. Fundom., Vol. 10, No. 3, 1971
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coalescence r u w from day to day was so great, however, t h a t it F a s decided that a coiisistent technique of materials preparation would produce results as good as those obtained with ultrapure materials. The impurities tolerated should be of low molecular weight, rather than high-molecular-weight compounds which often act as surface-active agents. In a study of the effect of drop aging, drops which were not aged or aged only 15 see coalesced in a n average of 0.9 or 0.6 sec less, respectively, than drops which had been aged for 1 miii (re = 0.267 c m ) . Only a difference of 0.04 see was observed when the aging time was changed from 1 t o 3 min. Therefore, all drops were aged 1 min before release, with the exception of a few runs in which the drop size was too small t o allow good control of the drop formation process. Effects of Drop Size and System Physical Properties. I < y interchanging t h e droppiiig t i p , t h e effect of drop size 011 droll rcst tinies could be determined. As many a s four drol) sizes were used with a given system, allowing t h e spherical droi)-ec~uivalentradius of the drops to be changed by about a factor of 2. Five different two-component, systciris werc used t o ascertain the effects of a chaiige in physical properties. Ileiisity differences ranged from 0.0089 to 0.4505 g/cm3; viscosities ranged from 0.590 to 203 cl'; mid interfacial tensions ranged from 7.4 t o 40.9 dyii/cm.
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The coalescence distribution curves for the systems waterbenzene, water-anisole, ethylene glycol-benzene, tri-n-butyl phosphate-water, and water-Aroclor 1248 are given in Figures 3 through 7 , respectively. I n the first three systems, the drop phase was the denser one and drops were allowed to fall t o the interface; in the latter two systems, the drops were less dense and were allowed to rise to the interface. The reproducibility of the d a t a was often poor because of the strong influence of minute traces of contaminants. The distribution curves for large drops were also less reproducible because of the large surface disturbances caused by their impact. These surface disturbances, in the form of largeamplitude waves, were very noticeable in low viscosity systems. In all except two of the systems studied (including the systems containing a surface-active agent discussed below), coalescence occurred in a stepwise manner yielding as many as seven successive daughter drops. Ih the water-Aroclor 1248 a u d ethylene glycol-benzene systems, the coalescence was single stage. This observation confirmed the finding of Charles and Mason (1960a), who observed single-stage coalescence whenever the ratio of viscosities of the two phases was less t h a n 0.02 or greater t h a n 11.0. Induced Disturbances. T h e discussion of hydroInd. Eng. Chem. Fundam., Vol. 10, NO. 3, 1971
345
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dynamic instability by Laiig and Wilke (1971) suggested the possibility of creating disturbances in some manner. I n general, the effect of an intense sonic dist'urbaiice would be to decrease t'he drop rest time by initiating an instabilit'y before the naturally present disturbances could initiate an instability. It is also possible for a sonic disturbance to prolong drop rest times by causing the drop to vibrate up and down independently of the planar interface, effectively increasing the film thickness. I n these studies, the effect of trace contamination was minimized by the use of a stat'istical chain design (Cochran and Cox, 1957). In this experimental design, three runs were made daily on each of four successive days; one of the three daily runs was made under conditions identical with a run of the previous day, and another of the runs was duplicated the following day. The chain mas closed by performing one of the series in the same manlier as one of the runs on the first day. Thus, runs using four of the sets of operating coiiditions were performed twice, and runs with the other four sets of conditions were performed once. The method of analysis yields a correction factor that is a measure of the day-to-day drift in the properties of the liquid materials. This correction factor was used to shift the time scale of all of the coalescence distribution curves to eliminate the daily drift. These experiments were performed with both the wat'er-benzene and the tributyl phosphate-water systems. The day-to-day drift was generally toward longer rest times, 346 Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
