Scaling of Rayleigh-Taylor mixing in porous media

TL;DR

This study uses numerical simulations to analyze Rayleigh-Taylor instability-driven mixing in porous media, revealing a linear growth of plumes, a linear relationship between Nusselt and Darcy-Rayleigh numbers, and dimensional differences.

Contribution

It provides new insights into the scaling laws and dimensional effects of Rayleigh-Taylor mixing in porous media at high Péclet numbers.

Findings

Plume length grows linearly with time.

Nusselt number scales linearly with Darcy-Rayleigh number.

Significant differences between 2D and 3D mixing processes.

Abstract

Pushing two fluids with different density one against the other causes the development of the Rayleigh-Taylor instability at their interface, which further evolves in a complex mixing layer. In porous media, this process is influenced by the viscous resistance experienced while flowing through the pores, which is described by the Darcy's law. Here, we investigate the mixing properties of the Darcy-Rayleigh-Taylor system in the limit of large P\'eclet number by means of direct numerical simulations in three and two dimensions. In the mixing zone, the balance between gravity and viscous forces results in a non-self-similar growth of elongated plumes, whose length increases linearly in time while their width follows a diffusive growth. The mass-transfer Nusselt number is found to increase linearly with the Darcy-Rayleigh number supporting a universal scaling in porous convection at high Ra numbers. Finally, we find that the mixing process displays important quantitative differences between two and three dimensions.