Abstract
The e ect 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.
Highlights
Incompressible Newtonian liquid layers confined in a horizontal Hele-Shaw cell
Suppose that the Hele-Shaw cell is submitted to horizontal oscillatory motion according to the law of displacement a cos(ωt) x, where a and ω designate, respectively, the displacement amplitude and the dimensional frequency of the oscillatory motion
As in the traditional Hele-Shaw flow where the aspect ratio of the cell is considered smaller than unity, a first approximation is obtained from Eqs (1) and (2) as follows [11,12]
Summary
On the vertical walls, the no-slip boundaries conditions are: Fig. 1.
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