Stability of miscible Rayleigh-Taylor fingers in porous media with non-monotonic density profiles

TL;DR

This paper investigates how non-monotonic density profiles influence the stability of Rayleigh-Taylor fingers in porous media, introducing a new dimensionless group to better understand and control the instability.

Contribution

It introduces the gradient Rayleigh number (Ra$_g$) to analyze the stability of RT fingers with non-monotonic density profiles in porous media.

Findings

Density gradients significantly affect RT finger stability.

The gradient Rayleigh number (Ra$_g$) effectively predicts instability.

Controlling density gradients can manage RT fingering.

Abstract

We study miscible Rayleigh-Taylor (RT) fingering instability in two-dimensional homogeneous porous media, in which the fluid density varies non-monotonically as a function of the solute concentration such that the maximum density lies in the interior of the domain, thus creating a stable and an unstable density gradients that evolve in time. With the help of linear stability analysis (LSA) as well as nonlinear simulations the effects of density gradients on the stability of RT fingers are investigated. As diffusion relaxes the concentration gradient, a non-monotonic density profile emerges in time. Our simple mathematical treatment addresses the importance of density gradients on the stability of miscible Rayleigh-Taylor fingering. In this process we identify that RT fingering instabilities are better understood combining Rayleigh number (Ra) with the density gradients--hence defining a new dimensionless group, gradient Rayleigh number (Ra$_g$). We show that controlling the stable and unstable density gradients, miscible Rayleigh-Taylor fingers are controllable.