A micropolar fluid model for hydrodynamics in the renal tubule

Abstract

The creeping flow of an incompressible micropolar fluid in a small-diameter permeable tube is studied. The fluid absorption at the tube walls is taken as a function of wall permeability and the pressure gradient across the tube wall. Closed-form solutions of the governing equations for the pressure, velocity and micro-rotation fields are obtained. Expressions describing variations in the axial volume flow rate, mean pressure, wall leakage flux, wall shear stress and the fractional re-absorption are derived. Effects of the wall permeability coefficient K , the micropolar parameter m and the coupling number N on flow variables are graphically presented and implications of results are discussed briefly. The obtained solutions are applied to the flow problem in the proximal renal tubule and probable values of the wall permeability parameter and the mean pressure drop in the tubule are obtained. It is found that the mean pressure drop in the proximal tubule is higher for the micropolar fluid than for the Newtonian fluid. It is also found that the volume flow rate of the micropolar fluid decreases exponentially as a function of the axial distance. This is a biologically significant result which is well accepted and is reported in the literature by earlier researchers too. The derived solutions coincide well with the existing solutions for the Newtonian fluid flow in a permeable tube as a special case.