Rayleigh–Taylor mixing in porous media at an extreme viscosity contrast

Abstract

We present experimental findings of Rayleigh–Taylor (RT) instability within porous materials, with a significant viscosity contrast of M ≈ 106, where M represents the ratio of the dynamic viscosity of heavy fluid to that of light fluid, M = μH/μL, and Ra = 6.62 × 104–6.67 × 105, and Rayleigh number (Ra) quantifies the relative significance of buoyancy forces compared to viscous forces. We observe that the lighter fluid diffuses into the denser one, creating a transient diffusive boundary layer that rapidly becomes unstable, transitioning into a convection-dominated regime. Initially, the instability manifests as small fingers protruding upward. However, these fingers coalesce and form fewer major fingers. Convection persists until fingers reach the upper boundary, transitioning into a shutdown regime. During the convection-dominated phase, the extracted solute concentration exhibits a linear relationship with time on a log –log scale, suggesting a constant mass flux. However, this flux diminishes upon entering the shutdown regime. The steady flux, quantified by the Sherwood number, correlates with the Rayleigh number as Sh = 0.046Ra, indicating independence from the height of the porous medium. We have also developed a simple conceptual model that effectively captures the dynamics of RT mixing.