Solute transfer in fluid flow in permeable tubes with application to flow in glomerular capillaries

Abstract

A mathematical model for solute transfer in an ultrafiltering glomerular capillary has been proposed. The solute transfer, by diffusion and convection, within and across the tube wall has been considered. Effects due to the presence of red cells are neglected and the blood is assumed to be Newtonian fluid with constant viscosity. The rate of fluid movement at the wall is assumed to be proportional to the difference between the net hydrostatic and osmotic forces — Starling's law. The velocity and concentration profiles, at different positions along the axis, the axial distribution of hydrostatic and osmotic pressures and the total solute clearance have been obtained. It is found that the osmotic pressure has relatively greater influence on capillary mass transfer than the hydrostatic pressure. Radial concentration gradients of considerable order have been observed, particularly near the entrance portion of the tube. The radial concentration gradient increases with ultrafiltration parameter and decreases, as the diffusion coefficient increases. The influence of transmittance coefficient (solute wall permeability coefficient) is found to be predominant at higher ultrafiltration rates (higher concentration difference across the membrane). The generalized nature of the present model has been illustrated by obtaining some of the existing results as the particular cases of this model. Using relevant data, the physiological implications of some of the obtained results have been briefly discussed.