Stability of macroemulsions

Co&ids and Surfaces, 29 (1988) 53-69 Elsevier Science Publishers B.V., Amsterdam -

53 Printed in The Netherlands

Stability of Macroemulsions RANDY D. HAZLETT Mobil Research and Development Corp., Dallas Research Laboratories, 13777 Midway Road, Dallas, TX 75244 (U.S.A.) ROBERT S. SCHECHTER* Department of Chemical Engineering, (U.S.A.)

The University of Texas at Austin, Austin, TX 78712

(Received 27 April 1986; accepted 1 April 1987)

ABSTRACT The rupture of the thin films separating emulsion droplets has long been considered to be triggered by the long-range, attractive van der Waals forces; however, this study conducted in a shearfield coalescer shows that systems containing surfactant may, in some cases, yield trends contrary to predictions based on this hypothesis. These trends can be understood in terms of a new mechanism leading to film rupture which is called here percolation-enhanced coalescence. Those regimes in which this new mechanism dominates can be determined based on simple equilibrium phase behavior studies of the surfactant, oil, and water mixtures using the percolation mode1 proposed here.

INTRODUCTION

Macroemulsions are thermodynamically unstable. Given sufficient time, the dispersed droplets will coalesce and phase separate. The coalescence process can usefully be divided into three separate stages. First, two drops must collide. Brownian motion or externally applied fields (gravity, shear, electrical, etc.) are all mechanisms which can bring two drops into contact. These mechanisms and their mathematical representation are reasonably well understood. The second phase of a coalescence episode is the thinning of the film separating the two droplets. Again, hydrodynamics plays an essential role. The variables of importance are, for example, the fluid viscosities, interfacial tension, interfacial tension gradients, the surface viscosities, etc. which are all macroscopic. The crucial issue generally addressed is the rate at which the film between two colliding drops thins. If this rate is sufficiently fast, then coalescence may take place before the encounter runs its course and the two drops again separate. *To whom all correspondence should be addressed.

0166-6622/88/$03.50

0 1988 Elsevier Science Publishers B.V.

54

An important question relates to the distance of the nearest approach necessary to bring about film rupture. At this point, it is thought that the molecular forces come into play. The Derjaguin, Landau, Verwey, and Overbeek ( DLVO ) theory [ 11, which has proven to be enormously successful in dealing with flocculation, is also generally invoked in the consideration of droplet coalescence. This theory portrays the interaction between two drops separated by a thin film as a competition between the repulsive double layer forces and the attractive long-range van der Waals forces. Thus, changes in the system which tend to reduce the double layer interaction also, according to the theory, tend to promote coalescence or flocculation. This trend seems to be quite generally satisfied for flocculation; however, in the case of emulsion stability, certain contradictions have appeared. Baldauf et al. [ 21 have observed that under changing conditions which promote increased surfactant concentrations at the oil/water interface, thereby increasing the double layer repulsion, the rate of coalescence increases markedly rather than decreases as would be expected from the DLVO theory. Similar observations have been reported by Vinatieri [ 31 and Saito and Shinoda [ 41. An interesting and important aspect of these studies is the profound relationship which exists between the stability of macroemulsions, microemulsion phase behavior [ 561, and the phase-inversion temperature. It is this relationship which is to be explored in this paper. It is proposed here that, under certain conditions, macroemulsion stability (film rupturing) is not determined by the DLVO theory but is related to the composition of the continuous phase. When the continuous phase surrounding the dispersed phase contains swollen micelles or is a microemulsion, then thin films separating the drops can rupture at larger distances of separation than predicted by the DLVO theory. In this phenomenon, called here percolation-enhanced coalescence, the submicroscopic structures which exist as a part of the continuous phase provide large scale pathways for bulk transfer between corresponding macroemulsion droplets. This concept is illustrated by Fig. 1. Shown are two drops in proximity of each other. The film separating them is a micellar solution, and the swollen micelles are depicted as small spheres distributed throughout the continuous phase. According to our concept, film thinning occurs until the film becomes unstable because of the long-range van der Waals forces or because the swollen micellar spheres form a continuous percolating network from one macroemulsion droplet to the other. In either case, coalescence is a catastrophic event characterized by the sudden merging of the two drops. This paper provides experimental evidence to support the existence of percolation-enhanced coalescence. It is seen that coalescence rates can increase by two orders of magnitude when this mechanism is dominant. Percolation theory provides the foundation on which a fundamental understanding of this mode of coalescence is based. Pertinent results from the percolation theory are

