Supercritical Dynamics of an Oscillating Interface of Immiscible Liquids in Axisymmetric Hele-Shaw Cells

Abstract

The oscillation of the liquid interface in axisymmetric Hele-Shaw cells (conical and flat) is experimentally studied. The cuvettes, which are thin conical layers of constant thickness and flat radial Hele-Shaw cells, are filled with two immiscible liquids of similar densities and a large contrast in viscosity. The axis of symmetry of the cell is oriented vertically; the interface without oscillations is axially symmetric. An oscillating pressure drop is set at the cell boundaries, due to which the interface performs radial oscillations in the form of an oscillating “tongue” of a low-viscosity liquid, periodically penetrating into a more viscous liquid. An increase in the oscillation amplitude leads to the development of a system of azimuthally periodic structures (fingers) at the interface. The fingers grow when the viscous liquid is forced out of the layer and reach their maximum in the phase of maximum displacement of the interface. In the reverse course, the structures decrease in size and, at a certain phase of oscillations, take the form of small pits directed toward the low-viscosity fluid. In a conical cell, a bifurcation of period doubling with an increase in amplitude is found; in a flat cell, it is absent. A slow azimuthal drift of finger structures is found. It is shown that the drift is associated with the inhomogeneity of the amplitude of fluid oscillations in different radial directions. The fingers move from the region of a larger to the region of a lower amplitude of the interface oscillations.

Keywords

• interface
• conical Hele-Shaw cell
• viscosity
• oscillations
• Saffman–Taylor instability