Stokes flow through a slit with periodic reabsorption: An application to renal tubule

Abstract

This paper is concerned with the Stokes flow of an incompressible viscous fluid through a slit with periodic reabsorption at the walls. The momentum equation for the two dimensional flow is exactly solved in terms of stream function for two different cases of boundary conditions. Dimensional forms of stream function, velocity components, axial flow rate, pressure distribution, mean pressure drop, wall shear stress, fractional reabsorption and leakage flux are obtained. The points of maximum velocity components are also identified for fixed axial distance. Using physiological data of rat kidney, the theoretical values of periodic reabsorption and pressure drop for various values of fractional reabsorption are tabulated. The graphs of flow properties for both the cases are compared with the case of uniform reabsorption. It is shown that the periodic reabsorption parameter for both the cases plays a vital role in altering the flow properties, which are useful in analyzing flow behavior during the reabsorption of glomerular filtrate through a renal tubule in normal and diseased conditions. It is found that 50% reabsorption of fluid from a single nephron can be achieved by setting α=3.197500134cm for one of the cases which indicates that there is a need of artificial kidney for survival. In case 2, a minor treatment is needed as the value of α for 80% reabsorption is not possible. Streamlines are also drawn to analyze the flow behavior through an abnormal renal tubule.