In order to account for the hydrodynamic interaction (HI) between suspended particles in an average way, Honig et al. [J. Colloid Interface Sci. 36, 97 (1971)] and more recently Heyes [Mol. Phys. 87, 287 (1996)] proposed different analytical forms for the diffusion constant. While the formalism of Honig et al. strictly applies to a binary collision, the one from Heyes accounts for the dependence of the diffusion constant on the local concentration of particles. However, the analytical expression of the latter approach is more complex and depends on the particular characteristics of each system. Here we report a combined methodology, which incorporates the formula of Honig et al. at very short distances and a simple local volume-fraction correction at longer separations. As will be shown, the flocculation behavior calculated from Brownian dynamics simulations employing the present technique, is found to be similar to that of Batchelor's tensor [J. Fluid. Mech. 74, 1 (1976); 119, 379 (1982)]. However, it corrects the anomalous coalescence found in concentrated systems as a result of the overestimation of many-body HI.

A simple procedure for the quantification of flocculation (k(f)) and coalescence (k(c)) rates from emulsion stability simulations (ESS) of concentrated systems is presented. It is based on a simple analytical equation, which results from the sum of well-known formulas for the separate processes of flocculation and coalescence. The expression contains k(f) and k(c) as fitting parameters and is found to reproduce the behavior predicted by ESS spanning a wide range of volume fractions (1 < phi < 30%) and surfactant concentrations (1.2 x10(-5) < C < 1.2 x 10(-4) M). This procedure allows interpretation of ESS data in terms of the referred kinetic rates. Furthermore, it could also provide an additional mean for the direct comparison of the simulation data with experimental results.

To simulate the evolution of an oil-in-water emulsion toward flocculation and coalescence, a modification of a standard Brownian dynamics algorithm was made. The resulting program takes into account the effects of surfactant diffusion and interfacial adsorption on the drop−drop interaction potential. Different realizations of the possible surfactant distributions are considered. In this work, the evolution of a small 64-particle system in the presence of a surfactant concentration gradient is studied. These results are compared with the predictions of well-known analytical formulas, which do not account for non-homogeneous surfactant distributions or a time-dependent surfactant adsorption. The particles are assumed to interact through a DLVO potential, which changed with surfactant concentration. The variation of the total number of particles with time follows the analytical predictions of Borwankar et al. for initial and intermediate steps of the flocculation/coalescence process. However, significant differences in the drop size distribution were found for longer times.

The effect of dynamic surfactant adsorption on the stability of concentrated oil in water emulsions is studied. For this purpose, a modification of the standard Brownian dynamics algorithm (Ermak, D.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352) previously used to study the behavior of bitumen emulsions assuming instantaneous adsorption (Urbina-Villalba, G.; García-Sucre, M. Langmuir 2000, 16, 7975) was employed. In the present case, dynamic adsorption (DA) was accounted for through a time-dependent electrostatic repulsion between the drops, a function of the surfactant surface excess. The surface excess was allowed to evolve with time according to well-established analytical expressions which depend parametrically on the surfactant diffusion constant (Ds) and the total surfactant concentration (C). The investigation required appropriate incorporation of hydrodynamic interactions in concentrated systems. This was achieved through a novel methodology, which expresses the diffusion constant of each particle as a function of its local concentration and the shortest distance of separation between nearest neighbors. In model systems, the variation of the number of drops as a function of time was followed for different magnitudes of the apparent diffusion constant D(app) of the surfactant. For each of these values, the effect of C and the volume fraction of internal phase (phi) was considered. DA was found to influence emulsion stability appreciably at moderately high phi. In this case, the average collision time between drops is comparable to the time required for the occurrence of a substantial surfactant adsorption, but the interdrop separation is sufficiently large to prevent a considerable slowdown of particle movement due to hydrodynamic interactions.

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