55

Fig. 1. Destabilization of thin films by percolating microemulsions.

cited here and are used to identify hanced coalescence dominates.

those

regions for which percolation-en-

THEORETICAL CONSIDERATIONS

Microemulsions Since submicroscopic structures less then 500 A in diameter (often much less), which exist in the continuous phase surrounding the much larger drops ( > 0.5 pm) of dispersed phase, are the essential focus of this work, it is necessary to consider them briefly. Because the drop sizes are small, solutions containing them are sometimes called microemulsions. According to Reed and Healy [ 51, microemulsions are “thermodynamically stable, translucent micellar solutions of oil and water that may contain electrolyte and one or more The basic submicroscopic structure amphiphilic compounds or surfactants”.

56

of microemulsions is the focus of much past and present research. Many researchers have shown the presence of multiple structural transitions with the change in overall concentration of one or more of the components. The environment of favorable microemulsion formation can be manipulated with any one of a multitude of variables: electrolyte concentration, temperature, surfactant structure, hydrocarbon, and cosurfactant concentration. The system variables which govern the microemulsion environment may be modeled in terms of hydrophile-lipophile balance (HLB [ 61) . At high HLB, the surfactant prefers an aqueous external environment; therefore, one observes microemulsion in brine. On the other hand, low HLB favors microemulsion in oil formation. At intermediate values, microemulsion which can neither be said to be oil continuous nor aqueous continuous may be in equilibrium with excess brine and oil phases. Bicontinuous structures have been proposed to describe these middle-phase microemulsions [ 71. However, perhaps these systems may best be modeled through the fluctuation theory [ 81, where time average probabilities may be calculated for coexistence of oil and aqueous-continuous domains. By changing the surfactant’s environment, for example, by varying the cosurfactant concentration, the system can be transferred from a microemulsion which is water continuous and which can exist in equilibrium with an excess oil phase (Type I) to systems in which the microemulsion exists in equilibrium with an aqueous phase (Type II). By blending two conjugate phases together, a macroemulsion is created. The microemulsion phase is generally the continuous phase irrespective of the volumetric proportions blended [91. Given disproportionate volumes of microemulsion and conjugate phases which favor the microemulsion phase to be the dispersed phase, multiple emulsions have been observed to form where the dispersed microemulsion phase also contains macroemulsion droplets of the conjugate phase. The rate of coalescence can thereby be studied for a variety of systems: o/microemulsion, w/microemulsion, and for the case of a middle-phase system which consists of three phases, the coalesence of four different systems (o/w, w/o, o/microemulsion, and w/microemulsion) can all be studied. Because the coalescence rates are slowest for those systems in which the surfactant phase is the continuous one, only systems for which this condition is satisfied are studied here, thereby reducing the number of experiments. Thus, for the w/microemulsion conjugate pair, the coalescence of water drops in microemulsion has been studied. Percolation

There colation or lattice neighbor

is much evidence in the literature that microemulsions exhibit a perthreshold [lo]. In percolation modeling, sites composing a medium are randomly assigned values, usually on a binary system. Nearest sites of equal value define bonds between sites. Sets of connecting

