Interfacial instability of two superimposed immiscible viscous fluids in a vertical Hele-Shaw cell under horizontal periodic oscillations

摘要

The effect of horizontal periodic oscillations on the interfacial instability of two immiscible, viscous fluids ofndifferent densities, confined in a vertical Hele-Shaw cell, is investigated. An inviscid linear stability analysis ofnthe viscous basic flow leads to the periodic Mathieu oscillator describing the evolution of interfacial amplitude.nWe examine mainly the effect of the periodic oscillations and the influence of the viscosity on the stability of theninterface. The results showthat a decrease in the viscosity contrast has a stabilizing effect on theKelvin-Helmholtzninstability, which is displaced towards the long-wave region. The effects of other parameters such as the frequencynnumber and the Weber number are also examined.