Mathematical Model of Solute Transport in a Permeable Tube with Variable Viscosity

Abstract

AbstractThe purpose of this paper is to investigate the influence of variable viscosity on solute transfer in fluid flow through a permeable tube with possible applications to the blood flow in glomerular capillaries. The difference in transcapillary hydrostatic pressure and the equivalent difference in colloid osmotic pressure regulates solute transport through the glomerular capillary wall(Starling’s law). Fluid flow in a capillary is assumed to be viscous, incompressible, and Newtonian with variable viscosity. The nonlinear and coupled equations regulating fluid flow and solute transport are solved analytically and numerically. Graphs have been used to discuss the impacts of varying viscosity and flow parameters on hydrostatic and osmotic pressures, and solute concentrations using a set of physiological data. It is observed that increasing the viscosity coefficient raises the hydrostatic pressure while decreasing the osmotic pressure at the capillary’s end. As the viscosity coefficient increases, the solute concentration at the exit falls and the solute clearance increases through the capillary wall.KeywordsStarling’s lawUltrafiltrationVariable viscosityPermeable wallFinite difference method