Hydrodynamics Of The Flow Of A Newtonian Fluid Through A Linearly Absorbing Renal Tubule Filled With Porous Medium

Abstract

The present study is motivated by the flow of fluid inside renal tubule in a kidney, which filters urine and reabsorbs fluid and useful substances into the body. When the tube is diseased, several substances block the pores on the surface of the tubule, and can also get suspended in the tubular cavity. Firstly, the medium inside the tubule acts as a porous medium and secondly, the reabsorption at wall surface does not remain constant. The detailed study of both these phenomena together is missing in literature. Therefore, we study the mathematical problem of creeping flow through a renal tubule slit taking into account both the disease effects assuming linear reabsorption rate at walls. We also compute fluid velocities and various other physically relevant quantities like pressure differences, leakage flux, fractional reabsorption etc, and to analyse the flow characteristics graphically.