One of the key objectives of the Centre is to develop and test experimentally a mathematical model of soil dynamics. The approach adopted in the research is that, to describe water and solute transport in soils at the microscale, some form of a single-phase or multiphase Lattice-Boltzmann model will useful. Alternatives could be envisaged, such as the more traditional network models. However, the advantage of the LB method is that it could use compute tomography data directly as input (with or without prior thresholding) and therefore makes fewer assumptions about the geometry of pore spaces than other approaches. As a trade-off, the size of soil samples that can be modelled by LB models is in general smaller than that handled by network models. Yet we feel that the benefits outweigh the drawbacks in this case, and that the LB method provides a solid foundation, on which to add fungal and microbial growth, and chemical reactivity at surfaces.
Once the planned model is available, it will be used to analyze in detail how micro-scale soil dynamical processes result in emergent properties at the macroscale (typical of measurements) and what type of upscaling is needed to account for observed macroscopic behaviours. We are planning to proceed to a detailed scenario analysis, in which the spatial heterogeneity patterns are modified systematically in the soil samples considered in the modelling. In each scenario considered, we shall attempt to relate the micro-scale spatial heterogeneity with the predicted outcomes at the macroscale, for example in terms of carbon dynamics or contaminant degradation. We are interested in trying to find a statistical or geometrical descriptor of the spatial heterogeneity, which correlates well with macroscopic emergent behaviours. Observations in this respect will help inform parallel work on theoretical upscaling methods. In this respect, it is clear that traditional upscaling, involving volume averaging or the equivalent homogenization, is not satisfactory. It is not because, on average, in a soil sample, bacteria coexist with given nutrient sources, that at the microscopic level, the microbial cells actually access the nutrients at all. Clearly, some other macroscopic descriptor is needed, besides volume or mass averages.
The role of scaling laws in upscaling:download here