Stokes flow impinging on a spherical cap on a plane wall

Axisymmetric Stokes flow impinging upon a spherical cap on a solid plane wall is analysed. An analytical integral expression for the streamfunction is obtained from separation of variables in toroidal coordinates; Mehler-Fock transforms are used in applying the boundary conditions. Streamlines are shown for spherical caps ranging from very flat to very round. Regions of recirculation are found near the edges of caps fuller 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 insenstiive to the degree of flattening for caps of fixed volume. Implications of the results for the deformation of red blood cells and other deformable particles are examined.