Hydrodynamical study of flow in a permeable channel: Application to flat plate dialyzer

Abstract

This article investigates the problem of creeping motion of a Newtonian fluid in a permeable slit. The seepage velocity at the slit walls is assumed to obey the Darcy's law whereas the tangential velocity is taken in accordance with the Beaver's and Joseph's slip boundary condition. Exact solution of the hydrodynamical equations is obtained using the separation of variables technique. Expressions describing various quantities of interests are also derived. The influence of slip parameter is observed on the velocity and pressure field. The obtained results are applied to the physiological problem of blood flow in a flat plate dialyzer. Using the available data in the literature, theoretical values of filtration coefficient and the mean pressure drop in a flat plate dialyzer are computed and found to be in good agreement with the corresponding available experimental values.