Towards a transport equation that acknowledges mixing and spreading rates

Solute transport has been traditionally simulated with the advection-dispersion equation (ADE), even though this equation fails to reproduce many field observations (scale dependence of dispersion, time dependence of kinematic porosity, tailing, etc). Worse, the ADE equates mixing and spreading, which is severe because mixing controls the actual rate of fast reactions (tautologically, those whose rate depends on the rate at which reactants mix). Mixing is controlled by internal disorder within a solute plume, which is driven by heterogeneity in velocity. As such, it is linked to dispersion, which defines the rate of spreading of a solute plume. Still, the distinction between mixing and spreading is important for conceptually accurate transport. Effective transport equations based on non-local formulations can provide such a separation but introduce additional parameters that must be calibrated in each situation. In order to predict mixing from descriptions of hydraulic parameters, we must first understand its dynamics. To this end, we perform detailed simulations of transport through heterogeneous media. We analyze results in terms of mixing, as quantified by the scalar dissipation rate (rate of destruction of concentration variance), and spreading, as quantified by the rate of growth of the 2nd moments of the spatial distribution of concentration. We find that mixing is activated by the shear of solute bodies (spreading), which generates transverse gradients and activate