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. (c) 2021 Elsevier B.V. All rights reserved.