Experiments and Simulations of Reversible Fickian Dispersion in Periodic Radial Subsurface Flow

Solute dispersion in groundwater is an artifact of the upscaling of pore-scale behavior. The velocity of solute parcels varies in magnitude and direction as they travel through pores of different sizes, shapes, and orientations. Upscaling this variability to the Darcy scale produces concentration distributions that exhibit spreading in the directions longitudinal and transverse to flow. We typically label this spreading under the heading of dispersion to contrast it with mixing arising from molecular diffusion. In this presentation, we show that under high Peclet number conditions, reversing flow also reverses solute travel paths, which can reverse spreading at the Darcy scale. Reversible Fickian dispersion at the Darcy scale was observed and quantified both experimentally and numerically. A solute transport experiment was conducted in a 50 cm x 50 cm x 4.4 cm apparatus filled with monodisperse glass beads and glycerin, using Rhodamine 6G dye as the solute. Laser-induced fluorescence was used to track the dye movement through two cycles of radial push-pull flow. Depth-averaged concentration was measured during the experiment and integrated over the angular direction during post-processing to obtain a radial distribution of concentration. The experimental results were replicated using a novel particle tracking approach that simulates advection and dispersion in the radial direction, including reversible dispersion during extraction. Results show that spreading of the measured concentrations follow a Fickian dispersion model during steps with radial outward flow, which is reversed during radial inward flow.