Effect of Varying Viscosity on Two-Fluid Model of Blood Flow through Constricted Blood Vessels: A Comparative Study

Most of the previously studied non-Newtonian blood flow models considered blood viscosity to be constant but for correct measurement of flow rate and flow resistance, the hematocrit dependent viscosity will be better as various literature suggested the variable nature of blood viscosity. Present work concerns the steady and pulsatile nature of blood flow through constricted blood vessels. Two-fluid model for blood is considered with the suspension of all the RBCs (erythrocytes) in the core region as a non-Newtonian (Herschel-Bulkley) fluid and the plasma in the cell free region near wall as a Newtonian fluid. No slip condition on the wall and radially varying viscosity has been taken.

For steady flow the analytical approach has been taken to obtain the exact solution. Regular perturbation expansion method has been used to solve the governing equations for pulsatile flow up to first order of approximation by assuming the pulsatile Reynolds number to be very small (much less than unity).

Flow rate, wall shear stress and velocity profile have been graphically analyzed and compared with constant viscosity model. A noteworthy observation of the present study is that rise in viscosity index leads to decay in velocity, velocity of plug flow region, flow rate while flow resistance increases with rising viscosity index (m). The results for Power-law fluid (PL), Bingham-plastic fluid (BP), Newtonian fluid (NF) are found as special cases from this model. Like the constant viscosity model, it has been also observed that the velocity, flow rate and plug core velocity of two-fluid model are higher than the single-fluid model for variable viscosity.

The two-phase fluid model is more significant than the single-fluid model. Effect of viscosity parameter on various hemodynamical quantities has been obtained. It is also concluded that a rising viscosity parameter (varying nature of viscosity) significantly distinguishes the single and two-fluid models in terms of changes in blood flow resistance. The outcome of present study may leave a significant impact on analyzing blood flow through small blood vessels with constriction, where correct measurement of flow rate and flow resistance for medical treatment is very important.