Averaged Dynamics of Fluids near the Oscillating Interface in a Hele-Shaw Cell

The steady flow in a Hele-Shaw cell filled with fluids with a high viscosity contrast in the presence of fluid oscillations is experimentally studied. The control of oscillatory dynamics of multiphase systems with interfaces is a challenging technological problem. We consider miscible (water and glycerol) and immiscible (water and high-viscosity silicone oil PMS-1000) fluids under subsonic oscillations perpendicular to the interface. Observations show that the interface shape depends on the amplitude and frequency of oscillations. The interface is undisturbed only in the absence of oscillations. Under small amplitudes, the interface between water and glycerol widens due to mixing. When the critical amplitude is reached, the interface becomes unstable to the fingering instability: Aqueous fingers penetrate the high-viscosity glycerol and induce intensive mixing of miscible fluids and associated decay of the instability. After the disappearance of the fingers, the interface takes a U-shape in the central part of the cell. A similar effect is observed for immiscible fluids: The oscillating interface tends to bend to the side of a high-viscosity fluid. Again, when the critical amplitude is reached, the fingering instability arises at the convex interface. This paper focuses on the causes of bending of the initially undisturbed interface between miscible or immiscible fluids. For this purpose, we measure the steady flow velocity near the interface and in the bulk of a high-viscosity fluid using Particle Image Velocimetry (PIV).