Stability of oscillatory two-phase Couette flow: Theory and experiment

Abstract

The interfacial instability due to viscosity stratification is studied experimentally in a closed Couette geometry. A vertical interface is formed between two concentric cylinders with density-matched fluids of unequal viscosity. The outer cylinder is rotated with a time-harmonic motion, causing spatially periodic disturbances of the interface. The wavelengths and growth rates predicted by linear theory agree well with experimental results. Application of Fjo/rtoft’s inflection point theorem shows the neutral stability curves to be consistent with an internal instability occurring in the less viscous phase. Because the standard Floquet theory yields only time-averaged growth rates, the instantaneous behavior of the system is examined numerically. This reveals the flow to be unstable to a disturbance which has a maximum that oscillates between the interface and a location within the less viscous fluid. Surprisingly, it is found that interfacial wave amplification originates with the internal disturbance, and is not directly caused by interfacial shear. This unsteady instability may explain the growth of waves in “transient” process flows, e.g., fluids encountering changing flow geometry. It is also demonstrated that in the long wave limit the problem of steady-plus-oscillatory plate motion is simply additive. This implies that it is possible to use oscillations to stabilize steady waves over a limited range of parameter values, but only when the less viscous phase is adjacent to the moving boundary.