57

bonds define clusters. On an occupation basis, as the probability of occupation, the probability of larger cluster formation also increases. Above some critical occupation probability,p,, there exists a nonzero probability that a randomly chosen site will belong to an infinite cluster which will percolate the lattice. The cluster probabilities are lattice dependent and are usually obtained by Monte Carlo techniques [ 111 or by series expansion [ 12,131. Percolation probabilities are often defined on infinite lattices free from boundary effects. Many Monte Carlo simulation techniques apply periodic boundary conditions to avoid end effects. Kirkpatrick [ 141 studied the effect of lattice size on the percolation probability by Monte Carlo methods. Chandler et al. [ 151 accounted for finite-size effects for percolation models of porous media. Finite-size restrictions on the lattice serve to depress the percolation threshold. This will prove to be important here because the thin films considered have a thickness of the order of the size of a lattice spacing. It is reasonable to assert that the correlation length, which is some measure of the connectivity of the lattice, be restricted to values smaller than the physical limits of the system. If, therefore, we define a film thickness, L, to be

p, increases,

(1)

LEAN

where A is the lattice spacing and N is the number of (d- 1) -dimensional infinite lattice layers; or equivalently for lattices finite in only one dimension, the number of nodes in the finite direction, by analogy with Fisher [ 161, one expects a shift in the critical percolation probability to obey the scaling relation pc

(4

_pc

(N) =AN-‘/”

where pccm) is the infinite system percolation threshold, pccN’ is the finite system percolation threshold, and Yis a critical exponent. Hosen et al. [ 171 report values of v=O.97?0.11 and a proportionality constant of 0.32 from Monte Carlo simulation on a simple cubic lattice for this fractional dimension or “layer cake” percolation problem. These results appear particularly pertinent with regard to percolation-enhanced coalescence. A lattice model may be modified to describe a collection of randomly distributed d-dimensional discs inscribed about sites in the lattice. Although the percolation threshold is lattice dependent, the critical area or volume appears to occur at approximately a constant value ( 181. For three-dimensional models in which the diameter of the sphere equals the lattice spacing, the critical volume fraction, v~, is approximately 0.16. The resulting clusters are composed of touching spheres. If the inscribed radius is much larger than one-half of the lattice spacing, the critical volume to establish the resulting infinite chain of overlapping spheres is 0.29. These two critical volumes are of interest in modeling percolation of microemulsion solutions. An expression analogous to Eqn (2) in terms of volume can correct for finite-size shifts in the apparent percolation threshold.

Percolation models described previously apply to systems of noninteracting spheres. The interaction potential for microemulsion droplets has been studied and the hard-sphere model found to be inadequate [ 191. The model can be improved by including an interaction distance. Following Huh [ 201, an effective volume fraction, v, defined as rl= (I+A)3@me

(3)

is introduced. Here 1 is b/a where b is half the minimum interaction distance between drops, a is the drop radius, and &,e is the volume fraction of the dispersed micellar pseudophase. The interaction distance is assumed to be of the form b = cl /K, o/w microemulsion b=cpam1/21,

w/o microemulsion

(4)

where l/~ is the Debye thickness, cy is Flory’s expansion parameter, m is the number of segments in the surfactant lipophile chain, 1 is the segment length, and ci and c2 are empirical constants. Huh [ 201 has developed an expression for the free energy as a function of q and A starting from the osmotic pressure equation of state for hard spheres experiencing van der Waals attraction. It is proposed A= A( [ electrolyte],

[ cosurfactant 3, T, . .. )

(5)

In effect, one varies the effective volume fraction of microemulsion droplets and phase behavior concurrently when any one of these variables is changed. It is the effective volume fraction which determines the percolation limit, not the actual volume fraction. Furthermore, the critical volume fraction found for hard, noninteracting spheres would be expected to be reduced if the spheres attract one another. Thus, the presence of a sphere at a lattice point will increase the probability that a second sphere will be located at a neighboring point. We are not aware of a comprehensive study of percolation in the presence of attractive forces; however, it may be anticipated that the actual value of the volumetric percolation limit measured for microemulsion droplets will be smaller than vc found for hard, noninteracting spheres. EXPERIMENTAL RESULTS

Microemulsion system Cazabat et al. [ 211 reported near critical behavior in microemulsion systems composed of brine, toluene, n-butanol, and sodium dodecyl sulfate (SDS) ; and these have been selected for study. Evidence of critical phenomena was observed near the transition from a middle-phase to an upper-phase microemulsion, but data at the lower salinity transition from a middle- to a lower-phase

