Three-layered Couette flow of polar fluid with non-zero particle spin boundary condition at the interfaces with applications to blood flow

Abstract

In this paper, Couette flow of blood is modelled as a three-layered flow. The model basically consists of a core (red-cell suspension) and plasma (a Newtonian fluid) in the top (near the moving plate) and bottom (near the stationary plate) layers. Flow is assumed to be steady and laminar and fluids are incompressible. A spin boundary condition at the interfaces is used by introducing two parameters. Analytic expressions for velocity, total angular velocity and effective viscosity have been obtained and their variations with spin parameters S and s, layer thickness, coupling number N and characteristic length ratio L are computed and shown graphically. One of the important observations of the analysis is the permissible values of the coupling number N is between 0 and $1\mathrm{/}\sqrt{2}$ (in the existing literature, the range of N is 0 to 1). The present model include s Couette f low of one and three-layered Newtonian fluids and one-layered polar fluid models as its special cases. Applications of the proposed model to blood flow have been briefly discussed.