The effect of non-uniform microscale distribution of sorption sites on solute diffusion in soil

Conventional models of solute transport in soil consider only soil volumes large enough to average over microscale heterogeneities, and it is assumed that microscale variations are unimportant at the macroscale. In this research we test this assumption for cases in which the microscale distribution of solute-sorbing sites is patchy. We obtain a set of equations at the macroscale that allow for the effect of the microscale distribution with the mathematical technique of homogenization. We combine these equations with an image-based model that describes the true microscale pore geometry in a real, structured soil measured with X-ray computed tomography. The resulting models are used to test the microscale averaging assumptions inherent in conventional models. We show that, in general, macroscale diffusion is little affected by microscale variation in the distribution of sorption sites. Therefore, for most purposes the assumption of microscale averaging used in conventional models is justified. The effects of microscale heterogeneity are noticeable only when (i) the rate of sorption is slow compared with diffusion, but still fast enough to affect macroscale transport and (ii) the defined macroscale volume approaches the microscale. We discuss the effects when these conditions are met