Effects of the Particle Distribution Shape upon Dispersion Stability

Ian M. Klink1, Stephanie R. Dungan2, and Ronald J. Phillips1. (1) Chemical Engineering and Materials Science, U.C. Davis, One Shields Ave, Davis, CA 95616, (2) Food Science & Technology, Chemical Engineering and Materials Science, University of California, Davis, One Shields Ave., Davis, CA 95616

A discretized population balance has been developed utilizing the moving pivot technique in order to model destabilization of emulsions and other dispersions. The model conserves both number and mass within the system, and uses a shear kernel to describe inter-droplet collision rates. The shear kernel is modeled by the Smoluchowski collision rate adjusted for the stability ratio of the colliding droplets. We have been using this approach to understand effects of the droplet distribution shape upon the dispersion stability. Discretization is performed using an adjustable grid that can be adapted to capture different varying degrees of resolution of the drop size distribution. Simulations on a lognormal initial distribution yield a rate of coalescence that is independent of drop size, and depends only upon the width of the distribution. The simulations also show that the level at which the drop size distribution is taken into account, or the “grid size” used, strongly affects the predicted evolution of the microstructure. If the size distribution is resolved poorly, or the grid size is large relative to the width of the distribution, the predicted rate of coalescence is bounded by the Smoluchowski rate for a monodisperse distribution. As the resolution of the grid is improved, the rate of aggregation approaches that predicted by the moment solution for the distribution, assuming self-similar evolution. An interesting, non-intuitive result is that the rate of coalescence of an emulsion comprised of two droplet populations, with a bimodal distribution, can be as much as two times slower than what would be present with either of the two populations in isolation. This and other findings related to the effect of droplet size distribution on coalescence rate will be discussed and analyzed.