Reaction rates in the hyporheic zone explained by the lamellar theory of mixing

At the interface between aquifers and rivers, hyporheic zones are shallow sediment layers where surface and subsurface waters mix and react. In these zones, the dynamic of solute transport and mixing is a crucial and limiting component for many biogeochemical reactive processes (arsenic and nitrates degradation for instance). In particular, the understanding of the consequence of flow path heterogeneity on solute mixing and reactivity is key to develop physically-based upscaled models of the hyporheic function. By simulating the evolution of reacting fronts under simple 2D and 3D heterogeneous hyporheic flows created by bed superficial pressure gradients, we show that incomplete mixing of reacting solutes systematically precludes the use of macro-dispersion models as upscaled models of the hyporheic function, both in steady and unsteady flow conditions.
Based on these simulations, we propose an alternative theoretical framework, based on the concept of solute lamellae stretched by flow velocity gradients, to correctly upscale local reaction rates at the reach and basin scale. Finally, we compare our numerical and theoretical results to reacting fronts in a laboratory scale hyporheic mixing experiment.