Effect of varying viscosity on two-fluid model of pulsatile blood flow through porous blood vessels: A comparative study.

Abstract Present work concerns the pulsatile blood flow of two-fluid model through porous blood vessels under the effect of radially varying viscosity. Blood is modeled as two-phase fluid model consisting a core region by non-Newtonian (Herschel-Bulkley) fluid and a plasma region modeled as Newtonian fluid. No slip condition has been used on wall and pressure gradient is taken as periodic function of time. Up to first order approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in flow resistance between our model and previously studied single and two-fluid models without porous layer near wall has also been done. The wall of the blood vessel is composed by a thin Brinkman (porous) layer. The stress jump condition has been imposed on fluid-porous interface. Analytical expressions for the velocity profile, flow rate, wall shear stress and flow resistance have been obtained for different regions and the effect of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the flow variables are pictorially discussed. It is perceived that values of flow rate for two-fluid model with porous region near wall is higher in comparison to two-fluid model without porous region near wall. Present study reveals a significant impact of glycocalyx layer on blood flow through blood vessels with a porous layer near wall. Highlights • In the present work, pulsatile nature of blood flow of two-fluid model through porous blood vessels under the effect of radially varying viscosity has been done. • The combined effect of plasma layer thickness (and hence porous layer thickness), varying viscosity parameters, permeability and viscosity ratio parameter on hemodynamical quantities have been pictorially analyzed and compared with constant viscosity model. • The viscosity ratio parameter (and hence porosity of arterial wall) affects the plug core radius (and hence the yield plane location). • Due to presence of porous region near wall, there is slight phase difference in flow rate and flow resistance between two-fluid model with and without porous region near wall which completely agrees with Tiwari and Deo [A. Tiwari, S. Deo, Pulsatile flow in a cylindrical tube with porous walls: Applications to blood flow, Journal of Porous Media 16(4) (2013) 335-340] approach. • The outcome of above work shows a significant impact of the viscosity ratio parameter and permeability arising due to existence of glycocalyx layer near wall on various hemodynamical quantities such as rate of flow and resistance offered against the flow. [ABSTRACT FROM AUTHOR]