Density jump in high-speed Hele-Shaw flows

Abstract

We considered the high-speed displacement of fluids from a Hele-Shaw cell where jumps on the interface in both viscosity and density drive the instability and the generation of viscous fingers. Mathematically, the density is a prior factor in the inertial nonlinear terms in the full–averaged Navier–Stokes–Darcy model. Therefore, we investigated the influence of inertial effects on the fingering process. We performed linear stability analysis and numerical simulations by finite–difference method considering dependences on two dimensionless parameters: density ratio and Reynolds number. Two main conclusions could be drawn. The first is that as the Reynolds number increases, the interface becomes more stable in the initial phase of displacement. The second is that the displacement of a denser fluid by a less dense one is more unstable than the opposite case, where a denser fluid displaces a less dense one. We also performed nonlinear simulations that also showed pronounced viscous bubble formation even when the viscosity ratio was relatively small.