Stability of oscillatory two-phase Couette flow

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Abstract
The authors investigate the stability of two-phase Couette flow of different liquids bounded between plane parallel plates. One of the plates has a time-dependent velocity in its own plane, which is composed of a constant steady part and a time-harmonic component. In the absence of time-harmonic modulations, the flow can be unstable to an interfacial instability if the viscosities are different, and the more viscous fluid occupies the thinner of the two layers. Using Floquet theory, it is shown analytically in the limit of long waves that time-periodic modulations in the basic flow can have a significant influence on flow stability. In particular, flows which are otherwise unstable for extensive ranges of viscosity ratios can be stabilized completely by the inclusion of background modulations, a finding that can have useful consequences in many practical applications.

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