STOKES-FLOW IMPINGING ON A SPHERICAL CAP ON A PLANE WALL

Axisymmetric Stokes flow impinging upon a spherical cap on a solid pla ne wall is analysed. An analytical integral expression for the streamf unction is obtained from separation of variables in toroidal coordinat es; Mehler-Fock transforms are used in applying the boundary condition s. Streamlines are shown for spherical caps ranging from very hat to v ery round. Regions of recirculation are found near the edges of caps f uller than a hemisphere. The pressure distribution on the cap, and the net force in the axial direction, are also determined for a range of shapes. The axial force is proportional to the volume of caps of fixed shape, but relatively insensitive to the degree of flattening for cap s of fixed volume. Implications of the results for the deformation of red blood cells and other deformable particles are examined.