The effect of slip parameter in an axisymmetric oscillatory Stokes flow

A general solution of Stokes equations for the problem of an axisymmetric oscillatory flow of an incompressible, viscous fluid past a sphere satisfying general boundary conditions is obtained. The behavior of the magnitude of drag is observed with the variation of the slip parameter. Some more interesting behaviors are detailed, and several existing results pertaining to steady flows and flows with rigid and shear free boundary conditions are recovered as special cases. The corresponding results are discussed for four different axisymmetric oscillatory Stokes flows, namely, uniform flow, flows generated due to a dipole, a source, and a Stokeslet. A few interesting streamline patterns like formation, elongation, and disappearance of viscous eddies in the vicinity of the sphere with a periodic reversal of the flow are observed at different frequencies for different values of the slip parameter.