2025/05/16 by De Paoli, Marco, Yerragolam, Guru Sreevanshu, Verzicco, Roberto +1 · 1 citation
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geophysics (physics.geo-ph)
paper · doi:10.48550/arxiv.2505.11005
We analyse the process of convective mixing in two-dimensional, homogeneous and isotropic porous media with dispersion. We considered a Rayleigh-Taylor instability in which the presence of a solute produces density differences driving the flow. The effect of dispersion is modelled using an anisotropic Fickian dispersion tensor (Bear, J. Geophys. Res. 1961). In addition to molecular diffusion (Dm^*), the solute is redistributed by an additional spreading, in longitudinal and transverse flow directions, which is quantified by the coefficients Dl^* and Dt^*, respectively, and it is produced by the presence of the pores. The flow is controlled by three dimensionless parameters: the Rayleigh-Darcy number Ra, defining the relative strength of convection and diffusion, and the dispersion parameters r=Dl^*/Dt^* and Δ=Dm^*/Dt^*. With the aid of numerical Darcy simulations, we investigate the mixing dynamics without and with dispersion. We find that in absence of dispersion (Δ→∞) the dynamics is self-similar and independent of Ra, and the flow evolves following several regimes, which we analyse. Then we analyse the effect of dispersion on the flow evolution for a fixed value of the Rayleigh-Darcy number (Ra=104). A detailed analysis of the molecular and dispersive components of the mean scalar dissipation reveals a complex interplay between flow structures and solute mixing. The proposed theoretical framework, in combination with pore-scale simulations and bead packs experiments, can be used to validate and improve current dispersion models to obtain more reliable estimates of solute transport and spreading in buoyancy-driven subsurface flows.