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Langmuir 1998, 14, 2702-2706
Some Stability Criteria for Double Emulsions M.-F. Ficheux, L. Bonakdar, F. Leal-Calderon,* and J. Bibette Centre de Recherche Paul Pascal, Av. A. Schweitzer, F-33600 Pessac, France Received November 19, 1997. In Final Form: March 5, 1998 Double W/O/W emulsions consist in an inverse emulsion which is dispersed within a water continuous phase as direct emulsion droplets. The aim of this paper is to explore the basic rules that govern the stability of double emulsions. By associating both water- and oil-soluble surfactants in various concentrations, we produce W/O/W double emulsions. We identify two types of instabilities that are responsible for the evolution of double emulsions: (i) coalescence of the small inner droplets with the globule interface or (ii) coalescence between the small inner droplets within the oil globule. The first type of instability leads to a complete delivering of the small inner droplets toward the external phase whereas the second one does not. We show that the kinetics associated with the release of the small inner droplets due to this former instability is clearly related to the hydrophilic surfactant concentration in the external phase. Depending on the value of this concentration, multiple emulsions may be destabilized with a time scale ranging from several months to a few minutes. We discuss the basic criteria which are responsible for the suppression or the starting of these instabilities, emphasizing the influence of the composition of the interfacial films.
Introduction Emulsions are dispersions of two immiscible fluids such as water and oil. Direct emulsions are dispersions of oil droplets into water whereas inverse emulsions are composed of water droplets dispersed into oil. Emulsions are obtained by shearing one phase into the other in the presence of surface active species (surfactant, polymers, etc.). They may remain metastable and may persist long enough to be useful in many industrial applications such as paints, surface coating, food products, and cosmetics. From their preparation to their destruction these soft dispersions (direct, inverse, multiple) reveal numerous kinds of both reversible and irreversible phase transitions. The reversible phase transitions arise from the presence of attractive droplet interactions and generally lead to the formation of various structures: flocs coexisting with dilute droplets1-5 or emulsion gels which consist of a network of adhesive connected droplets.6 Irreversible phenomena lead to coarsening which may originate from either coalescence or Ostwald ripening.7 When the two phases are very poorly miscible, the diffusion of one phase through the other one is practically suppressed and the coarsening is only due to coalescence phenomena. Coalescence consists of the rupture of the thin film that forms between two adjacent droplets. The rupture requires the formation of a hole within the thin film which will grow, resulting in the fusion of two droplets. This evolution is activated and therefore controlled by an energy barrier which has to be overcome. In some cases, coalescence may be observable in dilute systems where droplets, due to their surface tension, are still spherical.8 (1) Aronson, M. P. Langmuir 1989, 5, 494. (2) Bibette, J.; Roux D.; Nallet, F. Phys. Rev. Lett. 1990, 65, 2470. (3) Leal-Calderon, F.; Gerhardi, B.; Espert, A.: Brossard, F.; Alard, V.; Tranchant, J.-F.; Stora, T.; Bibette, J. Langmuir 1996, 12, 872. (4) Meller, A.; Stavans, J. Langmuir 1996, 12, 301. (5) Binks, B. P.; Fletcher, P. D. I.; Horsup, D. I. Colloids Surf. 1991, 61, 291. (6) Bibette, J.; Mason, T. G.; Gang, H.; Weitz, D. A. Phys. Rev. Lett. 1992, 69, 981. Bibette, J., Mason, T. G., Gang, H., Weitz, D. A., Poulin, P. Langmuir 1993, 9, 3352. (7) Lifshitz, I. M.; Slezov, V. V. J. Phys. Chem. Solids 1961, 19, 35. Kabalnov, A. S.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1987, 118, 590.
