Particle interactions with permeable drops in shear flow

Abstract

Motivated by particle removal from suspension by agglomeration with drops, the behavior of a spherical solid particle as it approaches a spherical drop covered with a rigid, permeable film is examined numerically. The particle and drop are in an external shear flow where viscous forces dominate. First, we revisit the classical problem of a particle interacting with a non-permeable drop, which includes closed orbits and open trajectories, but no collisional trajectories (without attractive forces present). Next, permeability is introduced, which modifies the two-sphere mobility functions for the system. For permeable drops, four types of trajectories are found, including infinity to drop (collision), infinity to infinity (miss), finite drop-to-drop, and closed-orbit trajectories. The collision efficiency as a function of the particle/drop size ratio and film permeability is then calculated. The efficiency dramatically increases with permeability, and it is maximum when the particle and drop are of nearly equal size.