59

microemulsion exhibit a much less pronounced effect indicating the transition to be removed from the critical point. To better understand the various mechanisms which can contribute to increased coalescence and their relationship to critical phenomena, it is desirable to firmly establish the critical endpoints. The method used in locating critical tie lines was based upon the assumption of interchangeability of the variables: salinity, alcohol concentration, and temperature [ 221. Samples near the phase boundary were prepared with different surfactant concentrations. Since temperature was the easiest and most accurately controlled variable, the phase volumes were recorded as a function of temperature. From the trends in the phase volume-temperature relationships near the phase-transition temperature, critical tie lines were quickly identified [ 23,241. The studies indicate the intersection of the two critical tie lines to be at the mix point satisfying the surfactant requirements at each phase transition of 0.02 g SDS/cm3 toluene and 0.008 g SDS/ cm3 brine. A plot of the relative phase volume fraction as a function of the cosurfactant (1-butanol) concentration is provided in Fig. 2 for an overall mix point slightly below the intersection of the two critical tie lines. Electrical conductivity The electrical conductivities have been measured using a conductivity bridge with platinum electrodes. These measurements are shown in Fig. 3 as a function of the overall butanol concentration. In the middle-phase region, three conductivities are reported: the oil, the microemulsion, and the water. As the alcohol concentration is increased, the microemulsion is found in equilibrium with brine. It can be seen from these experiments that the electrical conductivity for the oil-rich microemulsion begins its rapid climb at an alcohol concentration noted as the percolation threshold. At this point a continuous pathway of water is thought to exist extending from one electrode to the other. This corresponds to the infinite-system threshold percolation limitpCCa’. Note also that a second increase is seen in Fig. 3 near the critical phase boundary. Lagues and Taupin [lo]suggest that this denotes the onset of phase inversion. It is of interest to note the volume fraction of the swollen micellar pseudophase at the percolation threshold. These volumes are shown in Fig. 4. It is seen that the percolation threshold has been reached when the volume fraction of the inverted micellar phase is somewhat less than 11%. This value is smaller than the theoretical one for hard spheres which is expected in accordance with our previous discussion. Emulsion stability Most studies characterizing the stability of emulsions compare relaxation times defined, for example, as that time required for one-half of the dispersed

60

e #

‘:

z

d

SALINTY 7551 g NoCI/ dl SDS : Toluene 0.019 g /cc SDS : Brine 0.0076 g/ cc TEMPERATURE

z 2 ?I z

30.0

Brine

‘C

“, . d

-3.20

2.40

2.60

2. 60

3. DO

VOLUflE PERCENT

3. 20

3. 40

60

I-EUTRNOL

Fig. 2. Phase behavior with cosurfactant addition.

AQUEOUS PHASE

--_

2 PHASE

REGION

:

I-BUTANOL

OILPHASE

PERCOLATION THRESHOLD 1 o. 01 0.10

CONCENTRATION

0.15

4 c>.55

DIFFERENCE, CBUOH-C&O,,

Fig. 3. Evidence of percolation in microemulsions.

phase volume to coalesce and to separate. This relaxation time for the system considered here is shown in Fig. 5. These results are observed when equal volumes of two pre-equilibriated phases are vigorously mixed in graduated tubes. Despite the lack of controllability of the initial drop-size distribution which this procedure entails, the result of a given experiment is reproducible to a reasonable degree. Furthermore, the trends shown in Fig. 5 are similar to those found by others [ 2,3,25].

61

7.551g NaCl/dl Brine 0.020g SDSkcToluene 0.008g SDS/ccBrine T= 3O.O"C

3: 35

3: 40

3: 45

VOLUME PERCENT 1-BUTANOL Fig. 4. Micellar pseudophase

volume fraction.

8

VOLUME Fig. 5. Qualitative

PERCENT

1 -BUTANOL

emulsion stability

in microemulsion

systems.

