On the history term of Boussinesq-Basset when the viscous fluid slips on the particle

Within the framework of the Stokes approximation, a method is proposed for calculating the drag and the torque acted on a rigid particle by an incompressible viscous fluid, when the fluid-particle boundary conditions are slip conditions. By using the Fourier Transform and a reciprocity formula, the drag and torque are deduced from these obtained for two simple vibration motions of the particle in a fluid at rest. The results are explicitly given in the case of a spherical particle. They are in agreement with the formulae known in various special cases.