Stability of interface between liquids with high viscosity contrast in unevenly rotating cavity

Abstract

Abstract The effect of modulation of the cavity rotation rate on the interface of liquids of different densities and high viscosity contrast is studied experimentally. The cavity is a short horizontal cylinder rotating around its axis. The end walls of the cavity form a narrow gap. Under uniform rotation the interface has an axisymmetric shape. With the modulation growth, the axisymmetric boundary loses stability. Instability manifests itself in the appearance of a regular quasistationary relief at the interphase. The relief excitation is associated with the Kelvin-Helmholtz instability. Tangential velocity discontinuity under modulation arises due to various interaction of liquids with the cavity end walls because of viscosity contrast. The viscosity contrast, on the one hand, is responsible for tangential velocity discontinuity; on the other, it has a significant effect on the threshold of Kelvin-Helmholtz instability. It results in decrease of stability threshold and an increase of relief wavelength.