Impact of saturation on mass transfer rate between mobile and immobile waters in solute transport within aggregated soils

Solute transport in aggregated soils is controlled by pores both inside and between the aggregates. Because the intra-aggregate pores are much smaller than the inter-aggregate pores, in chemical transport modelling the water in the former was often assumed to be immobile in comparison with water in the latter. How to describe mass transfer between the two waters has been studied intensively for saturated soils but poorly for unsaturated soils. In this paper, we investigated this using pore-scale modelling and tomography. The binary structures of porous materials acquired using tomography in our previous work served as the aggregated soils. Since the sizes of the intra-aggregate pores were smaller than the resolution of the tomography, they cannot be explicitly resolved in the tomography. As a result, the solids in the binary structures were porous aggregates and their impact on solute movement was described by an effective diffusion coefficient. In all simulations, the aggregates were assumed to be fully saturated and water distribution between the aggregates was determined by inter-aggregate pore sizes and pore connectedness. Solute movement from water within the inter-aggregates into the aggregates under different saturations was simulated using a pore-scale model. The simulated concentration and flux at pore scale were spatially averaged, and they were then used to calculate the volumetric average mass transfer rate between the two waters. The calculated average mass transfer rates were linked to the memory function widely used in the literature to model solute transport in structured soils. The results indicate that the commonly-used linear mobile-immobile transfer model with its transfer rate coefficient proportional to water content cannot fit the memory function calculated at any saturation. We fitted the simulated results to an empirical formula. The comparisons reveal that in the earlier stage, the memory function decreases with time in a power-law, and in the later stage it decreases exponentially. The time it takes such a transition to complete increases as the saturation decreases. We also explained and proved how to extend these results to simulate reactive solutes. (C) 2014 Elsevier B.V. All rights reserved.