Collision-Induced Dispersion of Droplets Attached to Solid Particles

Abstract

Kinetic equations have been derived to analyze the dispersion of an oil phase, distributed in the form of patches or droplets over the surface of suspended spherical solid particles. Results of dynamic simulations were compared with an analytical model as well as with some experimental data. Creation or disappearance of patches occurs when oil bridges are formed and subsequently broken during particle collisions. Agreement between the analytical results and dynamic model simulations is very good in the limiting case of a few small patches per particle when the total coverage of the solid surface is low. The dynamic simulation can account for collisions involving many patches and provides full information on the size distribution of the surface droplets. Both models show that for a low volume fraction of the oil phase a large number of small patches are created on the particle surface. For higher volume fractions a plateau is reached very quickly and there is a tendency to create big droplets on the solid surface. As long as the coverage is low, the process of creating new patches is self-accelerating because the fraction of the solid surface coated by the oil phase increases with the number of droplets. Saturation occurs as a result of collisions between two or more patches, leading to a dynamic equilibrium between the formation and disappearance of patches. Comparison with experimental observations confirms the trends predicted theoretically.