In other situations, coalescence is only observable when the emulsion is sufficiently concentrated so that the droplets are strongly deformed, exhibiting large facets at each contact.9 There is so far no general understanding of the emulsion metastability, leading to an essentially empirical approach in formulating these dispersions. However, various rules have been proposed to account for the main experimental results concerning the formation and the destruction of simple emulsions (inverse and direct). The earliest guidance was provided by the Bancroft rule,10 the HLB (hydrophilic lipophilic balance),11 and PIT (phase inversion temperature)12 concepts. All of these aimed at linking the surfactant thermodynamics within the emulsion continuous phase to the topology (O/W or W/O) of the emulsion which forms and persists.13 Double emulsions may be either of the water-in-oil-inwater type (W/O/W) (with dispersed oil drops containing smaller aqueous droplets) or of the oil-in-water-in-oil type (O/W/O) (with dispersed aqueous globules containing smaller oily dispersed droplets). Taking advantage of this double (or multiple)-compartment structure, an increasing interest has been devoted to these multiple systems since their first description in 1925,14 as they can be considered as reservoirs of encapsulated substances to be released under variable conditions. The industrial domains showing evident interest toward the technological development of such complex systems are various. One can list the food industry, with its research in new “light” products, in the improvement of the organoleptic properties of foods, or in taste-masking, and the cosmetic industry, with easily spreadable and prolonged efficiency products which would ideally contain both oily and water-soluble active ingredients; products formulated as multiple emulsions may also be very appreciated in other domains such as agriculture and housekeeping. But the major part of (8) Das, K. P.; Chattoraj, D. K. Colloids Surfaces 1982, 5, 75. (9) Bibette, J.; Morse, D. C.; Witten, T. A.; Weitz, D. A. Phys. Rev. Lett. 1992, 69, 2439. Narsimhan, G. Colloids Surf. 1992, 62, 41. (10) Bancroft, W. D. J. Phys. Chem. 1913, 17, 501. (11) Griffin, W. C. Soc. Cosmet. Chem. 1949, 1, 311. (12) Shinoda, K.; Saito, H. J. Colloid Interface Sci. 1968, 26, 70. (13) Kabalnov, A.; Wennerstro¨m, H. Langmuir 1996, 12, 276. (14) Seifriz, W. J. Phys. Chem. 1925, 29, 738.
S0743-7463(97)01271-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 04/21/1998
Some Stability Criteria for Double Emulsions
applications concerns the human pharmaceutical field: water-in-oil-in-water (W/O/W) emulsions have mostly been investigated as potential vehicles for various hydrophilic drugs (vaccines, vitamins, enzymes, hormones) which would then be progressively released. A strong worldwide activity is still led around multiple emulsions.15,16 Active substances may also migrate from the outer to the inner phase of a multiple emulsion, providing in that case a kind of sorbent reservoir particularly suitable for detoxification (overdose treatment) or, in an again different domain, in the removal of toxic materials from wastewater. The impact of double emulsions designed as drug delivery systems would then be of significant importance in the controlled release field, for oral, topical, or parenteral administrations, provided that the stability and release mechanisms may be more clearly understood and monitored. The problems associated with multiple emulsions are numerous and remain mostly unsolved, though one can find rather much literature about the subject essentially published during these past two decades.17,18 First are the formulation and the manufacture aspects: from “empirical” preparations to more controlled procedures, the experimentalist must pay great attention to the composition of his/her system. Indeed, the emulsifier combination as well as the nature of the oil phase and the volume ratios between the different media are basic and essential parameters. Then, the emulsification can be achieved using different processes such as self-emulsification, homogenization, and mechanical high and/or low shear, for example, in a one- or a two-step method. The resulting (meta)stability of the multiple emulsion, to be discussed now, is of crucial importance, since it governs the storage and the potential use of such dispersions. The inherent instability exhibited by multiple emulsions can be seen at several levels: (i) between small inner droplets, (ii) between large globules, and (iii) between the globule and the small droplets dispersed within it. These phenomena for which the rupture of films is involved remain most often unexplored. Besides, the diffusion process has extensively been investigated as a possible mechanism for transport of active substances:19,20 here, the concentration gradient exerted by the whole set of various molecules (surfactant, electrolytes, actives) is involved, and a reverse micellar transport is mainly suggested.21 The resulting breakdown of these multiple emulsions, according to one of or a combination of all of these scenarios, leads, at various rates, to the release of the active ingredient(s) entrapped in the inner phase to the outer phase in an uncontrolled way. This is why the use of multiple emulsions as commercial products is actually so restricted, though much attention has been paid to their many potential practical applications.17,22,23 The aim of this paper is to explore the basic rules that govern the stability of double W/O/W emulsions. By (15) Taylor, P. J.; Miller, C. L.; Pollock, T. M.; Perkins, F. T.; Westwood, M. A. J. Hyg. 1969, 67, 485. Silva Cunha, A.; Grossiord, J. L.; Puisieux, F.; Seiller, M. J. Microencapsulation 1997, 14, 321. (16) Zheng, S.; Beissinger, R. L.; Wasan, D. T. J. Colloid Interface Sci. 1991, 144, 72. (17) Florence, A. T.; Whitehill, D. Int. J. Pharm. 1982, 11, 277. (18) Garti, N. Colloids Surf., A 1997, 123-124, 233. (19) Chiang, C.; Fuller, G. C.; Frankenfeld, J. W.; Rhodes, C. T. J. Pharm. Sci. 1978, 67, 63. (20) Matsumoto, S.; Kang, W. W. J. Dispersion Sci. Technol. 1989, 10, 455. (21) Magdassi, S.; Garti, N. J. Control. Release 1986, 3, 273. (22) Garti, N.: Frenkel, M.; Schwartz, R. J. Dispersion Sci. Technol. 1983, 4, 237. (23) Becher, P. Encyclopedia of Emulsion Technology; Marcel Dekker: New York, 1985; Vol. 2.