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suggesting that there may have been a n accumulation of brace contaminat,ion. The correction factors for the waterbenzene experiment,s were more erratic, possibly as a result of more severe contami~iation.As a result, although the waterbenzene data are reported for completeness, t'he tributyl phosphate-water data are believed to be more reliable. The effects on coalescence times of seven frequencyvoltage combinations applied to the swimming pool speaker were compared with the results of an experiment in which no disturbances were produced. The coalescence curves for the water-benzene and tributyl phosphate-water systems are shown in Figures 8 and 9 and the results of the statist'ical calculations are summarized in Table 11. It can be seen that none of t,he differences in t,he runs with the water-benzene systems showed statist,ical significance a t the 5% level, but' five of the seven types of disturbances showed statistical significance in the tributyl phosphate-water runs. I n every significant case, the sonic disturbance decreased the rest times of the drops. The dat'a in Table I and eq 1, 22, and 30 from Lang and Kilke (1971) can be used to calculate the minimum frequency disturbance which can affect a liquid drop a t an interface. We calculate that only vibrations of frequencies higher than 69 and 31 Hz can influence coalesceiice in the water-benzene and -tributyl phosphate systems, respectively. Therefore, all frequencies except the 50-Hz measurements in the water-benzene studies should have influenced the rest h i e s . The lack of a statistically significant
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Water-Aroclor 1248 system coalescence rest-time curves
effect of the 110-Hz disturbance in the tributyl phosphatewater experiments could possibly be due t o some secondary effect not considered in the theory. The theory (Lang and Wilke, 1971) suggests t h a t disturbances of low frequency should be extremely effective in promoting coalescence. However, such disturbances must have frequencies greater than the minima calculated above (69 Hz in the water-benzene system). A study was conducted t o determine the effect of disturbances having a frequency lower t h a n this minimum. Subsonic disturbances of 1, 5, and 10 i3z were generated by producing interference beats between two R-C oscillators in parallel, each generating a signal close t o 70 He. The results are summarized in Table 111. The pure 70-Hz frequency established a resonance which greatly lengthened the coalescence times compared to no disturbance. The increased rest timr was caused by a n oscillation of the drops a t the planar interface due to a system of small-amplitude waves (visible to the naked eye) in the interface between the bulk fluids. X o oscillations of the drops themselves were apparent. Subsonic disturbances of 5 or 10 beats/sec reduced the rest times despite the stabilizing effect of the 70-Hz resmance frequency. One beat per second caused the same rest time as the pure 7 0 - H ~frequency. Apparently the 5and 10-Hz beats reduced but did not eliminate the resonance caused by the 70-Hz frequency. Effect of Surfactants. As noted by Nielsen, et al. (1958), great difficulty was experienced in obtaining reproducible coalescence rest time curves. The greatest source of error appeared to be due t o minute traces of contaminating materials which exhibited marked surface activity. One might anticipate a priori t h a t trace contamination would be more likely to be caused by high-molecular-weight compounds, such as fats, oils, and nonvolatile hydrocarbons, t h a n by low-molecular-weight compounds. This deduction f o l l o w from a study of the cleaning methods usually used. The \oIveiits, acid solutions, and other materials used would be far more likely to remove the lower molecularweight materials than the higher ones. Accordingly, a series of experiments was performed to determine how small a quantity of high-molecular-weight material would be needed to affect coalescence times strongly. The materials used were
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drop r e s t - t i m e
(sec)
Figure 8. Effect of sonic disturbances produced b y swimming-pool speaker on water-benzene coalescence distribution curves. Curves adjusted for day-to-day drift. Runs are described in Table II Symbol
Run
G H A E
38, 41 39 40 42,45 43 44
F C
Symbol
1 8 J I
K
D
Run
46,49 47 A8 50, 53 51 52
Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
347
0
12
6
30
24
Adjusted drop rest-times
36
(sec)
Figure 9. Effect of sonic disturbances produced by swimming-pool speaker on tributyl phosphate-water coalescence distributions curves. Curves adjusted for day-to-day drift. Runs are described in Table II
Table II. Effect of Sonic Disturbances on Drop Rest Times Disturbance frequency,
Hz
Run"
System
Water-benzene
38, 41, 52 51 43, 46, 49 44 39, 42, 45 40 47, 50, 53 48
Tributyl phosphate-water
Change in median rest time due to disturbances, sec
Level of statistical significance
None 50 50
...
...
...
3.4 18.4
250
40.0
500
25.5 125 15.3 85
-0.2 +1.3 +0.3 f0.4
Not, sign. a t 5% Not sign. a t 5% Not sign. at 5% Not sign. a t 5% Not sign. a t 5% Not sign. at 5y0 Kot sign. at 5%
500 738 2095
None
54, 67 69 55 59 66 56, 57 65, 68 62, 64
Rms sound pressure, dyn/cm2
70 110 200 300 500 1000
... 250 260 29 48 135 670
-0.1 -0.6 -0.3
... -0.8 +0.7 -1.2 -1.7 -1.4 f0.4 -1.7
I
.
