Analytical solution for two-phase flow between two rotating cylinders filled with power law liquid and a micro layer of gas

This paper deals with the effects that a thin gas layer exerts on the hydrodynamic aspects of power law liquid in a radial Couette flow between two cylinders. Analytical solution is made to determine the velocity profile in the two-phase flow system occupied by the power law liquid and the micro layer of a gas. It is shown that the thin (micro) gas layer contributes in reducing torque to set the fluid in motion in most cases. However, by considering generalized power law liquids, this paper limits the credibility for the positive role of the gas layer on reducing the torque for lubrication. For instance, when n < 0.5 (n is the behavior index of the liquid), slight increment in the torque (about 6%) is reported. Finally, energy gradient method is used for stability analysis. It is shown that the stability nature may be changed based on behavior index of the liquid.