Effect of varying viscosity on a two-layer model of the blood flow through porous blood vessels

Abstract

The present work concerns the effect of radially varying viscosity on blood flow through blood vessels with porous walls. Blood is assumed as a two-fluid model consisting of a core region of suspension of all red cells constituted by the Herschel-Bulkley fluid and a peripheral layer of plasma free from the cells modeled as a Newtonian fluid. No slip condition has been used on the wall and the pressure gradient has been taken as constant. The wall of the blood vessel is composed of a thin porous (Brinkman) layer representing the glycocalyx layer. On the fluid interface the stress jump boundary condition as suggested by Ochoa-Tapia and Whitaker has been used. Analytical expressions for velocity profile, wall shear stress, rate of flow and resistance to flow have been obtained for different regions and the effects of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the hemodynamical quantities are discussed and depicted graphically. A comparative analysis for a relative change in flow resistance between our model and the previously studied single and two-fluid models without porous walls has been done. The effects of various parameters on hematocrit and Fahraeus effect have also been analyzed and results of earlier works have been established as special limiting cases of the present study. A novel observation is that a decreasing viscosity ratio parameter (λ1) leads to decay in average concentration of RBCs leading to decay in hematocrit (Ht). It is concluded that a thick porous layer with high porosity at wall due to either a glycocalyx layer or the deposition of fatty plaques of cholesterol may lead to significant decay in hematocrit Ht and may lead to anemia.