.
5%
Not sign. a t 5% 5% 1% 1%
Not sign. at 5% White ... 1% noise a Runs 38 and 41, 46 and 49, 42 and 45, and 50 and 53, respectively, analyzed as single runs. Only the first 25 measurements in runs 57 and 59 were used in the analysis because of contamination due to leakage at a ground-glass joint.
Table 111. Effect of Subsonic Disturbances on Drop Rest Times. fm,
Disturbance
None Pure 70 H z 70 H z ) 1 beat/sec 70 Hz, 5 beats/sec 70 H a , 10 beats/sec
sec
Change in median rest time due to disturbance, sec
4.9 13.0 13.8 9.1 7.1
... ... +0.8 -3.6 -5.4
a Water-benzene system, with = 0.267 cm. The sound pressure was 94 dyn/cm2 rms for pure 70 Hz, and 133 dyn/cm2 rms for beats.
348
Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
surface-active agents, but it should be emphasized that this study ivas not designed t o elucidate the effects of surfaceactive agents in general. However, some preliminary conclusions can be drawn about the effect of the type of surfaceactive agent. The effect of the concentration of the surfactant on the mean coalescence time can be seen in Table IV. The very strong effect of concentrations as low as 0.02 m-11 should be noted. Natural Sonic Disturbances, I t was of interest t o determine t h e characteristics of the natural sonic disturbances in the coalescence cell to see if these disturbances could initiate a hydrodynaniic instability leading t o ultimate coalescence. The microphone was placed in the coalescence
-
Table IV. Effect of Surfactants on Coalescence Time
Surfactant
Equilibrium concn in aqueous phase, m M
Span 80
0.0031 0.031
Tween 81
0.00244 0.0244 0.244
Sodium oleate
0.0566 0.566 5.56
Run no.
86 84 85 83 82 81 89 87 88 90 92 91 95 93 94 101 99 100 102 104 103 106 105 177
rer cm
sec
0,310 0.245 0,191 0.230 0.182 0.143 0.299 0.236 0.184 0.266 0.210 0.164 0.213 0.168 0.132 0.321 0.253 0.200 0.277 0.218 0.171 0.193 0.152 0.120
6.7 8.1 7.5 93.4 28.6 20.0 4.5 5.1 3.9 11.3 9.5 5.7 133.7 70.1 58.5 7.3 10.3 7.7 25.6 35.1 23.1 9.0 12.1 6.3
fnl,
Table V. Computed Sonic Disturbances Test
G
H J
Numbered peak
1 2 3 4 5 1 2 3 1 2 3 4 5
YO,
HZ
151 240 358 498 790 140 810 991 111 141 338 47 1 632
P,',
a, sec
dyn/cm2
0,0338 0.0431 0.0286 0.0326 0.0386 0.0426 0.0408 0,0375 0.0418 0.0321 0.0289 0.0320 0,0208
3930 1690 2620 2430 5900 2200 3210 2410 2490 2340 2420 57 80 2490
cell in t h e position normally occupied by t h e coalescence cup and was then connected to t h e wave analyzer. The time-average microphone-voltage output was converted to a n rms frequency spectrum by means of the microphone calibration curve. Typical frequency spectra taken o n different days are sho\\n in Figure 10. The spectra have both very marked similarities and differences. If the reasonable assumption is made t h a t the disturbances creating these spectra consisted of short bursts of sound having time duration 2a, they can be described mathematically as
Frequency,
Y
= w / 2 r (cpsl
Figure 10. Rms frequency spectra of naturally occurring sonic disturbances. The circulation pump to the coalescence thermostat was turned off, but the pump and stirrers in the materials storage thermostat (which were normally allowed to run during coalescence measurements) were in operation
The data corresponding t o the numbered peaks in Figure 10 were fitted to eq 2 by means of a table of the function (sin x)/x. The resulting rms pressure amplitude, frequency, and halftime period are presented in Table V. The intensibies of these natural disturbances are much greater than the pressure fluctuations produced by t,he swimming-pool speaker. This explains the difficulty of influencing coalescence times by artificially induced sonic disturbances. Discussion and Analysis of Results
where P,,, and w0 are the rms sound pressure amplitude and frequency, respectively. These disturbances would then have the Fourier transform-or equivalently, the frequency spectrum amplitude (a)-given by
A theoretical explanation of the coalescence process has been developed (Lang aiid Kilke, 1971). The model consists of two successive steps: a film-t,hiniiing step and a film-rupture step. The film thins under the effect of gravity aiid surface forces until it becomes thin enough to be subject t o film rupture. The film rupture occurs when a disturbance either initiates a Taylor instability (because the disturbance has a frequency in the appropriate range) or produces a sufficiently Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
