The kinetics and mechanism of ultracentrifugal demulsification

The kinetics and mechanism of ultracentrifugal demulsification

The Kinetics and Mechanism of Ultracentrifugal Demulsification A L I C E U L H E E H A H N AND R O B E R T D. VOLD Department of Chemistry, Universit...

606KB Sizes 0 Downloads 100 Views

The Kinetics and Mechanism of Ultracentrifugal Demulsification A L I C E U L H E E H A H N AND R O B E R T D. VOLD

Department of Chemistry, University of Southern California, Los A ngeles, California 90007 Received August 12, 1974; accepted December 9, 1974 The ultracentrifugal stability of Nujol-water-sodium dodecylsulfate (SDS) and olive oil-water-SDS emulsions was determined as a function of the concentration of SDS and of added sodium chloride. Nujol emulsions with concentrations of SDS below the critical micelle concentration (cmc) separate oil according to a first order rate law, which changed to a zero order when the cmc is reached, whether by increasing the concentration of SDS or by adding salt at a lower concentration of SDS. Olive oil emulsions separate oil according to a second order rate law at concentrations of SDS both above and below the cmc. Salt increases the stability of Nujol-water-SDS emulsions but makes olive oil-water-SDS emulsions less stable. These observations are discussed in terms of the various possible rate-determining steps in demulsification. The results are consistent with the hypothesis that a "collision rate" between drops is rate-determining in the case of olive oil emulsions, that the rate of film rupture controls the process with Nujol emulsions below the cmc of SDS, and that coalescence occurs only at the interface between emulsion and bulk oil with Nujol emulsions above the cmc. INTRODUCTION We have recently shown (1) that the separation of oil from oil-in-water emulsions in the ultracentrifuge can be represented b y classical rate equations if a proper choice of variables is made. Emulsions with 50 vol. % Nujol-50 vol. °7o water-0.2 % sodium dodecylsulfate (SDS) (on the basis of the aqueous phase) separated oil according to a first order rate law while 50% Nujol-50% water-0.4% SDS emulsions obeyed a zero order rate law. Olive oil-water emulsions with a 50-50 phase volume ratio and 0.2% SDS as emulsifier spearated oil according to a second order rate expression. The present experiments were undertaken to identify what factors cause the difference in the kinetics of demulsification (here defined as separation of bulk oil), and to investigate whether the observed changes could be used to deduce the mechanism of demulsification and to identify the rate-determining step in the different cases.

Accordingly, the rate of ultracentrigufal demulsification of both Nujol and olive oil emulsions was studied as a function of the concentration of SDS with particular attention to its effect on the order of reaction. The effect of added sodium chloride on both the ultracentrifugal stability and the order of reaction was also determined, since added electrolyte would be expected to affect rates dependent on flocculation differently from rates dependent on the rheological properties of an interfacial film of adsorbed emulsifier. The effect of added electrolyte on numerous other parameters which m a y help to determine the rate of demulsification can also be predicted (2), so it was hoped that the present work would show more clearly which of these factors could be important in the rate of the over-all process. MATERIALS AND METHODS The same samples of sodium dodecylsulfate (Eastman Kodak # 5967), Nujol, and olive oil 133

Copyright ~ 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 51, No. I, April 197S

134

H A H N A N D VOLD TABLE I EFFECTOFCONCENTRA~ONoFSDSINTHEEQUILIBRIUM AQUEOUSPHASEONTHE RATE ORDER AND RATECONsTA~ OF DEMu~IFICATIONOF50% NUJOL-50~ WATEREMuLSIONS a

Initial Conc. of SDS, wt. %

Rate Order

0.5 0.4 0.35 0.25 0.20 0.15

0 0 1 1 1 1

Emulsion H111573b

Emulsion H113073o

Conc. of SDS in equil, liquid, moles/l. X 103

Rate Constant

Cone. of SDS in equil, liquid, moles/1. X 103

Rate Constant

12.68 9.64 7.54 5.09 3.23 2.10

0.740 mm3/min 0.725 mm3/min 1.86 X 10-3 rain-x 3.59 X 10-3 min - t 8.19 X 10-3 min -1 14.4 X 10-3 min -1

