Arbitrary oscillatory Stokes flow past a porous sphere using Brinkman model

The present paper deals with the hydrodynamics of a porous sphere placed in an arbitrary oscillatory Stokes flow. Unsteady Stokes equation is used for the flow outside the porous sphere and Brinkman equation is used for the flow inside the porous sphere. Corresponding Faxén’s law for drag and torque is derived and compared with few existing results in some special cases. Examples like uniform flow, oscillatory shear flow and oscillating Stokeslet are discussed. Also, translational oscillation of a weakly permeable sphere is discussed.