HYDRODYNAMIC INTERACTION OF A SPHERICAL-PARTICLE WITH A PLANAR BOUNDARY .2. HARD-WALL

Using a general method developed in a previous paper we construct the grand resistance and mobility matrices for a hard sphere moving in an incompressible viscous fluid bounded by a hard wall. Starting from an explicit form of the Green tensor for the semi-infinite fluid we compute the matrices whose matrix elements give the scalar resistance and mobility functions describing translation and rotation of the sphere in a general direction and orientation relative to the hard wall. We give explicit series expansions for these functions in inverse powers of the normal distance from the sphere centre to the wall. We find that the series expansions for the friction functions are better behaved than are those for the mobility functions. By combining our series results with known asymptotic formulae valid for close approach of sphere and wall we obtain explicit expressions accurate at all separations of particle and wall.