Effect of the Volume Fraction on the Average Flocculation Rate

Abstract

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.

Influence of Drop Deformability on the Stability of Decane‐in‐Water Emulsions

“…The curves of n versus t show a progressive decrease as a function of time, as is usually exhibited in the case of fast aggregation. For a flocculating-coalescing emulsion of nondeformable drops where DV T B 12.7k B T, ESS [10,54] confirm the validity of Eq. 23, provided that the number of aggregates is counted as prescribed by Danov et al [11].…”

Nanoemulsion stability: Experimental evaluation of the flocculation rate from turbidity measurements

“…However, they demonstrated that if the coalescence rate of an emulsion is significantly faster than the flocculation rate, and big drops are counted as single particles, the expression of Smoluchowski for the total number of aggregates is recovered. This result was repeatedly validated by ESS of non-deformable drops [103,104]. In fact, an alternative expression for the total number of aggregates was deduced [103].…”

“…32. Despite these limitations and the ones previously mentioned regarding the effect of polydispersity, the mixed flocculation-coalescence rates observed at high ionic strength (Tables 5 and 6) are of the same order of magnitude as the one predicted by Emulsion Stability Simulations (ESS) for the case of very dilute emulsions in the absence of a repulsive force is k f = k FC = 6.4 × 10 −18 m 3 s −1 [103].…”

“…This result was repeatedly validated by ESS of non-deformable drops [103,104]. In fact, an alternative expression for the total number of aggregates was deduced [103]. This expression is valid for systems of distinct polydispersity with 0.01 < φ < 0.30, 10 −5 M < C sur f < 8 ×10 −5 M (where C sur f is the surfactant concentration).…”

“…This expression is valid for systems of distinct polydispersity with 0.01 < φ < 0.30, 10 −5 M < C sur f < 8 ×10 −5 M (where C sur f is the surfactant concentration). In the absence of a repulsive barrier, limiting values for the mixed flocculationcoalescence rate (k FC ) of non-deformable drops were also calculated [103]. [56,107,61,108,106] drops subject to coalescence has been extensively studied by our group using simulations.…”