Slipping Stokes flow around a slightly deformed sphere

When a fluid may slip at the surface of a particle, the conventional boundary condition must be modified to incorporate the tangential stress at the surface. Even for the simplest nontrivial shapes of the slip particle, the resulting Stokes problem could not be analytically solved. We present a first attempt to obtain analytical approximations for the resistance relations for a rigid, slightly deformed slip sphere in an unbounded Stokesian flow. To the first order in the small parameter characterizing the deformation, we derive expressions for the hydrodynamic force and torque exerted on the particle, which are found to be in very good agreement with the available numerical results, even in the case in which deformations are not small. The drag force on a spheroid is found to be an either decaying or growing function of the aspect ratio of the particle.