Roll convection of binary fluid mixtures in porous media

TL;DR

This paper theoretically analyzes the nonlinear behavior and stability of roll convection in binary fluid mixtures within porous media, revealing deformation effects and new instability mechanisms compared to classical Rayleigh-Bénard convection.

Contribution

It introduces a theoretical framework for binary mixture convection in porous media, highlighting deformation of streamlines and identifying new instability mechanisms.

Findings

Streamline deformation in Soret regime explained by Darcy equation

Stability regions are limited by crossroll, zigzag, and oscillatory instabilities

Comparison with pure fluid convection shows qualitative similarities

Abstract

We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh-B\'enard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared to one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh--B\'enard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios which are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism.