Three-dimensional Stokes flow caused by a translating-rotating sphere bisected by a free surface bounding a semi-infinite micropolar fluid

Explicit velocity and microrotation components and systematic calculation of hydrodynamic quasistatic drag and couple in terms of nondimensional coefficients are presented for the flow problem of an incompressible asymmetrical steady semi-infinite micropolar fluid arising from the motion of a sphere bisected by a free surface bounding a semi-infinite micropolar fluid. Two asymmetrical cases are considered for the motion of the sphere: parallel translation to the free surface and rotation about a diameter which is lying in the free surface. The speed of the translational motion and the angular speed for the rotational motion of the sphere are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian approximation. A linear slip, Bassettype, boundary condition has been used. The variation of the resistance coefficients is studied numerically and plotted versus the micropolarity parameter and slip parameter. The two limiting cases of no-slip and perfect slip are then recovered.