Entraining porous media gravity currents

Porous media gravity currents are primarily horizontal flows driven by a density difference between fluids and limited by Darcy flow through the porous medium. They have been studied extensively both experimentally and theoretically under the assumption that the interface separating the two fluids is sharp. Here we present new experimental results performed using the dye-attenuation technique that quantify the amount of mixing within the spreading current. We find that the mixing may be significant even in homogeneous porous media, and particularly for heterogeneous media. This motivates our theoretical model, in which we assume that dispersive mixing between the ambient and injected fluid may be modelled using an entrainment hypothesis motivated by the well-known turbulent plume theory. Using this modified, porous media gravity current model we predict that for constant input flux the spreading and mixing of the current are self-similar and find good agreement between the experimental data and theoretical model. Moreover, we extend our entrainment model to examine the case of fixed volume, where a late-time cross-over from a dispersion to molecular diffusion limited regimes is possible. The behaviour of these regimes is confirmed using simplified numerical modelling.