Stability of an interface with ultra-low tension in a Couette flow

Abstract

The stability analysis of an interface driven by a plane Couette flow at a low Reynolds number is revisited. Motivated by recent experiments on interfaces with ultra-low tension, we focus on the regime of large capillary numbers. The discussion is restricted to unbounded flows, with particular emphasis given to the role played by surface tension. We first discover that the flow is always unstable when the tension and the density difference are strictly zero. It is then shown that, when either the tension or the density difference are finite, the stability is controlled by both the viscosity and the mass density ratio. The first condition for the flow to be unstable is that the denser fluid is also the more viscous. We then identify a second requirement stating that the kinematic viscosity of the lower fluid has to be smaller than that of the upper fluid, otherwise the flow is stable. Finally, the results are discussed in light of recent experiments.