12.50 9.20 7.30 4.74 3.10 1.85

0.730 mm3/min 0.720 mm3/min 1.79 X 10-3 rain -1 3.45 X 10- 3 rain-I 7.44 X 10-3 rain-1 13.7 X 10-3 rain-1

The critical micelle concentration of a sodium dodecylsulfate solution is 8.1 X 10- a moles/liter (8). b The i n t e f f a d a l area of emulsion Hl11573 is 1.65 X 104 cm2/ml oil. ° The interfacial area of emulsion Hl13073 is 1.80 X 104 cm2/ml oil.

were used as in previous work (1, 3) in this laboratory. The SDS was extracted with ether in a Soxhlet extractor for twenty hours to eliminate any traces of lauryl alcohol present as an impurity. The methods used for preparation and characterization of the stock emulsions (50% Nujol-50% water-0.2% SDS and 50% olive oil-50% water 0.2%-SDS) were the same as described by Vold and Groot (4). Emulsions of the same drop size distribution but with higher concentrations of SDS, or with sodium chloride, were prepared by gently mixing 5 ml. of SDS solution of the requisite concentration with or without added salt with 45 ml. of the stock emulsion. Nujol-water emulsions with 0.15% SDS were prepared by first separating a little of the aqueous phase from the stock emulsion by centrifugation in a Servall angle centrifuge at 5,000 r.p.m., under which conditions no coalescence and separation of oil occurs. 1.25 ml. of aqueous phase separated from a 45 ml. sample of emulsion was then replaced with 6.25 ml. of water. Ultracentrifugation was carried out under the same conditions as in our previous work (1) (39,460 r.p.m, at 20°C). The equilibrium concentration of SD S in the aqueous phase of the emulsion was determined as before by the cetyl pyridinium bromide two phase titration method (4), following exactly the procedure of Vold and Mittal (5). The Journal of Colloid and Interface S~ience, Vol. 51, No. 1. April 1975

specific interracial areas of the emulsions were determined from the adsorption isotherm as described by Vold and Groot (4), but using 54 A2 as the area of the SDS molecule adsorbed at the interface (6). RESULTS

Nujol-water-SDS emulsions. A series of these emulsions, all prepared from the same master batch, and containing from 0.15 to 0.5% initial concentration of SDS and either zero, 0.05, or 0.1 M NaC1, were ultracentrifuge& Two different master batches were used so as to obtain independent duplicate results for each experiment. The kinetic order of separation of oil was determined, as described previously (1), by testing the data for conformity to standard rate equations. Since the volume fraction of emulsion remaining during the ultracentrifugation is relatively large, there is frequently difficulty because plots on the assumption of either first or zero order may appear nearly equally linear. Consequently, before the rate expression was reported as zero order, it was shown by ultracentrifugation in centerpieces with three different cross sections that the rate of separation of oil was directly proportional to the interracial area between bulk oil and residual emulsion, and that the same zero order specific rate constant was obtained independent of the size of the ultra-

135

K I N E T I C S OF D E M U L S I F I C A T I O N lOOt

80

mm 3

60

i 40

20

0

16

32

48

6a

Time in minutes

FIG. 1. Volume of oil separated vs time of ultracentrifugation from 50% Nujol-50% water-0.2% SDS emulsions. A, emulsions in water; O, emulsions in 0.1 M NaC1.

centrifuge cell. Complete details can be found in Mrs. Hahn's dissertation (7). It is apparent from the data given in Table I that the rate order of separation of oil changes when the critical micelle concentration (cmc) of sodium dodecylsulfate (SDS) is reached in the equilibrium aqueous phase of the emulsion.