Langmuir, Vol. 14, No. 10, 1998 2703
associating both water- and oil-soluble surfactants (high and low HLB, respectively) in various concentrations, we produce W/O/W double emulsions. Following the behavior of double emulsions by observations using optical microscopy, we identify two types of instabilities that are responsible for the evolution of double emulsions: (i) coalescence of the small inner droplets with the globule interface or (ii) coalescence between the small inner droplets within the oil globule. The first type of instability is due to the rupture (coalescence) of the thin nonaqueous film that forms between the external continuous phase and the inner small water droplets. This leads to a complete delivering of the small inner droplets toward the external phase whereas the second one does not. Instead, it leads to an increase of the average diameter of the internal droplets and a decrease of their number. The former instability which irreversibly transforms a double emulsion into a simple direct one may be particularly suitable in delivering water-soluble substances. In parallel to our first observations, we also note that this instability occurs more or less rapidly depending on the ratios of surfactant concentrations used: by increasing the hydrophilic surfactant concentration, the destabilization of the multiple emulsion, leading to the complete release of the internal droplets toward the outer phase, may be varied from several months to a few minutes. Experimental Section We now describe our process so as to characterize this phenomenon, emphasizing the influence of the composition of the phases. In our study an electrolyte (NaCl) plays the role of the substance to be released from the inner to the outer phase. We first focus on the behavior of a nonionic/ionic surfactantbased system: the instability revealed through microscopic experiments is then kinetically investigated. The temperature behavior of such double emulsions is also accounted for. When turning to other systems (i.e. association of two nonionic surfactants), we show that the same phenomenology still applies. (1) We first prepare a monodisperse inverted emulsion of waterin-dodecane, stabilized by Span 80 (Sorbitan Monooleate, HLB ) 4.3, provided by Sigma). We prepare our emulsion by slowly introducing the aqueous dispersed phase (80% by volume) under low shear into the continuous phase (1:1 weight mixture of Span 80 and dodecane). Salt (NaCl, 0.1 mol/L) is added to the dispersed phase in order not only to simulate the active ingredient but also to avoid the coarsening phenomena.24 From our initial polydisperse emulsion we get a monodisperse one by using a fractionated crystallization technique.25 The droplet diameter is 0.4 µm, as deduced from dynamic light scattering experiments. When diluted in dodecane to 10% by volume, with a surfactant concentration set to 2% by mass and at a temperature of 20 °C, there is no aggregation or phase separation, as previously reported.3 Moreover, the emulsion does not exhibit any coarsening for weeks. We then prepare a double emulsion by dispersing the inverted one within the aqueous continuous phase containing sodium dodecyl sulfate (SDS, HLB ) 40, purchased by BDH) which has a critical micellar concentration (cmc) of 8 × 10-3 mol/L. The SDS concentration in the external aqueous phase is set to cmc/10. The double emulsion is composed of 90% by volume of the aqueous external phase and 10% of the inverted one. A high shear rate (Ultraturrax) is applied for 10 s to a total volume of 50 cm3 of the global composition and leads to double droplets in which the water droplet size is apparently conserved. The obtained double emulsion is polydisperse with an average globule size of around 10 µm, as measured with a commercial granulometer (Malvern, Mastersizer S). Figure 1 shows a microscopic picture of a double emulsion where the SDS concentration within the external phase Ce is cmc/10, after 2 months of storage at (24) Aronson, M. P.; Petko, M. F. J. Colloid Interface Sci. 1993, 159, 134. (25) Bibette, J. J. Colloid Interface Sci. 1991, 147, 474.
