Hydrodynamic stability of a layer of viscous gravity-driven power-law fluid flow under rotating centrifugal force

Abstract

This article investigates the stability of a thin power-law liquid film flowing down along the outside surface of a rotating vertical cylinder. The result is improved through the introduction of the flow index and the rotating centrifugal force into the governing equation. In contrast to most previous studies presented in the literature, the solution scheme employed in this study is based on a power series approximation approach rather than an analytical method. The growth rate of the amplitudes, the wave speeds, and the threshold conditions are obtained subsequently as the by-products of stability solutions. When the fluid film flows down the outside surface of a stationary vertical cylinder, the degree of instability in the film flow is further intensified by the lateral curvature of the cylinder. As the cylinder starts to rotate, the flow becomes relatively more unstable as the cylinder radius is increased at larger values of the Rossby and Reynolds numbers. Notably, this finding is the opposite of that observed for film flows along a stationary vertical cylinder. Furthermore, the size of the supercritical region increases significantly as the cylinder rotates. The analysis results also indicate that by increasing the flow index, the film flow can become relatively less unstable while traveling down along the rotating vertical cylinder.