Infiltration experiments demonstrate an explicit connection between heterogeneity and anomalous diffusion behavior

Transport in systems containing heterogeneity distributed over multiple length scales can exhibit anomalous diffusion behaviors, where the time exponent, determining the spreading length scale of the transported scalar, differs from the expected value of n=1/2. Here we present experimental measurements of the infiltration of glycerin, under a fixed pressure head, into a Hele-Shaw cell containing a 3-D printed distribution of flow obstacles; a system that is an analog for infiltration into a porous medium. In support of previously presented direct simulation results, we experimentally demonstrate that, when the obstacles are distributed as a fractal carpet with fractal dimension H < 2, the averaged progress of infiltration exhibits a subdiffusive behavior n < 1/2. We further show that observed values of the subdiffusion time exponent appear to be quadratically related to the fractal dimension of the carpet.