{
  "id": "2505.11005",
  "version": "v1",
  "published": "2025-05-16T08:51:12.000Z",
  "updated": "2025-05-16T08:51:12.000Z",
  "title": "Solute mixing in porous media with dispersion and buoyancy",
  "authors": [
    "Marco De Paoli",
    "Guru Sreevanshu Yerragolam",
    "Roberto Verzicco",
    "Detlef Lohse"
  ],
  "categories": [
    "physics.flu-dyn",
    "physics.geo-ph"
  ],
  "abstract": "We analyse the process of convective mixing in 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 ($D_m^*$), the solute is redistributed by an additional spreading, in longitudinal and transverse flow directions, which is quantified by the coefficients $D_l^*$ and $D_t^*$, 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 $r=D_l^*/D_t^*$ and $\\Delta=D_m^*/D_t^*$. With the aid of numerical Darcy simulations, we investigate the mixing dynamics without and with dispersion. We find that in absence of dispersion ($\\Delta\\to\\infty$) 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 ($Ra=10^4$). 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-16T08:51:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "porous media",
      "solute mixing",
      "anisotropic fickian dispersion tensor",
      "rayleigh-darcy number",
      "solute produces density differences driving"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}