The position of the two critical points are represented by the dashed lines in Fig. 5. At intermediate alcohol concentrations between the two critical points, three conjugate phases are observed; and there are, therefore, three different two-phase combinations which can be characterized by a relaxation time. It is noted that emulsion stability decreases rapidly near the critical boundaries. This observation has been reported previously. It might be speculated that the rapid coalescence observed to initiate near

62

the critical tie lines is due to a mechanism directly attributable to critical phenomena. This is not, however, believed to be the case. First of all, as shown by Fig. 5, emulsions between near critical phases and the noncritical phase near a critical endpoint exhibit rapid coalescence. Secondly, Hazlett and Schechter have shown that emulsions created from near critical systems containing no surfactant do not become more unstable as the critical point is approached ]261. Modified stability ratio The relaxation times shown in Fig. 5 are interpreted in terms of droplet coalescence rates; but since the process of creating the emulsion is not well controlled and since the physical properties of the phases, especially the microemulsion, are sensitive to the alcohol concentration, there are many factors in addition to the coalescence rate which contribute to the relaxation time. Other experiments probe more directly into the film drainage process. Wasan et al. [ 27,281 have studied emulsions based on photographic methods and Flummerfelt et al. [ 291 measured coalescence times by bringing two drops together in an inclined spinning-drop tensiometer. In the latter experiments, the force causing coalescence and the surface area of contact are well controlled. These experiments revealed that middle-phase systems coalesed rapidly in agreement with the small relaxation times shown in Fig. 5. To better elucidate the coalescence process, especially near the boundaries of the three-phase region, the rates of coalescence have been measured in the annular region between a rotating inner cylinder and a fixed outer cylinder. The geometry yields a region in which the shear rate is constant and the number of drop-drop collisions per unit of time can be calculated. The details of the experimental apparatus are given elsewhere [ 301. The procedure entails creating a drop-size distribution in a continuous phase containing a small volume fraction (less than 1% ) of the dispersed phase by spinning the inner cylinder at a rotational rate which exceeds the limit of Taylor stability. The rotation speed is then reduced and the drop-size distribution measured based on differential interference photomicrographs using a method of computer analysis developed by Hazlett et al. [ 311. The typical results are shown in Fig. 6. The plots shown in Fig. 6 are straight lines when the distribution is lognormal. Although, as seen, some deviation from straight line behavior is detectable, the data are represented satisfactorily by the two parameter probability density function In”(E) f(x) =&

exp

---2 ln2a {

1

(6)

63

18

a1O

0 t = 0.0 min 0 b * + x

9

0.01

1.0

16.0

CUMULATIVE

50.0

84

t = 2.0 min t =5.0 min t = 8.0 min t=ll.Omin 14.0 min

t= 0

PERCENT

99.0

99

99

UNDERSIZE

Fig. 6. Evolution of the drop-size distribution.

where x is the droplet radius, p is the geometric mean radius, and o is the standard deviation. By fitting the data, p and o can be determined as a function of time. The volumetric mean, x,, is determined from the well-known relationship between moments for this distribution lnx,=In~+1.51n2a

(7)

Given x, and the volume fraction of the dispersed phase, the number concentration is, therefore, obtained. The decay in the number concentration is then found as a function of time. The data show that the log-normal distribution tends to persist. This would imply that the coalescence process tends to be self-preserving. Based on this hypothesis, it can be shown that dlnm, p= dz where

-i

(m, +3mo-2~gm,13/gm2-2/9)

64

rn(J =-

MO NO Ml

ml==

M2

mz=jQ-$7

&LY_t nw “g =;

7cx,3(o)

