Dynamics of a sphere with inhomogeneous slip boundary conditions in Stokes flow

Abstract

The dynamic resistance of a sphere with a general inhomogeneous slip boundary condition is analysed in Newtonian unbounded uniform flow at low Reynolds number. The boundary condition is treated as a perturbation to a homogeneous sphere, assuming that the slip length magnitude b is much smaller than the sphere radius a. To first order, the effect of inhomogeneous slip is the same as that of a radial deformity of magnitude b. Full resistance tensors are presented and the dynamics of a hemispherical inhomogeneous sphere, such as a Janus particle, are explicitly calculated.