349
Table VI. Summary
of Effects of Variables on Coalescence Rest Times. According to Theory (Lang and Wilke, 1971)
Variable
Drop radius
Dependence o f coalescence time i f thinning-film model is assumed rate determining
Time approx proportional to fifth power of drop radius No dependence Time directly proportional to p2 Time approx proportional
to
AR
Time approx inversely proportional to uz No dependence Disturbance frequency
No dependence
Dependence of caalescence time i f large amplitude wave model i s assumed rate determining
Dependence o f coalescence time if Taylor instability film-rupture model is assumed rate determining
Radius imposes lower limit 011 frequencies to which drop is subject Time increases with increasing p1 Time increases with increasing p2 Time decreases with increasing Ap Time increases with increasing u Time decrease with increasing P,,,
Radius imposes lower limit oii frequencies to which drop is subject KO dependence
KO dependence Time increases with increasing Ap a t very low frequencies. KO dependence a t higher frequencies Time increases with increasing U
A high P,,,, mill rupture films that cannot be ruptured by a lower P,,, Higher P,,, is required to rupture films a t higher frequencies
Coalescence times pass through a minimum within a range of permissible frequencies Low-molecular-weight solute (not KO dependelice a t very low Time decreases due to pres- If presence of solute causes inpresent in equilibrium concenence of solute if interconcentrations terfacial turbulence, film trations in both phases) facial turbulence is may be ruptured more created easily High-molecular-weight solute Time increases with inHigher P,,,is required to Time increases with in(below critical micelle concn) rupture films a t higher coiicreasing conceiitration of creasing concentration of centrations of solute solute solute a More precisely, time in the thinning-film model means the time required for the film to decrease in thickness to a specified constant value, at which time coalescence would occur; time in the Taylor instability model refers to the time required for a specified thickness film to be ruptured; in the large amplitude wave model, a given distribution of various intensity disturbances is assumed, and the coalescence time represents the time lapse until a sufficiently intense disturbance (high P,,,) occurs.
large amplitude wave. Because the disturbances are randomly distributed in time, frequency, and intensity, rest times are not constant. The theory appears to describe many of the features of the coalescence process but, because of the stochastic nature of the disturbance pattern, the theory cannot quantitatively enable the prediction of rest-time distribution curves. An initial attempt t o study natural sonic disturbances was described above, and more detailed studies appear to be necessary. I n the two-stage coalescence mechanism, the slower of the steps is the rate-determining one. Because the film-rupture step is dependent upon a statistical disturbance pattern, one generalization can be made. I n an environment with few and weak disturbances, the film-rupture step is likely to be rate determining and rest times will be shorter for systems whose physical properties cause a weaker phase-2 film. Conversely, in a n environment with many and strong disturbances, the film-thinning step is likely to be rate determining and short rest times are favored by systems with rapidly thinning films. In the following discussion, we emphasize the importance of the two-step mechanism. For convenience, many of the results of the theory are summarized in Table V I . Effect of Physical Properties. The data in Table I will now be examined considering the two-step mechanism and t h e summary of the theory in Table VI. Several of t h e systems have a sufficiently high phase-2 viscosity t h a t t h e film-thinning step is certainly the rate-determining one. In this step, the time required for the film t o thin to 350 Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
