Circular Couette Flow between Porous Cylinders

Abstract

Circular Couette flow between porous cylinders is treated in this paper. Exact solutions of Navier-Stokes equations for the flow in the gap between cylinders and of Darcy-Brinkman-Lapwood equations for the flow in porous rings are found analytically by matching velocities and stresses on the porous boundaries, without making any previous assumptions concerning the slip velocities. In the special case in which the inner cylinder is fully porous and stationary, and the outer cylinder is fully rigid and rotating, the torque exerted by the rotation of the outer cylinder on the inner one is found, and it is shown how the effective viscosity of the liquid can be determined in possible experiments.