On the control of small-scale heterogeneity and (spatially variable) diffusion on mixing-limited reactions in unsaturated soils

Soils are characterized by structural components on multiple spatial scales, originating from soil formation processes, soil-plant interactions, microbial activity and management operations. This leads to local heterogeneities for almost all measurements of physical, chemical and biological state variables. This includes the diffusion process, which is known to be affected by the tortuosity, and therefore the water content. Also, biochemical reactions in soils appear to be highly variable in space and time. Yet, the identification of the main controlling factors of the dynamic of reaction rates in unsaturated porous media remain partial.

Studying biochemical reaction in real-world soil-plant-atmosphere systems is highly challenging since the true underlying structures can never be absolutely known. For this, it is appealing to employ synthetic experiments. In this study, we consider a simple A+B à C reaction and investigate the potential impact of small-scale heterogeneity, infiltration fluxes and diffusion on apparent reaction rates in a series of synthetic soils geostatistically described by the Miller-Miller theory. Reactive transport is solved using the random-walk particle-tracking approach to properly account for dispersion and mixing conditions.

Results indicates a synergetic control of the intensity of soil heterogeneity, the Peclet number and the spatial variability of the (tortuosity-dependent) diffusion coefficient on mixing conditions, which has a great impact on effective reaction rates and on the formation of hot-spots and hot-moments. The initial location of the reactants appears to also condition the mixing state of the system and, therefore, the dynamic of reactions. We illustrate then the high complexity of reactive systems in unsaturated soils, which makes the use of average macroscopic reaction rates (as in most agriculture, environmental and geoengineering models) at least questionable.