h', is approximately proport'ional to Appz/uz. Let us first examine the water-lroclor and mercury-glycerol systems. The long median rest times of 42 t o 206 see i n t h e water-droclor system are primarily due t'o the high viscosity of bhe .$roclor. However, the rest times for the mercury-84yo glycerol system are much shorter in comparisou to those for lvater-Aroclor than can be explained by the decrease in ,.Q. Rest times for mercury-96y, glycerol are the longest of all. Calculated values of A p p 2 / u 2 are 0.0596, 0.0546, and 0.00978 for the systems mercury-96Yo glycerol, water-=lroclor, and mercury-%Yo glycerol, respectively, and the rest times decrease in the same order for these systems. Film rupture was t,he rate-determining step in the other systems examined. A n interest'ing comparison can be made between the water-anisole and the wat'er-benzene systems. With the exception of A p , their physical properties do not differ great'ly. If film thinning were rat,e determining, wateranisole would have the short'er rest times because of the very low value of its A p . However, t,he rest times for this system are much greater than those for water-benzeiie, and thus film rupture is the rate-determining step. Both the tributyl phosphate-water and the water-anisole systems have small values of Ap, so t'hat film rupture probably occurs according t'o the large amplitude wave model. Therefore, the system with the smaller interfacial tension should have the shorter rest time. The data in Table I show that the tribut'yl phosphatewater system with u = 9.9 has shorter rest time than does the wat,er-anisole system which has u = 25.5. The carbon tetrachloride-water and water-heptane systems are two more
illustrations of dominance of the film-rupture mechanism over the film-thinning one in the determination of rest' times. Because of the large A p in these two systems, the rest' times would be greater t h a n those of the water-benzene system if film thinning were the rate-determining step. However, both the carbon tetrachloride-water and water-heptane systems exhibit rest times of only several seconds and, thus, film rupture is the rate-determining step. It is difficult t,o interpret, the data on the ethylene glycol-benzene system. The rest times obtained in this work were about twice as great, as those found by Koiinecke for similar-size drops with the syst'em (Konnecke, 1959). The discrepancy may have been the result either of differing levels of natural disturbance or of contamination. Despite insufficient information coiicerning the disturbance patterns during the coalescence runs, qualitative agreement between the experiments and the theory is fairly good. However, we do lack additional information coiicerniiig the natural disturbance patt,ern, aiid so cannot evaluate the model completely. Effect of Drop Size. The theory (Lang and IYilke, 1971) suggests t h a t a knowledge of t h e average thickness of t h e phase-2 film a t t h e time of coalescence is important in t,he predict,ion of drop rest times. Film thicknesses corresponding to t h e median rest times (tm) found in this study and in several others in t h e literature were calculated by means of eq 1 and 3 f r o m Lang and TYilke (1971) and are given in Table I. The film-thinning theory predicts t h a t , if drops of various sizes coalesced when the phase-2 films reached a particular thickness, rest times for a given system would vary approximately as the fifth pon-er of drop radius. The film-rupture theory shows that larger drops, because of both their larger radii and their larger zone angles, are subject to disturbances of lower frequency. Figure 10 (Lang and Kilke, 1971) illustrates t h a t the energy necessary t o rupture a given film decreases with decreasing frequency of t,he disturbance. Because of these competing effects and the stochastic distribution of disturbances, t'he effect of drop size seems t o be very difficult t o predict. -111 examination of Table I reveals some tenis in which rest times increase wit,h size, some t h a t decrease with size, and others which sholv no pattern. 111 aclditioii, the surface disturbance created by a large drop falling oiilj- a short distance t o the interface can strongly influence rest times as discussed above. Effect of Induced Disturbances. The t,heory (Laiig a n d Wilke, 1971) suggested t h a t we might be able to alter coalescence rest-time curves by inducing t h e proper types of cMurbaiices in the coalescence cell. The results presented above showed that, this endeavor was successful in certain cases. Wheii sonic frequency disturbances were introduced during measurements on the tributyl phosphate-water decreases in drop rest times of 0.8-1.7 sec were found (aiid shonii to be statistically significant). Because of the very large day-to-day scat,ter in the measurements, the low intensities of the disturbances used, and the high interfacial teiisioii, a statistical analysis of the 11-ater-benzene system did not show the effect of vibration. The large amplitude wave theory shoived t h a t the energy required t o rupture a given thickness of film iiicreased greatly n i t h increasing n-ave number (or illcreasing frequency). This trend n-as very apparent with the tributyl phosphate-wter resultj. The sound pressure of the 500-Hz disturbaiice was three times as great as that of the 300-Hz disturbance, but' the effect on coalescence
