Integral equation solution for the flow due to the motion of a body of arbitrary shape near a plane interface at small Reynolds number

The problem of determining the slow viscous flow due to an arbitrary motion of a particle of arbitrary shape near a plane interface is formulated exactly as a system of three linear Fredholm integral equations of the first kind, which is shown to have a unique solution. A numerical method based on these integral equations is proposed, and the problem of arbitrary motion of a sphere is worked out and compared with the available analytical solution. As an example the case of two equal sized spheres moving parallel and perpendicular to the interface is solved in the limiting case of infinite viscosity ratio.