At concentrations below the cmc, separation follows a first order rate law while at concentrations above the cmc it is a zero order process. The results with samples prepared from the two different stock emulsions are in good agreement, t h a t with the smaller average drop size (Hl13073) being slightly more stable (lower

TABLE I I EFFECT OP ADDED SODIUM CHLORIDE ON THE ULTRACENTRIFUGAL STABILITY OF 5 0 ~ WATER-SDS EMULSIONS Initial Conc. of SDS, wt. %

Cone. of NaCI, moles/ liter

Rate Order

0.4 0.4 0.2 0.2 0.2 0.15 0.15

0 0.1 0 0.05 0.1 0 0.1

0 0 1 1 0 1 1

Cmc," mmoles/ liter

8.1 1.4 8.1 2.25 1.4 8.1 1.4

Emulsion Hll1573b

Emulsion H113073o

Cone.of SDS in equil, liquid, mmoles/liter

Rate Constant

Conc. of SDS in equil, liquid. mmoles/liter

Rate Constant

9.64 8.59 3.23 1.90 1.75 2.10 1.12

0.725 mmS/min 0.439 mmS/min 3.56 X 10-3 min -1 1.19 X 10-3 min -1 0.79 mm3/min 6.25 X 10-3 min -1 2.95 X 10-3 min -1

9.20 8.45 3.10 -1.65 1.85 1.10

0.730 mm'~/min 0.410 mm3/min, 3.23 X 10-3 min -1 -0.75 mm3/min 5.95 X 10-3 min -l 2.35 X 10-3 min -1

Values of the critical micelle concentration are from Ref. (8). b The interfacial area of emulsion Hl11573 is 1.65 X 104 cm*/ml oil. The interracial area of emulsion Hl13073 is 1.80 X 104 cm2/ml oil. Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975

136

H A H N AND VOLD

40 30 =.9. 20 7

10 I 16

32I

I 48

I 64

I

32

I

48

I

64

.'.~ ~® ao a.:':a105

16

i

Time in minutes

FIG. 2. Separation of oil from 50% olive oil-50% water emulsions with varying concentration of SDS.

O, 0.15% SDS; [5, 0.2% SDS; A, 0.4% SDS; ~, 0.6% SDS. values of the rate constant for demulsification) in accord with previous experience (9). The independence of the rate of oil separation above the cmc of the volume fraction of emulsion remaining is consistent with the previous results showing attainment of saturation adsorption and of a close-packed adsorbed monolayer at the cmc (2). The addition of salt to these systems causes some dramatic changes in the behavior, as illustrated in Fig. 1. Here the volume of oil separated is plotted as a function of the time of ultracentrifugation for 50% Nujol-50°-/o water-0.2% SDS emulsions in water and in 0,1 M NaCI solution. The curved line for the aqueous emulsion shows that separation there is not occurring by a zero order process--in fact it is first order. But in the presence of 0.1 M NaC1 a strictly linear relation is found, indicating that the order has there become zero, a conclusion substantiated by data obtained in Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975

centerpieces giving different areas between emulsion and separated oil. The results of a systematic study of this effect are given in Table II. Regardless of whether separation of oil takes place according to a zero or first order rate law, addition of salt increases the stability in all cases. Even more significant, whenever the concentration of added salt becomes such that the equilibrium concentration of SDS in solution exceeds the cmc the rate order changes from one to zero. So here again, when saturation adsorption is reached as the concentration of SD S reaches the cmc, this time by increasing the concentration of indifferent electrolyte rather than that of SDS, demulsification occurs according to a zero order rate law. Olive oil-water-SDS emulsions. The behavior of this polar oil differs qualitatively from that found with Nujol. As appears in Fig. 2, which shows the separation of oil at various concen-

137

K I N E T I C S OF ] 3 E M U L S I F I C A T I O N

1.60

1.50

1.40 I/Vf 1.30

1.20

1.10

1DO 0

16

32

48

64

Time in minutes

FIG. 3. Reciprocal of volume fraction of emulsion remaining in 50% olive oil-50% water-SDS emulsions vs time of ultracentrifugation. O, 0.15% SDS; [~, 0.2% SDS; /% 0.4% SDS; ~ , 0.6% SDS.

trations of SDS as a function of the time in the ultracentrifugal field, in no case does the amount separated vary linearly with time as

would be required for a zero order reaction. Plots of the logarithm of the volume fraction of emulsion remaining against time were also

TABLE

III

EFFECT OF ADDED SODIUM CHLORIDE ON THE ULTRACENTRIFUGALSTABILITYOF 50~o OLIVE OIL-50% WATER-SDS EMULSIONS Initial Conc. of SDS, wt. %

Concl, of NaCI, moles/ liter

Rate Order

Cmc,~ mmoles/ liter

0.15 0.15 0.2 0.2 0.4 0.4 0.6 0.6

0 0.1 0 0.1 0 0.1 0 0.1

2 2 2 2 2 2 2 2

8.1 1.4 8.1 1.4 8.1 1.4 8.1 1.4

Emulsion H011074b

Emulsion H011574c

Conc. of SDS in equil. liquid mmoles/ liter

Rate Constant, %-1 min-l X 10~

Conc. of SDS in equil. liquid, mmoles/ liter

Rate Constant, %-1 rain -1 X l0 s

2.11 1.03 3.01 1.33 7.14 4.26 12.07 9.51

13.0 17.2 8.44 10.5 1.75 2.50 0.64 1.11

2.14 0.96 2.88 1.26 7.40 5.13 12.34 9.47

14.3 18.0 9.2 12.5 2.05 2.75 0.65 1.07

a Values of the critical micelle concentration are from Ref. (8). b The interracial area of emulsion H011074 is 4.91 X 104 cm2/ml oil. o The interfacial area of emulsion H011574 is 4.29 X 104 cm~/ml oil. Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975

138

KINETICS OF DEMULSIFICATION

curved, indicating that the process does not follow a first order rate law. However, as is shown in Fig. 3, good straight lines are obtained at all concentrations of SDS when the reciprocal of the volume fraction of emulsion present is plotted against time. This clearly indicates that in these emulsions the oil is separating according to a second order rate law.

The results obtained are summarized in Table III. In all cases, regardless of whether the equilibrium concentration of SDS is above or below the cmc, separation of oil takes place according to a second order rate law. The rate constant decreases with increasing concentration of SDS, showing that the increase in adsorption of the surfactant at the interface enhances the stability of the emulsion. As in the case of Nujol emulsions, the olive oil emulsions with the larger specific interracial area--and hence the smaller average drop size--separate oil less rapidly than those with the smaller interfacial area. The effect of added sodium chloride on the stability of these emulsions differs qualitatively from its action on Nujol emulsions. In all cases the stability is decreased by the addition

of salt. This is illustrated in Fig. 4, which shows a plot of the reciprocal of the volume fraction of emulsion as a function of time for a 50% olive oil-50v-/o water4).6v-/o SDS emulsion in water and in 0.1 M salt solution. The linearity of the relation shows that the rate order is the same in both cases, and the steeper slope in the salt solution shows that oil is separating more rapidly on addition of electrolyte despite the increased adsorption of SDS caused bv its presence. Qualitatively identical results were found at the other concentrations of SDS, as summarized in Table III, with no change in the order of the reaction at the cmc. That demulsification here follows a second order rate law suggests that its rate is determined by some sort of binary collision process (1, 10, 11) akin to a rate of flocculation. Since added salt decreases the zeta potential of the emulsified oil drops, it would increase the rate of flocculation, and so decrease the stability of the emulsion, as has already been reported experimentally in certain cases (12). DISCUSSION These results are of considerable value for examining whether or not a given possible

1.12

1.10

108 1/Vf 1.06

1.04

--

1.02

1.oc

I 16

I 32

I 48

I 64

I 80

Time in minutes

FIG. 4. Reciprocal of volume fraction of emulsion remaining in 50% olive oil-50% water-0.6% SDS emulsions. O, emulsions in water; 4, emulsions in 0.1 M NaCl. Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975

139

KINETICS OF DEMULSIFICATION TABLE IV SUMMARY OF THE RESULTS OF INCREASING S D S OR N a C 1 CONCENTRATION ON DEMULSlrlCATION OF OLIVE OIL AND NUJOL EMULSIONS IN WATER Variable

50% Nujol-50% Water

50% Olive Oil-50% Water

Increased concentration of SDS

Increased stability up to cmc; thereafter nearly constant. First order rate law below the cmc; zero order above the cmc. 1. Increases stability. 2. First order rate law at concentrations below the cmc; zero order rate law at higher concentrations.