In these equations, Mk are the moments of the log-normal distribution given by Eqn (6) and mk are the dimensionless moments. NO and xV3(0) are the initial values of the number of droplets and the volumetric mean drop radius, respectively. Based on the experimental results, these dimensionless moments are measured at the initial time. Thus, from the measured initial slope dln m,/dr where t is the time, the value of CO,the modified stability ratio, is calculated. The quantities r, the shear rate, and @,the volume fraction of the dispersed phase are experimentally adjustable parameters. A detailed analysis is presented elsewhere [ 261. The decay in number concentration corresponding to the data in Fig. 6 is provided in Fig. 7 along with the log-normally preserving moment solution. These results indicate close agreement between the experimental results and numerical simulation of the shear-field coalescence process. The modified stability ratio, o, is a measure of the number of collisions to yield a single coalescence event. The quantity o has been termed “modified” here because hydrodynamic effects which cause drops in a position to collide to bypass one another and any effect of the drop radius on the collision process in a shear field have all been included in o. Figure 8 shows the modified stability ratio plotted as a function of the alcohol concentration. Again, the dashedlines represent the concentrations at which a middle-phase microemulsion forms ( also shown in Fig. 2 ) . All of the data shown have been obtained at a constant r because the duration of an interdroplet contact is inversely proportional to r. Thus, variations in the stability ratio are entirely due to changes in the rates of film rupture. There are several features of Fig. 8 to be noted. The most striking result is that the trends shown, more or less, confirm the simple relaxation time experiments shown in Fig. 5. The modified stability ratio decreases markedly as the critical boundaries are crossed; however, there is an apparent continuity of the

65

Salinity 7.551 g NaCl/dl Brine SDS: Toluene ,020 g/cc SDS: Brine .006Ogkc 2.60 VOL% 143utanol Temperature 30.0% q5- 2.00E-03 r= 2.64E+03/min

00

ioo

s:oo

o:oo

Ii.

00

TIME, MINUTES Fig. 7. Experimental and log-normally preserving solutions for the decay in total particle concentration. (Line denotes numerical solution with initial conditions of Fig. 6 and o = 110.)

10'

10"

SALINITY

2’ 75 VOLUM

2551

g

3: DO PERCENT

NaCl/dl

3: 7.1

Brine

3: so

14JTANOL

Fig. 8. C!oalescence in microemulsion systems (r = 2800 min - 1) .

modified stability ratio across these critical transitions. This tends to substantiate the contention that critical phenomena are not the source of the increased rates of film rupture. At high alcohol concentrations, surfactant partitions preferentially into the hydrocarbon phase. As cosurfactant concentration is reduced, surfactant interfacial activity is increased and more stable emulsions are produced in full agreement with the DLVO theory. However, as seen in Fig. 8, further increase in surfactant interfacial activity results in a decreased modified stability ratio. It is proposed that this decrease, which contradicts predictions based on the

66

DLVO theory, is due to percolation-enhanced be further developed.

coalescence.

This approach

can

MODEL DEVELOPMENT

A distribution of coalescence times is observed when drops come into contact. This stochastic quantity may be thought to be divided into two parts as follows t coal

=

tft

‘Prupture [ 0

( tft ) I

(9)

where tft is the time required for the film separating two interacting drops to thin to an interdroplet distance L and prupture is the probability of thin film rupture at this distance L.The quantity tft includes hydrodynamic effects such as the relative velocity between the two drops, surface tension gradients, fluid viscosities, etc. The mechanisms contributing to tft have been modeled by Radoev et al. [ 321 for the case of identical drops. The additional assumptions limiting this analysis have been discussed [ 331. The most difficult to justify would seem to be that of parallel plane geometry, a constant force, and the limitation to small variations of surfactant concentration. Despite these evident limitations, the model does include the essential features of the thinning process and does provide a quantitative relationship between tft and L.A part of the stochastic nature of the collision process arises because tft depends on variables which change from interaction to interaction. A more complex issue involves the factors which determine prupture. The accepted approach is to examine the stability of a thin film subjected to those forces accounted for by the DLVO theory [ 341.To a first approximation, the outcome of the analysis is a critical film thickness, L,.At this film thickness, perturbations in the bounding surfaces of the thin layer grow spontaneously under the influence of the attractive van der Waals forces, and the film ruptures. We assert that a second, entirely different mechanism may lead to coalescence for film thicknesses larger than L,.This new mechanism presumes that film rupture takes place when a percolation pathway exists across the film. This concept can be given quantitative substance provided a lattice with spacing, d, equal to the size of microemulsion droplets is considered. Bellocq et al. [ 191 review experimental results on microemulsion structures as determined from light scattering, small angle neutron scattering, diffusion, and ultracentrifugation. Measured radii fall in the range of 30 to 100 A. Interfacial thicknesses were found to account for approximately 9 to 12 A of these values. If the microemulsion is modeled as a collection of hard spheres distributed upon this lattice in the thin film, then a critical volume fraction, vC,exists such that at a film thickness, L,,a percolation pathway has a probability of existing. Since by definition L, is also the critical film thickness determined by DLVO

