Effect of hydrodynamic dispersion on spherical reaction front dynamics in porous media

Reaction fronts sustained by fluid mixing play a central role in a large range of porous media systems and applications. In many cases, pointwise continuous injection of a reactant that displaces a resident reactant in three dimensions leads to a growing spherical reaction front. While such configurations have until now been studied under the assumption of a constant diffusion coefficient, in porous media the dominant diffusive process at the continuum scale is hydrodynamic dispersion, which depends linearly on the flow velocity. Here we analyze the impact of this nonuniform and time-varying hydrodynamic dispersion on reactive transport occurring in such a spherically advected reaction front under point injection and at constant flow rate. During an initial transient regime, dispersion leads to a more advanced reaction front and a larger global reaction rate than when molecular diffusion is the only mixing process, as well as to different temporal scalings for the reaction front properties. At larger times, the reaction front eventually reaches a steady state, characterized by a static position and time-independent reactant concentrations and reaction rate, regardless of the presence and strength of dispersion. When dispersion is weak, the steady-state front is positioned in a region where dispersion is negligible compared to diffusion. Conversely, when dispersion is large, the steady-state front is positioned in the transition zone where dispersion and diffusion are comparable. Under this condition, hydrodynamic dispersion permanently affects the reaction front's transport by altering the steady state itself and augmenting the global reaction rate.