A boundary integral equation solution of the stokes flow due to the motion of an arbitrary body near a plane wall with a hole

A boundary integral equation technique is presented for solving the low Reynolds number hydrodynamic interaction of a rigid body with a plane wall and a hole. Such a problem occurs during the process of filtration by a multipore or similar devices. The proposed technique utilizes the Green function of the Stokes equation for the infinite plane wall 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. The proposed technique is applicable to a hole and a body of arbitrary shape and no symmetry is required.