Impact of saturation on dispersion and mixing in porous media: Photobleaching pulse injection experiments and shear-enhanced mixing model

Abstract

The dynamics of solute dispersion and mixing in unsaturated flows is analyzed from photobleaching experiments in two-dimensional porous micromodels. This technique allows producing pulse line (delta-Dirac) injections of a conservative tracer by bleaching a finite volume of fluorescent without disturbing the flow field. The temporal evolution of the concentration field and the spatial distribution of the air and water phases can be monitored at pore scale. We study the dispersion and mixing of a line of tracer under different water saturations. While dispersion in saturated porous media follows an approximately Fickian scaling, a shift to ballistic scaling is observed as soon as saturation is lowered. Hence, at the time scale of observation, dispersion in our unsaturated flows is dominated by the ballistic separation of tracer blobs within the water phase, between trapped clusters and preferential flow paths. While diffusion plays a minor role in the longitudinal dispersion during the time scale of the experiments, its interplay with fluid deformation is apparent in the dynamics of mixing. The scalar dissipation rates show an initial stretching regime, during which mixing is enhanced by fluid deformation, followed by a dissipation regime, during which diffusion overcomes compression induced by stretching. The transition between these two regimes occurs at the mixing time, when concentration gradients are maximum. We propose a predictive analytical model, based on shear-enhanced diffusion, that captures the dynamics of mixing from basic unsaturated porous media parameters, suggesting that this type of model may be a useful framework at larger scales.