Drop Squeezing through Arbitrarily Shaped Obstacles

Emulsions are encountered in a variety of environments, such as multiphase flow through fibrous materials, packed beds with complex pellet shapes, and tortuous subsurface settings. Efforts to numerically model droplet-resolved, nonwetting emulsions in complex environments have been stymied, chiefly due to the extremely close approach of fluid-fluid interfaces to solid surfaces. A multimesh desingularization technique is introduced to model the flow of tight-squeezing drops through arbitrary Lyapunov surfaces, i.e., smooth solid obstacles, using a boundary-integral formulation. The method utilizes a hierarchy of embedded mesh resolutions to approximate analytical single- and double-layer contributions from solid particles, for use by the high-order singularity subtraction scheme introduced by Zinchenko and Davis (2006). We present a fully three-dimensional study of drop squeezing through parallel cylindrical particles. Squeezing behavior through a fibrous material using this model is characterized with respect to capillary number, viscosity ratio and droplet size. The critical capillary number, below which trapping occurs, is found to lie between those of two-sphere and three-sphere constrictions.