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Figure 1. Microscopic picture of a double W/O/W emulsion after 2 months of storage at room temperature. This double emulsion is composed of 90% external phase and 10% double droplets. There is 10% water within the large double globules. We use 2% Span 80 within the oil and cmc/10 of SDS in the external water phase. room temperature. Double droplets are visible, each one containing smaller inverted water droplets, and coalescence between the large double globules is not observed at that SDS concentration after 2 months. Our experiment consists of varying the surfactant concentration within the external aqueous phase Ce after the double emulsion has been freshly prepared, and noting the lifetime of the inner water droplets. In the subsequent description the surfactant concentration Ce will be expressed in cmc units of SDS in pure water. We find that the double emulsion persists (more than a month) or transforms into a direct one (within a few minutes) depending on the SDS concentration. Practically, we observe a release of the internal droplets when the SDS concentration in the external phase reaches a value of about 10(cmc); the rate of release is dramatically accelerated beyond this concentration. As an illustration, Figure 2a shows the double emulsion right after its preparation for a SDS concentration of 30(cmc) whereas Figure 2b shows the same emulsion after 3 h. Repeated observations under the microscope reveal a gradual decrease of the inner droplet concentration and the absence of coarsening of the inverted droplets within the double globules. Moreover, since in the time scale of our experiment no significant change in the internal droplet size is visualized, we can definitely neglect the influence of osmotic effects due to the salt concentration mismatch between the inner droplets and the external aqueous phase. These observations suggest that only coalescence events between the tiny inverted water droplets and the large direct droplet interface are responsible for the observed evolution, as sketched in Figure 3. Now let us turn to the kinetic aspect of this coalescence-driven transformation leading a double emulsion to a simple one. The experiment consists of observing the evolution of double emulsions as a function of time, at a constant temperature of 20 °C, using phase-contrast optical microscopy. Several emulsions are prepared as described above: with 2% weight of Span 80 as the emulsifier of the primary emulsion and SDS, at various concentrations, as the high-HLB surfactant of the external continuous phase. These observations are performed taking into account the following requirements: we report the behavior of a selected size of oily globules (around 10 µm), which is identical for each of the studied double emulsions; we consider a characteristic lifetime τ of the inner droplets defined as the time needed for the chosen freshly prepared globules to become almost empty. Such experiments, though based on qualitative (visual) appreciations, reproducibly lead to a curve as illustrated in Figure 4. We find a dramatic decay of the characteristic lifetime of release as a function of the water-soluble surfactant concentrations in the external phase. In other words, when the surfactant concentra-
Figure 2. Structural evolution of a double W/O/W emulsion. The primary inverted emulsion (10% by volume) is stabilized by Span 80 (2% by weight) while the external phase contains SDS at a concentration equal to 30(cmc): (a, top) microscopic picture obtained immediately after preparation, double emulsion; (b, bottom) microscopic picture obtained after 3 h, simple direct emulsion.
Figure 3. Schematic representation of the transfer of the inner aqueous droplets toward the external phase. tion is much lower than a threshold value of about 10(cmc), the double emulsions remain stable without any release, while total release occurs within a few minutes (or even less) if the SDS concentration is above this threshold value. This instability seems to be clearly affected by the external phase surfactant concentration. We now discuss the possible role of the SDS concentration Ci within the inverse droplets. We repeat the same experiments as described above, but we now vary the concentration of SDS inside the inverted droplets from 0 to 10(cmc). We obtain the primary inverted emulsion following the same procedure as previously described. The aqueous dispersed phase (80% in volume) made of water, salt (NaCl, 0.1 mol/L), and SDS (Ci) is slowly introduced under low shear into the continuous phase (1:1 weight mixture of Span 80 and dodecane). After some purification steps,25 we obtain a size
Some Stability Criteria for Double Emulsions
Figure 4. Plot, at 20 °C, of the lifetime τ of internal droplets entrapped in oily globules as a function of the external phase surfactant concentration Ce. The double emulsions are composed of 90% external phase and 10% double droplets. There is 10% water within the large double globules. We use 2% Span 80 within the oil and SDS in the external water phase.
