Abstract
We investigate the effect of density gradients on miscible Rayleigh–Taylor fingers in homogeneous porous media using two families of concentration-dependent density profiles: (a) monotonic and (b) nonmonotonic. The first family consists of linear, quadratic, and cubic functions of the solute concentration, while the latter is described as a quadratic function of the solute concentration such that the density maximum (minimum) appears in time as diffusion relaxes the concentration gradient. With the help of these simple models, we are able to address one of the most puzzling questions about the fingering instabilities with nonmonotonic density profiles. Using linear stability analysis and nonlinear simulations, we show that density gradients play a pivotal role in controlling instability.
Highlights
There are several situations in which hydrodynamic instabilities occur due to an adverse density difference in the gravity field when a heavy fluid overlies a light fluid
We model the fluid density as piecewise smooth functions of a solute concentration and perform linear stability analysis based on the widely used method of quasi-steady state approximation (QSSA)
Motivated by the basic question in porous media convection, we developed a phenomenological theory to treat density gradients in the context of the dynamics of convective instability in porous media flow
Summary
There are several situations in which hydrodynamic instabilities occur due to an adverse density difference in the gravity field when a heavy fluid overlies a light fluid. In RT fingering, a convective motion is generated at the interface between two fluids. Numerical, and experimental research of this classical hydrodynamic instability in porous media, several questions remain unanswered. Gopalakrishnan et al. experimentally and numerically verified the relative role of convective and diffusive mixing in miscible RT fingering in porous media. Through systematic analysis, these authors concluded that in the fingered zone, both diffusion and convection have equal contributions. The other important aspect that has not been understood yet is the role of “transient density gradients” in miscible RT fingering. Relaxation of the concentration gradient changes the density gradient within the diffusive layer, unlike its immiscible counterparts
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