Oscillatory dynamics of immiscible liquids with high viscosity contrast in a rectangular Hele–Shaw channel

Abstract

The dynamics of the interface of liquids with a high viscosity contrast, performing harmonic oscillations with zero mean in a straight slot channel, is experimentally investigated. The boundary is located across the channel and oscillates along the channel with a harmonic change in the flow rate of the fluid pumped through the channel. Owing to the high contrast of viscosities, the motion of the more viscous liquid obeys Darcy's law, while the low-viscosity liquid performs “inviscid” oscillations. The oscillations of the interface occur in the form of an oscillating flat tongue of low-viscosity liquid that periodically penetrates into the more viscous one. The interface oscillations lead to the manifestation of two effects. One of these consists of changes in the averaged shape of the interface and the liquid contact line. The interface in the cell plane takes the form of a “hill,” the dynamical equilibrium of which is maintained by oscillations, while the deformation of the boundary is proportional to the amplitude of the oscillations and vanishes in their absence. The second effect consists of the development of finger instability of the oscillating boundary, which manifests itself in the periodic development of fingers of low-viscosity liquid at part of a period. The instability develops in a threshold manner when the relative amplitude of the interface oscillations reaches a critical value. It is found that the instability has a local character and manifests itself in those regions of the interface where the amplitude of the oscillations reaches a critical value. The stability threshold decreases with the dimensionless frequency.