Spontaneous emulsification prediction

Finally, we present an interpretation of our observations in terms of diffusion paths. Basically, the diffusion equations are solved for the case of two semi-infinite phases brought into contact under conditions where there is no convection and no interfacial resistance to mass transfer. Other simplifying assumptions such as uniform density and diffusion coefficients in each phase are usually made to simplify the mathematics. The analysis shows that the set of compositions in the system is independent of time although the location of a particular composition is time-dependent. The composition set can be plotted on the equilibrium phase diagram, thus showing the existence of intermediate phases and, as explained below, providing a method for predicting the occurrence of spontaneous emulsification. 

The diffusion path method has been used to interpret nonequilibrium phenomena in metallurgical and ceramic systems (10-11) and to explain diffusion-related spontaneous emulsification in simple ternary fluid systems having no surfactants (12). It has recently been applied to surfactant systems such as those studied here including the necessary extension to incorporate initial mixtures which are stable dispersions instead of single thermodynamic phases (13). The details of these calculations will be reported elsewhere. Here we simply present a series of phase diagrams to show that the observed number and type of intermediate phases formed and the occurrence of spontaneous emulsification in these systems can be predicted by the use of diffusion paths. 

Calculated diffusion paths also successfully predicted the occurrence of spontaneous emulsification in the systems. Near optimum salinity where this phenomenon first appeared, brine drops spontaneously emulsified in the oil but were isolated from the bulk brine phase by a microemulsion. At high salinities, a more common type of spontaneous emulsification was seen with brine emulsifying in the oil directly above a brine layer. 

Complete information on phase behavior including tie-lines and on diffusion coefficients is rarely available for oil-water-surfactant systems. Nevertheless, Raney and Miller used plausible phase diagrams for an anionic surfactant-NaCl brine-hydrocarbon system as a function of salinity to calculate diffusion paths that exhibited intermediate phase formation and spontaneous emulsification in agreement with experimental observations made using the vertical cell technique. For example. Figure 9.12 shows a diffusion path for a surfactant-alcohol-brine mixture of composition D in contact with oil for a case when initial salinity is high. An intermediate brine phase is predicted as well as spontaneous emulsification in the oil phase, both of which were, in fact, observed. 

Note that in Figure 6.23, part of the diffusion path for the primed phase (viz., the segment cd) hes within the two-phase region of the phase diagram. Ruschak and Miller (1972) proposed that when such behavior is found, spontaneous emulsification should be expected in the phase or phases having supersamrated compositions. Their experiments for three toluene-water-solute systems having tie-lines of different slope confirmed the ability of this scheme to predict both when emulsion would form and in which phase or phases. As Figure 6.23 indicates, one factor that favors spontaneous emulsification is diffusion of the solute into the phase in which it is more soluble. 

Section 9 dealt with prediction of diffusion paths and spontaneous emulsification for a particular unsteady state sitoation. We consider here determination of the diffusion path at steady state (Jackson, 1977). 

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