times was about the same. even more intense 1000 Hz did not show a statistical influence on coalescence times a t all. The measurements of the natural disturbances present in the system showed clearly why artificially iiiduced disturbances had a xeak effect. The maximum power t h a t could be dissipated in the swimming-pool speaker without danger of rupturing its diaphragm could only produce pound pressures of the order of hundreds of dynes per square centimeter. The calculations in Table T' show t h a t the natural disturbances, albeit very brief, were of intensities much higher than the artificial ones. Contamination a n d Surface-Active Agents. h third component can influence drop rest times either by increasing or decreasing them. The mechanisms of the two effects are quite different,. Jlrop rest times may he decreased u-hen a low-molecular-weight third compoiient is present in noiiequilibriuni concentrations i i i the t w o phases. Charles observed t.hat this effect in the chloroform-water system was due to a sinall quantity of ethanol (Charles and Mason, 1960b). I t has been further discussed by Groothuis and Zuideriveg (1960). This decrease in drop rest tiinei results from interfacial turbulence (oft,en called the Alaraiigoiii effect). Ilecause of small-scale eddies adjacent to the interface, concentration variations of the third conipoiieiit may exist, giving rise to local variat'ioiis in the interfacial tension. In aii attempt' t'o reduce its potential surface energy by extension or contraction of area, the surface undergoes turbulent motion (Davies and Rideal, 1961; Scriven and Steriiling, 1960; Steriiling and Scriveii, 1959) Ivhich may result in disturbances causiiig premature coalescence of the drop. The likelihood of such local interfacial tension variations arising in a stagnant system decreases as the concentration of the t,hird componeiit approaches equilibrium. Then decrease in drop rest times would be less likely t o occur. This theory is also in agreement with esperiment (Charles and Mason, 1960b). Drop rest times generally increase when the third component has,a high inolecular weight. This observation accounts for the necessity of a11 emulsifying agent to produce L: stable ernulsioii (Aldamsoii,1960). Many explanatioiis for the stability of emulsions have beeii giveii iii the literature (hdamsoii, 1960; Davies aiid Rideal, 1961). Only a few of the more relevant' ones will be nieiit,ioiied here wit'h regard to the effect of surfactants on drop rest times. The surfactant first decreases the rate of thinniiig of the phase-2 film mechanically and electrically. Several oriented layers of water of hydration may surround each molecule of surface-active agent, producing a mechanical barrier that must, be displaced or removed for coalescence to occur. Surface-act'ive agents enhance the elect'rical repulsioii forcej, which decrea3e the rate of film thiiiiiiiig. Surfactants tend to preveiit the growth of instabilities by damping wave3 a t interfaces in a manner similar t o that of viscoGty. Surfactaiits also make the film inore elastic by enabling the film to "heal" its OIW weak spots by changes in the dynamic interfacial tensioii (Ewers and Sutherland, 1952; Gibbs, 1961). Hodg3oii and Lee (1969) have observed that very Ion. concentrations of surface-active agents can completely overwhelm effects due to coiitamiiiaiits. The data in Table IT strongly support, the arguments t h a t surfactants increase drop rest times. Xs an example, the median rent time for 0.213-cin drops of 0.244-m.lf Tween 81 ill water a t a benzene interface was 133.7 see as compared to a median rest time of 4.9 see for 0.209-cm drops in the waterteni. For a given surfactant, the drop rest, times increased with coiiceiitratioii of t'he agent, with one esceptioii. Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
351
