Compression-driven displacement flows in an axisymmetric Hele-Shaw geometry #

Callum Cuttle, Liam Morrow, Christopher W MacMinn

14:50 Tuesday in 4Q08.

Part of the Microfluidics and flow in porous media session.

Abstract #

The displacement of a viscous liquid within a confined space by the injection of a gas holds relevance to a multitude of physical problems, from the storage of CO2 or hydrogen in subsurface reservoirs to certain types of volcanic erruption or the reopening of collapsed pulmonary airways. A recent study of uniaxial gas-driven displacement flows in a capillary tube demonstrated that the coupling between the viscous drainage flow and the spring-like compression of the gas generates complex nonlinear dynamical regimes, described by a simple ODE with a single dimensionless parameter. Here, we consider radial gas-driven displacement in an idealised axisymmetric Hele-Shaw geometry. We find that the evolving base-state of the flow adds further complexity to the underlying dynamical system, introducing a dependence on the initial radius of the gas-liquid interface, which may select between quasi-steady and burst-like displacement. We discuss the implications of this idealised system for the classical viscous fingering instability in real Hele-Shaw flows.