Figure 5. Influence of the internal surfactant concentration Ci on the τ ) f(Ce) curve, at 20 °C. System: Span 80/SDS as in Figure 4. The dashed and solid lines are only guides to the eyes. distribution centered around 0.4 µm for the inverted primary emulsion. We check that these inverted emulsions are stable over 1 month: we do not observe any substantial change in the size distribution over that period for any of these SDS concentrations from 0 up to 10(cmc). Therefore, for such inverse emulsions the water droplets do not coalesce even though their SDS concentration is reaching the previously reported threshold of about 10(cmc). We then set the water droplet concentration to 10% in order to recover the previous inverted emulsion compositions. The inverted emulsions are dispersed in an aqueous phase containing SDS at various concentrations below and above the previously detected instability threshold (10(cmc)) following the above-mentioned procedure. When the external SDS concentration Ce is significantly lower than 10(cmc), we do not observe any release of the internal droplets whatever the internal SDS concentration Ci, over a period of 1 month. However, we do observe that, in some cases, the inner water droplets may coalesce together when entrapped into the double globules. This is in striking contrast with the bulk inverse emulsion behavior, where no coarsening was apparent. This instability takes place rapidly and leads to a few larger water droplets still entrapped into the oil globules, and we note that this instability mainly occurs for Ci ranging from cmc/10 to a few cmc. Besides, if Ce is larger than 10(cmc), we observe a gradual decrease of the inner droplet concentration. In Figure 5 we plot the time for total release τ as a function of the external concentration Ce for different internal Ci values. Clearly, the kinetics of release are affected by the presence of SDS in the internal droplets: the rate of release increases with Ci. The diameter of the primary inverse emulsion also affects the characteristic time of release. In Figure 6 we plot τ as a function of the external surfactant concentration Ce for two emulsions with different internal droplet diameters (0.4 and 0.2 µm): we observe that τ becomes significantly lower for larger internal droplet size.
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Figure 6. Influence of the internal droplet diameter on the τ ) f(Ce) curve, at 20 °C. System: Span 80/SDS. The internalphase surfactant concentration Ci is set to cmc.
Figure 7. Influence of temperature on the τ ) f(Ce) curve. We use 2% Span 80 within the oil and TTAB in the external water phase. To experimentally investigate the influence of the temperature on the kinetics of release, we turn to a slightly different system. Since SDS is sensitive to hydrolysis above 20 °C, we replace this surfactant by TTAB (tetradecyltrimethylammonium bromide, from Aldrich, HLB ) 40, cmc ) 3.5 × 10-3 M). We again measure the time τ needed for 10-µm globules to become empty, as a function of the external TTAB concentration. We perform these experiments in the absence of TTAB within the internal droplets. We find the results presented in Figure 7 corresponding to three different temperatures: 20, 40, and 50 °C. At 20 °C, we confirm the same trends as in the SDS system: we find a sharp decay of the lifetime τ of the internal small droplets with the TTAB concentration in the external aqueous phase. The same behavior still applies when considering the two other temperatures investigated: 40 and 50 °C. Moreover, we note a strong decrease of the lifetime τ when raising the temperature, which suggests an activated nature for this coalescence phenomenon. Finally, to test the generality of our observations, we perform the same set of experiments using a nonionic high-HLB surfactant: Tween 80 (polyoxyethylene sorbitan monooleate, HLB ) 15, cmc ) 10-3 mol/L, purchased from Sigma). Here again, the transfer of the inner water droplets is affected by the external-phase surfactant concentration Ce. Let us note that for this system (a lower HLB surfactant than SDS or TTAB) the existence of the double emulsion may be extended much beyond the cmc. Indeed, below 200(cmc) no release of the internal droplets occurs for months while around 300(cmc) the observed lifetime τ is reduced to a few minutes. Moreover, if Tween 80 is incorporated within the inner droplets at concentrations ranging from cmc/10 to 300(cmc), we also observe the same coarsening phenomenon of the inverse droplets when entrapped within the oil double globules. As for SDS systems, this is in striking contrast with the bulk inverse emulsion behavior, where no coarsening was detected. This coarsening is again attributed to coalescence of the inverse droplets. We show microscopic pictures of double emulsion with Ci ) 100(cmc) and Ce ) cmc:
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Figure 8. Structural evolution of a double W/O/W emulsion. The external phase (90% by volume) contains Tween 80 at a concentration equal to the cmc: (a, top) microscopic picture obtained immediately after preparation; (b, bottom) microscopic picture obtained after 10 days. freshly prepared, Figure 8a; after 10 days, Figure 8b. When Ce is significantly higher than 200(cmc), the inner droplets are released with a rate that increases with Ci.
