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A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall on one side and a nondeformable gas-liquid interface on the other side is developed. The no-slip boundary conditions at the wall are satisfied by constructing an image system based on Lamb’s multipoles. Earlier results for the image systems for the flow due to a point force or a force dipole are extended to image systems for force or source multipoles of arbitrary orders. For the case of a film, the image system consists of an infinite series of multipoles on both sides of the film. Accurate evaluation of the flow due to these images is discussed, including the use of Shanks transforms. The method is applied to several problems including chains of particles, radially expanding particles, drops, and porous particles.

A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface