Mathematical modelling of leaching by irregular wetting fronts in chemically heterogeneous porous media

The wetting front zone where water invades and advances into an initially dry soil plays a crucial role in solute transport through the unsaturated zone. The leaching of chemicals by wetting fronts is influenced by two major factors, namely: the irregularity of the fronts and heterogeneity in the distribution of chemicals, both of which have been described by using fractal techniques.This paper presents a theoretical framework for studying the physical interplay between a stationary wetting front of fractal dimension D and a multifractal distribution of chemicals around it with a singularity spectrum f(α). If D1 is the entropy dimension of the distribution and α0 is the point where f(α) attains its maximum value, then, as revealed by mathematical analysis, the fractal curve must have a fractal dimension D equal to or greater than the entropy dimension D1 of the distribution for a positive amount of mass to be accommodated inside it. Also, α0 − D constitutes a scaling exponent for the likely mass inside an ε -covering of the curve reflecting the potential for leaching on the sole basis of the physical interplay between the wetting front and the surrounding chemical molecules.The proposed modelling approach and the results it provides can be useful with a view to obtaining supplementary information about the leaching process and its prediction. Since the present analysis is limited to stationary conditions further research is needed to extend it to dynamic conditions.