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

The interfacial instability due to viscosity stratification is studied expe rimentally in a closed Couette geometry. A vertical interface is formed bet ween two concentric cylinders with density-matched fluids of unequal viscos ity. The outer cylinder is rotated with a time-harmonic motion, causing spa tially periodic disturbances of the interface. The wavelengths and growth r ates predicted by linear theory agree well with experimental results. Appli cation of Fjortoft's inflection point theorem shows the neutral stability c urves to be consistent with an internal instability occurring in the less v iscous phase. Because the standard Floquet theory yields only time-averaged growth rates, the instantaneous behavior of the system is examined numeric ally. :This reveals the flow to be unstable to a disturbance which has a ma ximum that oscillates between the interface and a location within the less viscous fluid. Surprisingly, it is found that interfacial wave amplificatio n originates with the internal disturbance, and is not directly caused by i nterfacial shear. This unsteady instability may explain the growth of waves in ''transient'' process flows, e.g., fluids encountering changing flow ge ometry. 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 adjacen t to the moving boundary. (C) 1999 American Institute of Physics. [S1070-66 31(99)01504-4].