Increased stability presumably becoming nearly constant at the cmc. Second order rate law both above and below the cmc. 1. Decreasesstability. 2. Secondorder rate law at all concentrations of SDS.

Added NaC1

step is rate-determining in the over-all demulsification process, and for indicating the chief site of coalescence, and the mechanism of the process. It should be borne in mind that in the ultracentrifugal field the oil in the emulsion is not present as a suspension of independent drops, but is present in deformed oilcontaining, space-filling polyhedra separated by thin, interlamellar films of water containing dissolved surfactant in equilibrium with an adsorbed film of surfactant on the "drops" (2, 4, 9, 13, 14). Kinetic processes which might determine the over-all rate of separation of bulk oil include (2, 15) : (a) "collision" of oil "drops" (i.e., flocculation); (b) rupture of the film of adsorbed emulsifier at the oil-water interface; (c) rupture of the aqueous lamellae separating the "drops"; (d) drainage of the aqueous phase from the interstitial lamellae; (e) diffusion or sedimentation of the surfactant to or from the oil-water interfaces; (f) rate of transport of larger oil "drops" through the emulsion to the interface between emulsion and separated oil; and (g) penetration of a liquid crystalline phase of the surfactant surrounding the emulsion drop (16). All of these processes will be sensitive to the extent of adsorption of surfactant at the interface, it being here assumed that the rates of adsorption and desorption are more rapid than all the other rates once the surfactant molecule is actually at the interface. The rate of flocculation is determined by the

balance between electrical repulsion and van der Waals attraction, which gives the potential energy between the drops as a function of the distance of separation according to the DLVO theory, and the forces of thermal diffusion, convection and ultracentrigufal acceleration tending to bring them into contact (17). Rupture of the adsorbed film will depend primarily on its viscoelastic properties: viscosity, yield value, and elasticity. The rate of rupture of the aqueous films depends primarily on their thickness, and so may well be determined by the rate of drainage of the aqueous phase. The latter will depend on the "thickness" of the film, which is a complicated function of the forces tending to attract and separate the oil "drops" (2), and may be governed either bv suction at the Plateau borders when the film is sufficiently thin (18), or by viscous flow in the interior of thicker films. The rate of viscous flow depends on the dimensions of the channel, the intrinsic viscosity of the medium, and the magnitude of the accelerating force. Rates of diffusion and sedimentation depend on density differences, molecular and micellar weights, temperature, and presence or absence of swamping electrolyte. The rate of transport of larger drops, due to coalescence within the emulsion phase, to the interface with separated bulk oil will depend on the density and viscosity of the oil, the resistance to deformation of the distorted "drops" in the flocculated emulsion, and the magnitude of the Journal of Colloid and Interface Science, Vol. 51, No. 1, April 19~5

140

HAHN AND VOLD

centrifugal force. Almost all these possible rate-determining steps will be affected by adsorption of SDS at the interface, and resultant changes in the mechanical or electrical properties of the adsorbed film. A promising approach for attempting to determine which of these processes involved in demulsification is likely to be rate-determining for a given emulsion under specified conditions is to consider the effect of added electrolyte on the rate law and on the rate of separation of bulk oil, since its effect on the individual mechanistic steps can be at least qualitatively predicted. The experimental facts with which conjectures must comply are assembled in Table IV. It should be noted that with both Nujol and olive oil emulsions addition of salt markedly increases adsorption of SDS at the oil-water interface, as shown in Tables II and III by the decrease of the SDS concentration in the equilibrium liquid resulting from addition of salt to the system. The qualitatively different behavior of the emulsions with the two oils must be due to differences in the orientation and packing of the adsorbed SDS at the interface between water and hydrocarbon (Nujol) as contrasted with the interface between water and another hydroxylic polar liquid (olive oil), as well as to possible differences in solubility. As has already been mentioned, a zero order rate law indicates that coalescence at the interface between bulk oil and emulsion is the rate-determining step, a first order rate law that the intrinsic rate of coalescence between oil drops within the body of the emulsions-contingent on the probability of film-breaking --is the slowest step, and a second order rate law that the collision rate between the drops-rate of flocculation---is the determinant of the over-all rate of appearance of bulk oil. In the case of Nujol emulsions below the cmc of SDS there is bare interface between oil and water (2), at which coalescence apparently occurs within the body of the emulsion phase, but at a slower rate than the subsequent transport of the oil to the oil-emulsion interface and its coalescence there with bulk oil. Above the cmc, Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975

