Image representation of a spherical particle near a hard wall

The motion of a spherical colloidal particle suspended in a moving fluid near a planar hard wall or free surface is considered. The particle types include hard spheres with mixed slip-stick boundary conditions, droplets with high surface tension and porous particles. A general expression for the flow field is obtained in terms of a set of force multipoles induced on the particle and on its mirror image in the bounding surface. An earlier calculation of the friction and mobility functions for the particle is extended to include coupling to an incident linear shear flow. A numerical representation of all these functions is given which is accurate at all separations of particle and boundary. These results are used to study the position and orientation of a hard sphere falling towards a wall under gravity in the presence of a shear flow.