Stepping beyond perfectly mixed conditions in soil hydrological modelling using a Lagrangian approach

A recent experiment of Bowers et al. (2020) revealed that diffusive mixing of water isotopes (8 2 H and 8 18 0) over a fully saturated soil sample of a few centimetres in length required several days to equilibrate completely. In this study, we present an approach to simulate such time-delayed diffusive mixing processes, on the pore scale, beyond instantaneously and perfectly mixed conditions. The diffusive pore mixing (DIPMI) approach is based on a Lagrangian perspective on water particles moving by diffusion over the pore space of a soil volume and carrying concentrations of solutes or isotopes. The idea of DIPMI is to account for the self-diffusion of water particles across a characteristic length scale of the pore space using pore-size-dependent diffusion coefficients. The model parameters can be derived from the soil-specific water retention curve, and no further calibration is needed. We test our DIPMI approach by simulating diffusive mixing of water isotopes over the pore space of a saturated soil volume using the experimental data of Bowers et al. (2020). Simulation results show the feasibility of the DIPMI approach for reproducing the measured mixing times and concentrations of isotopes at different tensions over the pore space. This result corroborates the finding that diffusive mixing in soils depends on the pore size distribution and the specific soil water retention properties. Additionally, we perform a virtual experiment with the DIPMI approach by simulating mixing and leaching processes of a solute in a vertical, saturated soil column and compare the results against simulations with the common perfect mixing assumption. The results of this virtual experiment reveal that the frequently observed steep rise and long tailing of breakthrough curves, which are typically associated with non-uniform transport in heterogeneous soils, may also occur in homogeneous media as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.