Stability of rigid motions and rollers in bicomponent flows of immiscible liquids

The authors study the stability of flows of two immiscible fluids between two cylinders rotating at the same frequency. They show that this problem can be reduced to the minimization of a certain functional. Necessary and sufficient conditions for the stability of centrifuged configurations with the heavier fluid on the outside, are given. It is shown that the viscosity plays no role in the stability problem. This is different from shearing flows between rotating cylinders, where it is in fact possible to have the heavier fluid inside.