Reaction fronts, characterized as the region in which two miscible fluids, one of which displaces the other one, react with each other, are typically sustained by fluid mixing and play a central role in a large range of porous media systems and applications [1,2], an important example being remediation of aquifers by injecting biological entities (microbes) that consume the contaminant by reacting with it to form a less-toxic or potentially neutral product [3]. In many cases, point-wise 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.