The fluid dynamic forces on a particle near a plane wall with a hole.

A Boundary Integral Equation technique is presented for solving the low Reynolds number hydrodynamical interaction of a rigid body with a plane wall and a hole. Such a problem occurs in the process of filtration by a multipore layer or similar devices. The proposed technique makes use of the Green function for the infinite plane wall for the Stokes equation, to eliminate all unknowns on the plane wall. A system of two integral equations is derived, for the stresses on the surface of the body and for the velocity in the hole; this system is later reduced to a single equation. Unlike other methods, no axial symmetry is assumed for the hole and the body and, in fact, the same technique can deal with more than one hole without further modifications.