Creeping flow of a viscous fluid in a uniformly porous slit with porous medium: An application to the diseased renal tubules

Abstract

In this paper, exact solutions for the creeping flow of Newtonian fluid through a porous slit with uniform reabsorption at the porous walls and a porous medium in between are presented. The momentum equation is converted into the form of stream function and is then solved exactly. The solutions for corresponding problem without porous filling in the channel are also deduced and they match exactly with those present in literature. Expressions for other useful physiological quantities like longitudinal and transverse velocities, pressure difference, mean pressure drop across the slit, volume flow rate, wall shear stress, fractional reabsorption and leakage flux are derived. The absorption velocity for renal tubule in a rat kidney is computed for the relevant fractional reabsorption of 80%. The data are then used to tabulate pressure differences corresponding to various values of medium porosity. The results are also presented graphically and it is shown that there is a possibility of reverse flow, usually farther along the length of the slit, when the values of initial flow rate are not high or when the values of absorption velocity are too high.