Stokes Flow of Micropolar Fluid past a Porous Sphere with Non-Zero Boundary Condition for Microrotations

The Stokes flow problem is considered for micropolar fluid past a porous sphere assuming the flow at distant points is uniform and parallel to the axis of symmetry. A nonhomogeneous boundary condition for the microrotation vector i.e., the microrotation on the boundary of the sphere is assumed to be proportional to the rotation rate of the velocity field on the boundary, is used. The stream functions are determined by matching the solutions of Stokes equation for flow outside the sphere with that of the Brinkman equation for the flow inside the porous sphere. The drag force experienced by a porous sphere is evaluated and its variation is studied with respect to the material parameters. Some well-known results are then deduced from the present analysis.