Poiseuille flow of micropolar fluid with non-zero couple stress at boundary with applications to blood flow

Abstract

Poiseuille flow of a micropolar fluid has been reexamined from the point of view of its applications to blood flow. Couple stresses are assumed to be non-zero at the boundary, and a method has been proposed to determine such boundary conditions for a given suspension. Velocity profiles (both axial and rotational) as well as apparent viscosity have been computed for various values of s¯ (a boundary condition and concentration parameter). The results obtained have been compared with experimental values (for blood flow). It is found that they are in a reasonably good agreement. Some of the earlier workers have used solvent viscosity for the classical shear viscosity of the suspension and obtained infinite relative viscosity for a suspension concentration of 40 % which, according to experimental results, is not feasible. An appropriate expression for the classical shear viscosity has been used in the present analysis which removes the apparent viscosity anomaly, i.e., apparent viscosity tends to infinity as the concentration approaches 40 %, from the micropolar fluid theory. Finally, some biological applications of this theory have been discussed.