The rest times of the 5.56 mM sodium oleate-benzene system were about one-fourth as long as those of the 0.556 mM sodium oleate-benzene system. It was noticed t h a t the water phase was very turbid, and this observation suggested that the critical micelle concentration (cmc) had been exceeded. Harkins (1952) reported a cmc of 7-9 mdf for sodium oleate, a value very similar t o the sodium oleate concentration in the experiment discussed. Characteristics of solutions near the cmc are somewhat unusual, so t h a t a n effect on coalescence times is not surprising. Insufficient data are available to attempt a theoretical explanation of the influence of micelle concentration on coalescence times. In industrial emulsion technology, surfactants with lower hydrophilic-lipophilic balance (HLB) values are used to stabilize water-in-oil emulsions, and those with higher HLU values are used to stabilize oil-in-water emulsions (Ilavies and Rideal, 1961). Similar considerations should apply to drop rest times. The best way to make such a comparison, however, is to measure some rest times with the denser phase as phase 1, and other rest times with the lighter phase as phase 1 . A comparison of relative increases in rest time for the two modes of operation could be correlated with the HLB values. I3ecause such a comparison would have been beyond the scope of this work, this type of data was not taken. Acknowledgment
The authors are grateful for the helpful suggestions of Theodore Vermeulen and Peter W. 11. John. S. 13. L. expresses his thanks to the University of California and t o the National Science Foundation for financial help in the form of fellowships. This work was partially performed under the auspices of the U. S. Atomic Energy Commission. Nomenclature
a f
(0
gp) h m
P,,, re
t
352
half of time duration of periodic disturbance, sec random disturbance as a function of time = frequency spectrum of random disturbance = thickness of phase-2 film at median coalescence time, g = rms sound pressure amplitude, dyn/cm2 = equivalent spherical radius of drop, defined by V = 4/m-e3, cm = time, sec =
=
Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
t7n
V
= =
median drop rest time, sec volume of liquid drop, cm3
GREEKLETTERS = = P I , p ~ Ap , =
fi2 Y
U
w wo
= = =
absolute viscosity of phase 2 (cp) frequency, He density of phases 1 and 2 and density difference, respectively, .g/cm3 interfacial tension, dyn/cm angular frequency, equals ~ T V radians/sec , angular frequency of a discrete disturbance, radians/sec
literature Cited
Adamson, A. W., “Physical Chemistry of Surfaces,” Interscience Publishers, Inc., New York, N. Y., 1960. Allan, R. S., Mason, S. G., Trans. Faraday SOC.57, 2027 (1961). Beranek, L. L., “Acoustic Measurements,” Wiley, New York, N.Y . , 1949, pp 113-122. Charles, G. E., Mason, S. G., J . Colloid Sci. 15, 105 (1960a). Charles, G. E., Mason, S. G., J . Colloid Sci. 15, 236 (1960b). Cochran, W. O., Cox, G. PII., “Experimental Designs,’’ 2nd ed, Wiley, New York, N. Y., 1957. Cockbain, E. G., bIcRoberts, T. S., J. Colloid Sci. 8, 440 (1953). Davies, J. T., Itideal, E. K., “Interfacial Phenomena,” Academic Press, New York, N. Y., 1961. Ewers, W. E., Sutherland, K. L., Aust. J . Sci. Res., Ser. A 5, 697 (1952). Gibbs, J. W., “Scientific Papers,” Vol. 1, Dover Publications, Inc., New York, N. Y., 1961, pp 300-314. Groothuis, H., Zuiderweg, F. J., Chem. Eng. Sci. 1 2 , 288 (1960). Harkins, W. I]., “The Physical Chemistry of Surface Films,” Reinhold, New York, N. Y., 1952. Hartland, S., Trans. Inst. Chem. Eng. (London) 45, T97, T102 (1967). Hodgson, T. D., Lee, J. C., J . Colloid Interface Sci. 30, 94 (1969). Konnecke, H.-G., Z. Phys. Chem. (Leipig)211, 208 (1959). Lang, S. B., Lawrence Radiation Laboratory, Berkeley, Calif. UCRL-10097 (May 1962a). Lang, S. B., Ph.D. Thesis, University of California, 196213. Lang, S. B., Wilke, C. R., IND.ENG.CHEM.,FUNDAM. 10, 329 (1971). Lang, S. B., Wilke, C. It., Rev.Sci. Instrum. 36, 1255 (1965). Nielsen, L. E., Wall, R., Adams, G., J . ColloidSci. 13,441 (1958). Pearson, E. S., Hartley, H. O., “Biometrika Tables for Statisticians,” Vol. 1, Table 18, Cambridge - University Press, Cambridge,’ 1954. Picknett, It. G., Ph.D. Thesis, University of London, 1957. Scriven, L. E., Sternling, C. V., Nature 187, 186 (1960). Sternling, C. V., Scriven, L. E., A.1.Ch.E. J. 5 , 514 (1959). ’
RECEIVED for review August 18, 1965 RESUBMITTED February 25, 1971 ACCEPTED April 2, 1971