where the "drops" are coated by a close-packed monolayer of adsorbed SDS, coalescence apparently does not occur within the bulk of the emulsion, but only at the bulk oil-emulsion interface, since the rate of appearance of oil is directly proportional to the area of this interface and independent of the amount of residual emulsion. If the average drop size had changed due to coalescence within the emulsion phase this could scarcely have been the case, since the rate of separation of oil is known to increase with increasing drop size (9) whereas experimentally it remains constant during disappearance of half or more of the layer of creamed emulsion. With olive oil emulsions, contrariwise, the over-all rate is determined by the rate of approach of drops as shown by its obedience to a second order rate law. In the flocculated state in which the emulsion is present during ultracentrifugation while these measurements are being made, this process can bear little resemblance to a model involving collisions between independent drops, which underlies the usual theoretical explanations of flocculation (10, 17). Conceivably it can relate to the rate of approach of oil-containing polyhedra due to drainage of the interstitial aqueous phase which process in these emulsions may be slower than the rate of rupture of either such films or of emulsifier film coating the oil "drops." If this is the case no change in the mechanism of the process would necessarily be expected at the cmc where saturation adsorption is reached, which is in accord with the observations. The effect of added salt on the over-all rate of oil separation from emulsions of the two oils agrees with this interpretation. In both cases adsorption of SDS is increased. With Nujol this results in attainment of saturation adsorption of SDS at a lower concentration, and formation of an adsorbed layer of SDS with a lower probability of rupture, due to possible closer packing because of reduction of electrostatic repulsion between the charged heads of the dodecylsulfate molecules in the film by the added electrolyte, and a decrease in the rate of appearance of oil, which may here

KINETICS OF DEMULSIFICATION be governed by the rate of rupture of the adsorbed film. With olive oil emulsions this same reduction in the zeta potential on the oil, although it may increase film strength, decreases the electrostatic force opposing collision of drops, and so results in an increase in the rate of appearance of free oil, since it increases the rate of flocculation. It seems probable that the rate of diffusion or sedimentation of SDS molecules or micelles is more rapid than the rates of the other processes involved in demulsification. As separation of oil occurs there must be an instantaneous increase in the local concentration of SDS in the aqueous phase due to the decrease in the area of the oil-water interface. If the SDS were not removed from the site of coalescence very rapidly the rate of separation of oil at SDS concentrations below the cmc would decrease rapidly with time, since it has been shown to be very concentration-dependent with Nujol emulsions (4), and this does not occur. Added electrolyte would have little effect on the sedimentation or diffusion of simple dodecylsulfate ions, but would increase the rate of sedimentation of micelles and decrease their rate of diffusion. It has already been shown (2) that such an explanation cannot account for the effect of salt on the rate of separation of oil from Nujol emulsions. It is difficult to prove or disprove the hypothesis (16) that the existence of a liquid crystalline phase around the emulsion drops is responsible for a high degree of stability. The concentrations are such that liquid crystalline phases cannot exist in the bulk system, although they may possibly form because of enhanced concentration in the vicinity of the drops. However, the optical evidence of anisotropy in the published work can also be accounted for by orientation of molecules at the interface by cybotaxis. It is not possible from the present evidence alone to decide unambiguously under what conditions rate of drainage of the interstitial aqueous film is the rate-determining step, and where rupture of an adsorbed monolayer of surfactant is the more important process.

