The Effect of a Semi-Infinite Plane on the Motion of a Small Particle in a Viscous Fluid

Abstract

The Stokes flow due to the motion of a small spherical particle translating in arbitrary directions is investigated, in the presence of a semi-infinite plane. The solutions of the boundary value problem are obtained in closed forms to the point force approximation, by the use of the Green and Neumann functions supplemented by the edge function to remove the singularity at the edge of the plate. The force and the torque (or angular velocity) experienced by the particle are determined on the basis of this solution, with special reference to the side-force.