Density jump in high-speed Hele-Shaw flows

Abstract

We consider a high speed displacement from a Hele-Shaw cell when not only a viscosity jump but also a density jump on the interface drives the instability and the generation of viscous fingers. In a mathematical sense, density is a prior factor in the inertial nonlinear terms in the full-averaged Navier – Stokes – Darcy model. That is why we investigate the influence of inertial effects on fingering process. On that way, we have performed linear stability analysis and numerical simulations by finite-difference method considering dependencies on two dimensionless parameters: density ratio and Reynolds number. Two main conclusions can be done. The first is that with an increase of the Reynolds number, the interface is stabilized at the initial stage of displacement. And the second is that the displacement of a denser fluid by a less dense one is more unstable than the opposite case, when a denser fluid displaces a less dense one. Nonlinear simulations have also shown pronounced viscous bubble formation even when viscosity ratio is relatively small.