141

Addition of salt, by reducing the electrostatic repulsion between oil drops, would be expected to decrease the width of the channels through which drainage of the aqueous lamellae occurs, thus slowing its rate and increasing the stability of the emulsion if this were the ratedetermining step. However, added electrolyte would also be expected to decrease the viscosity of the solution (except in the unlikely event that it induced gelation), which would increase the rate of drainage and so have an opposite effect on the stability. Further evidence is needed to distinguish between these possibilities. There has been much recent effort devoted to investigating the importance of interfacial rheological parameters in determining emulsion stability (19, 20, 21). Since added salt increases the adsorption of SDS, resulting in closer packing in the interfacial film, it would be expected to increase surface viscosity and elasticity, and should therefore increase emulsion stability where rupture of the adsorbed layer of surfactant is the most important factor. This appears to be the case with the Nujol emulsions. That salt has the opposite effect on olive oil emulsions, decreasing their stability, is consistent with the conclusion, based on the rate order of separation of oil, that with these emulsions the rate-determining step involves the rate of approach of drops rather than that of film-breaking. REFERENCES 1. VOLB, R. D., AND HAHN, A. U., ACS Symposium Series, "Colloidal Dispersions and Micellar Behavior," in press. 2. VOLD, R. D., AND GROOT, R. C., J. Colloid Interface Sci. 19, 384 (1964). 3. VOLD, R. D., AND MITTAL, K. L., J. Colloid Interface Sci. 38, 451 (1972). 4. VOLD,R. D., AND GROOT,R. C., J. Phys. Chem.

66, 1969 (1962). 5. VOLD,R. D., ANDMITTAI.,K. L., Anal. Chem. 44, 849 (1972). 6. VOLD,R. D., GROOT,R. C., Am) OVERBEEK, J. TH. G., Abstracts of Papers presented at the 153rd American Chemical Society Meeting, Miami Beach, Florida, 1967. 7. HAHN, A. U., Kinetic Studies of Ultracentrifugal Journal of Colloid and Interface Science, Vol. 51, No. t, April 1975

142

8. 9. 10. 11.

12. 13.

HAHN AND VOLD Demulsificafion, Ph.D. dissertation, University of Southern California, Los Angeles, California, 1974. WILLIAMS, R. J., PHILLIPS, J. N., ANn MYSELS, K. J., Trans. Faraday Soc. 51, 728 (1955). VOLD, R. D., AND GROOT, R. C., J. Phys. Chem. 68, 3477 (1964). VAN DEN TE~PEL, M., Rec. Tray. Chim. Pays-Bas T72, 433 (1953). VAN DEN TE~FEL, M., "Proceedings of the Second International Congress on Surface Activity," Vol. 1, p. 439. Butterworth's Scientifc Publications, London, 1957. VAN DEN TEMPEL, M., Rec. Tray. Chim. Pays-Bas T72, 442 (1953). REgFELD, S. J., J. Phys. Cltem. 66, 1966 (1962).

Journal of Colloid and Interface .~cience. Vol. 51. No. l, April 1975

14. GARRETT, E. R., J. Pharm. Sci. 51, 35 (1962). 15. VOLD, R. D., AND MITTAL, K. L., J. Soc. Cosmet. Chem. 23, 171 (1972). 16. FRIBERG,S., J. Colloid Interface Sci. 37, 291 (1971). 17. VERW~.Y, E. J. W., AND OVERBEEK, J. TI~. G., "Theory of the Stability of Lyophobic Colloids." Elsevier, Amsterdam, 1948; KI~UYT, H. R., "Colloid Science," Vol. 1, pp. 245, 285. Elsevier, Amsterdam, 1952. 18. BIKERMAN, J. J., "Foams," p. 104. Reinhold, New York, 1953. 19. BECnER, P., Amer. Perfum. 77, 21 (July 1962). 20. SRIVASTAVA,S. N., AND HA¥DON, D. A., Proc. Int. Congr. Surface Activ. 4th, 2, 122 (1967). 21. BOYD, J., PARKINSON, C, AND SHERMAN, P., J. Colloid Interface Sci. 41, 359 (1972).