Effect of Varying Viscosity on Two-Layer Model of Pulsatile Flow through Blood Vessels with Porous Region near Walls

Abstract

The present work concerns the effect of hematocrit-dependent viscosity on pulsatile flow of blood through narrow tube with porous walls. Two-fluid model of blood is assumed to be consisting of a core region (Casson fluid) and a plasma region (Newtonian fluid). No slip condition is assumed on wall and pressure gradient has been considered as periodic function of time. The wall of the blood vessel composed of a thin porous (Brinkman) layer. The stress jump condition has been employed at the fluid–porous interface in the plasma region. Up to first order, approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in resistance offered against the flow between our model and previously studied single and two-fluid models without porous walls has also been done. Mathematical expressions for velocity, rate of flow and resistance offered against the flow have been obtained analytically for different regions and influence of plasma layer thickness, varying viscosity, stress jump parameter, permeability and viscosity ratio parameter on above quantities are pictorially discussed. It is perceived that the values of flow rate for two-fluid model with porous region near walls are higher in comparison with two-fluid model without porous region near walls. Dependency of hematocrit (Ht) on the porosity parameters is graphically discussed. The study reveals a significant impact of various parameters on hematocrit (Ht). A novel observation is that a slight increase in pressure wave amplitude leads to significant fluctuation in hematocrit (Ht) which also indicates how systole and diastole (which controls the pressure gradient amplitudes) leads to changes on blood hematocrit (Ht).