This research monograph presents a new model to explain why the dispersion of solutes carried by flow through a porous medium, is observed to depend on the scale of the flow path, unlike predictions from simpler diffusion-like models. Stochastic partial differential equations are used to describe how microscopic displacements caused by pore walls, and macroscopic variations in flow velocity, interact. An analytic solution for accelerating flow is followed by a detailed analysis, first for velocity steps and then for stepwise velocity fluctuation profiles. Fluctuations enhance dispersion, and...