Fundamental Steady F1ow of Polar Fluids

Abstract

A few fundamental steady flows of polar fluid, i.e., flow in a circular tube, flow between two parallel plates and flow between two ooaxial cylinders are analysed with the help of the theory of Eringen. Couple stress and spin angular momentum are considered in this approach. The exact solutions for velocity, micro-rotation, vortioity and shearing stress are obtained mathematically. These solutions are characterized by two parameters, i.e., the ratio of viscosities ε and the size effect parameter λ which do not appear in a Newtonian fluid. ε is the ratio of vortex visoosity to shear viscosity. λ means the size relation between the corpuscle and the characteristic length. The solutions are compared with those of Newtonian fluid and it is investigated how they vary with ε and λ. Apparent viscosity is determined for each flow. Material constants of polar fluid can be decided from these apparent viscosities.