Power-law fluid annular flows between concentric rotating spheres subject to hydrodynamic slip

Abstract

We report analytical solutions to the problem of non-Newtonian power-law fluid flows in the annular space between a pair of concentric spherical surfaces rotating at distinct angular velocities with the inner and outer wall boundaries subject to general asymmetric hydrodynamic slip conditions. Analytical solutions are possible because of assuming constant valued apparent hydrodynamic slip lengths in the linearized kinematic slip conditions, and our solutions can be validated against the limiting results of Newtonian fluids, no-slip conditions, or a single rotating sphere reported in previous literature. Comprehensive systematic parametric studies show that (additional to the power-law fluid flow behavior index) the degree of hydrodynamic slip at the inner surface is the dominant factor that determines the limiting values of the viscous torque exerted on the inner sphere as the outer-to-inner radius ratio assumes significantly large values. Nonetheless, the flow behavior index and outer slip length prove to be the crucial key parameters responsible for a variety of torque responses, which can be categorized by a compact analytical expression, as the outer-to-inner radius ratio is increased in the small to moderate regime. We propose a criteria which identifies the proper slip length and outer-to-inner radius ratio combinations for a given power-law flow behavior index such that the hydrodynamic slip wall effects of the outer surface can be minimized or eliminated. A simple method is also presented to characterize and quantify the apparent hydrodynamic slip effects by use of the concentric rotating spheres viscometer.