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.

Brownian dynamics simulations are used to study the effect of the volume fraction of internal phase (10 -5 e φ e 0.40) on the flocculation rate (k f ) of oil in water (O/W) emulsions. To cover the typical range of Hamaker constants, its characteristic value for a bitumen emulsion (A ) 1.24 × 10 -19 J) and its typical order of magnitude for a latex dispersion (A ) 1.24 × 10 -21 J) were used. Account of hydrodynamic interactions was made, using a new methodology [Urbina-Villalba et al. Phys. ReV. E 2003, 68, 061408], which incorporates local volume fraction corrections at intermediate separations, and exact hydrodynamic interactions at closer distances. The resulting flocculation rates and their half-lifetimes (t 1/2 ) were analyzed as a function of the volume fraction and the initial mean free path (l) between the drops. Useful approximate relations are found for a limited range of volume fractions. Despite the fact that φ and l -2 are related and t 1/2 should decrease with either one, while k f is expected to increase, the quality of the fittings was different, depending on the Hamaker constant and the variable chosen. For A ) 1.24 × 10 -21 J, the best correlation involves t 1/2 and φ. In the case of A ) 1.24 × 10 -19 J, the best fits contain k f and either φ or l -2 . In general, the flocculation rate decreases monotonically as the volume fraction lowers, approaching the theoretical estimation. Values of k f below the theoretical prediction, as those occasionally found in experimental evaluations of very dilute systems, were not observed.

According to recent simulations [Langmuir 16, 7975 (2000)], the flocculation rate (k f ) of concentrated oil in water (O/W) emulsions interacting through van der Waals forces, can reach values considerably higher than the one expected for a very dilute system of noninteracting spheres ð5:49 3 10 218 m 3 =sÞ: Similar calculations at a volume fraction f 5 0:001 using 64 particles only, already show a k f 5 5:83 3 10 218 m 3 =s; reasonably close to the theoretical prediction. In this report Brownian Dynamics (BD) simulations are used to study the effect of the volume fraction and the drop size distribution (DSD) on the flocculation rate. First, the dependence of k f with the maximum value of the thermal interaction between the particles and the solvent is studied. Following, the variation of the flocculation rate is studied as a function of polydispersity for f 5 0:15: As expected, there is a strong dependence of k f on f. Faster and slower aggregation rates are observed depending on the characteristics of the DSD.