Axisymmetric stagnation flow of a spherical particle near a finite planar surface at zero Reynolds number

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Abstract
The general axisymmetric creeping motion of a spherical particle in a stagnation region near a finite surface is modelled by the motion of a sphere of arbitrary size towards a disk for the follodg conditions: (a) pure translation in quiescent fluid, (b) uniform flow past a fixed sphere–disk configuration, and (c) a neutrally buoyant sphere carried by the fluid towards a disk. The combined analytic and numerical solution procedure is similar to that described in Dagan, Weinbaum & Pfeffer (1982b) for the motion of a sphere towards an orifice. The drag force acting on the sphere and on the disk under the flow conditions mentioned above is presented. In addition, the fluid velocity field has been obtained for the case of uniform flow past a fixed sphere–disk configuration. These solutions show the formation and coalescence of separated regions of closed streamlines adjacent to the sphere and the disk.