Effect of the Volume Fraction on the Average Flocculation Rate

Brownian dynamics simulations are used to study the effect of the volume fraction of internal phase (10 -5 ≤ φ ≤ 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.