Impact of hydrodynamic dispersion on mixing-induced reactions under radial flows

Mixing-induced reaction fronts play a key role in a range of subsurface processes. In many applications, reactive fronts develop under radial flows, where a reactant is injected and displaces another. Analytical solutions for reactive front dynamics under radial flows have been derived under the assumption of a constant diffusion coefficient. However, the impact of mechanical dispersion still remains unexplored. We investigate this question here by deriving approximate analytical expressions for the reaction front properties as a function of time, dispersion length and Péclet/Damköhler number, as well as from corresponding numerical simulations. Our results indicate that mechanical dispersion leads to a more advanced front and enhanced reaction rate, compared to the dispersion-free scenario. This leads to new scaling laws for the front position, width and reaction rate. We discuss the implications of these findings for field conditions over a range of temporal and spatial scales. Under most realistic scenarios, dispersion is expected to be dominant over diffusion, suggesting a broad relevance of these results.