Control of the Interfacial Instabilities in a circular Hele-Shaw cell oscillating with a periodic angular velocity

The stability of an interface of two viscous immiscible fluids of different densities and confined in a Hele-Shaw cell which is oscillating with periodic angular velocityis investigated. A linear stability analysis of the viscous and time-dependent basic flows, generated by a periodic rotation, leads to a time periodic oscillator describing the evolution of the interface amplitude. In this study, we examine mainly the effect of the frequency of the periodic rotation on the interfacial instability that occurs at the interface

Effect of Horizontal Vibration on the Interfacial Instability in a Horizontal Hele-Shaw Cell

The effect of periodic oscillations on the interfacial instability of two immiscible fluids, confined in a horizontal Hele-Shaw cell, is investigated. A linear stability analysis of the basic state leads to a periodic Mathieu oscillator corresponding to the amplitude of the interface. Then, the threshold of parametric instability of the interface is characterized by harmonic or subharmonic periodic solutions. We show that the relevant parameters that control the interface are the Bond number, density ratio, Weber number and amplitude and frequency of oscillations

Interfacial instability in a time-periodic rotating Hele-Shaw Cell

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