Integral equation solution for the flow due to the motion of a body of arbitrary shape near a plane interface at small Reynolds number (Q1081445)

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. In order to test this method valid for arbitrary particle shape, the problem of arbitrary motion of a sphere is worked out and compared with the available analytical solution. This technique can be also extended to low Reynolds number flow due to the motion of a finite number of bodies of arbitrary shape near a plane interface. 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.