Study of couple stresses and wall permeability effects on the flow in permeable membranes

This study focused on investigating wall permeability, and couple stresses effects on the fluid flow between two permeable membranes. These flows are encountered in a variety of industrial and applied biological processes, particularly in the fluid filtration process through dialyzer membranes. Darcy's law is employed to define the fluid suction and injection via surface of the membrane. Fluid motion is assumed to be steady and Stokesian, where the flow Reynolds number is low. The exact solution for the fluid flow field is obtained in conjunction with the lubrication approximation. Explicit expressions are derived for some useful quantities of flow interest. A significant change in the flow field is noticed for the presented non-Newtonian fluid model. Graphical results show that the flow field has prominent deviations when the inlet pressure, membrane permeability, and the couple stress parameters are changed. In order to validate results, numerical values of the filtration constant and the average pressure drop for a dialyzer membrane are computed. A comparison of the derived results with existing data reveals a good agreement with experimental and empirical results. The presented results are new and can be reduced to existing results in the literature for specified values of the couple stress parameters.