Discussion and Conclusion The results presented here are, at least to a certain extent, in agreement with the well-known Bancroft rule. Indeed, a double W/O/W emulsion turns into a simple direct one when a sufficient quantity of the water-soluble surfactant is added. Similarly, by shaking a 1:1 mixture of water and oil, each phase containing one of the two types of surfactants, we obtain a direct emulsion in the case where the aqueous phase contains a large amount of water-soluble surfactant. By contrast, when less of this surfactant is present, we can get a double emulsion that may persist. From the above-described set of experiments, we end up with the same type of conclusion: the double emulsion persists as long as the water-soluble surfactant concentration is not too high. One immediate interpretation would be that the inverse emulsion contained within each globule becomes unstable because most of its oil-soluble surfactant molecules are pumped outside, due to some increased affinity within mixed micelles. In fact, our experiments allow us to conclude that such a
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transformation (from a double emulsion to a simple one) is exclusively due to coalescence of internal droplets with the large globule interface. Indeed, there is no detectable solubility of the oil-soluble surfactant into water within the explored range of water-soluble surfactant concentration. Moreover, adding the low-HLB surfactant to the external phase has no effect on the rate of the transformation. Coalescence requires the formation of a hole, which is associated with an activation energy Ea. Following a mean field description of Arrhenius type, the frequency for a hole opening per unit surface may be written as ω ) ω0e-Ea/kT, where ω0 is the natural frequency involved in this process and kT is the thermal energy. Such a description, at least for some specific materials, has been shown to agree with experiments.26 As described in this paper, the destruction through coalescence of double emulsions into simple ones is affected by various parameters. The most remarkable one is the hydrophilic surfactant concentration within both the continuous phase and the internal droplets. We find a very dramatic dependence of the coalescence rate on these concentrations. We also find that, by raising the temperature or the internal droplet diameter, the coalescence rate is significantly increased. However we have repeatedly noticed that coalescence between small internal droplets and the globule interface preferentially occurs and that Ci and Ce do not have symmetric consequences on the rate of coalescence: in particular, we have observed that as long as Ce does not exceed some threshold values, the rate of coalescence remains essentially zero though Ci might be significantly increased. Once Ce reaches some identified threshold, Ci can speed up the rate and act in a more symmetrical way than Ce. We believe that our results highlight some possible consequences of binary mixtures of surfactant at interfaces, that is, two radically different types of surfactants (one is a low HLB, the other is a high HLB) adsorbed at the same interface. We propose that the activation energy may be severely coupled to the surfactant concentration fluctuations and therefore be responsible for some of the surprising behaviors: sharp decays of τ with Ce or Ci and the preferential coalescence of small droplets onto the globule interface. However, we expect the dissymmetric role of Ci and Ce might be rationalized on the basis of water-soluble surfactant migration between internal and external aqueous media: indeed, because the internal volume is 100 times smaller than the external one, we suspect Ci changes with time while Ce is expected to fix the chemical potential of this species. On the basis of these first observations, we hope that a quantitative measurement of the coalescence rate instead of the visually appreciated lifetime will allow us to determine the parameters Ea and ω0 (as a function of surfactant concentration and internal droplet diameter), as suggested by the temperature dependence that has already been detected. For example, the presence of salt in the inner droplets can be exploited to quantify the coalescence rate by measuring the electrical conductivity of the external water phase. Indeed, as the inner droplets coalesce, the ionic content of the external water phase will increase. Finally we believe that the very rich possibilities offered by double emulsions may be useful in many applications which take advantage of encapsulation and sustained release.27 LA971271Z (26) Deminie`re, B. Ph.D. Thesis, Universite´ Bordeaux I, 1997. (27) Bibette, J., Ficheux, M.-F., Bonakdar, L., Leal-Calderon, F. French patent no. 97 10154 (submitted).
