The normal force exerted by creeping flow on a small sphere touching a plane

The hydrodynamic force experienced by a small solid sphere of radius a p resting on a solid plane wall in axisymmetric stagnation flow, v∞ = Ω(- z² iz + zω̃ iω̃) , or in planar stagnation flow, v ∞ = Ω(− z 2 i z + 2 zx i x ), is computed on the basis of Stokes’ creeping flow equations. In both cases, as well as for any flow whose z component of velocity is −Ω z 2 , this force is found to be F z = − 60·87μΩ a p 3 , where μ is the viscosity of the fluid. The uniform flow parallel to the line of centres of two touching spheres of arbitrary radii is also solved.