67

IO”

IO’ LJCZ(a

Fig. 9. Controlling-mechanism

IO' t

b)l regimes on a simple cubic lattice.

theory, both percolation-enhanced coalescence and van der Waals induced film rupture become equally probable mechanisms. For r] < vC,the DLVO mechanism prevails. To evaluate qC,Eqn (2)) relating to a finite-sized lattice, applies. An analogous expression in terms of volume fraction can be written as follows:

rk

=sP) -A’

(2,,:;i,)-1’”

(10)

where ylC(Oo)is the percolation volume fraction corresponding to an infinite lattice and 2a (1 +A) is the effective diameter of a microemulsion droplet. Estimates for Q (a), A’, and Y are 0.16, 0.32, and 0.97, respectively. Very rapid coalescence is predicted for 7~. qCCrn)since clusters practically unlimited in size may exist. Since near the central regions between the two boundaries of the middle-phase region (see Fig. 2) the volume fraction of the oil and water phases exceed qCCco),rapid coalesce is predicted and observed. Equation (10) can be used to delineate those conditions for which the two parallel mechanisms dominate. Figure 9 shows such a graph. In viewing this figure, it should be recognized that typical values of L, range from 300 to 600 A while a nominal drop diameter for microemulsions may be on the order of 100 A. Values of L,/2a(l +A) may range from 5 to 15 and q, varies from 0.10 to larger values shown by Fig. 9.

68 RESULTS AND DISCUSSION

Figure 4 shows the volume fraction of the micellar phase as a function of the alcohol concentration. The percolation threshold, as determined by the electrical conductivity of the solution (see Fig. 3)) is denoted by ccp. The volume fraction of water which corresponds to &(O”) is approximately 0.11. It is seen in Fig. 8 that the maximum value of the modified stability ratio occurs at an alcohol concentration somewhat larger than ccp where the value of @is somewhat less than the critical value. Since the maximum represents the transition from a rupture process dominanted by the long-range van der Waals forces to a percolation controlled regime, a value of v < v,(~) is anticipated based on the model. The development presented here also accounts for the rapid breaking of emulsions at the phase inversion temperature noted by Saito and Shinoda [ 41. They stated that this instability “is due to the difficulty of maintaining the integrity of a thin film which can neither be characterized as water nor oil continuous” (middle-phase microemulsion). This view is consistent with the concepts developed here. Emulsion stability is, according to the view developed in this paper, intimately related to the microstructure which exists in the continuous phase surrounding emulsion droplets. This microstructure arises because surfactant molecules tend to form micelles Emulsion stability is related to this same microstructure. When liquid crystals rather than fluid micellar interfaces are formed by the surfactant in the continuous phase;,quite stable emulsions have been observed [ 28,291. This emulsion stability is not predictable based on the DLVO theory. Thus, one can say that highly stable or unstable emulsions are due to the microstructure arising because of surfactant aggregation in the continuous phase and not at all related to the influence of the long-range van der Waals forces on this film stability. ACKNOWLEDGEMENTS

This research was supported by a grant from the National Science Foundation, Grant No CPE-7813315. Dr Schechter holds the Getty Oil Company Centennial Chair in Petroleum Engineering.

REFERENCES 1 2 3 4

R.H. Ottewill, Colloid Science, Vol. 1, The Chemical Society, London, 1973, Ch. 5. L.M. Baldauf, R.S. Schechter and W.N. Wade, J. Colloid Interface Sci., 85 (1982) 187. J.E. Vinatieri, Sot. Pet. Eng. J., 20 (1980) 402. H. Saito and K. Shinoda, J. Colloid Interface Sci., 32 (1970) 647.

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5

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