On the spatial structure of reaction fronts in reactive porous media.*

The flow of reactive fluids in porous media generates changes in porosity and permeability. This phenomenon occurs in various contexts, such as flows in the Earth's mantle and crust, and in the formation of karst topography.  

However, a challenge remains in understanding the conditions under which smooth and sharp transitions between reacted and unreacted media should be expected. We develop a framework which approaches this by considering two phases with spatially variable porosity, with feedback between the two phases. 

We conduct a theoretical study of the properties of traveling wave solutions for the propagation of reaction fronts in the fundamental configurations of one-dimensional and axisymmetric injections. Using this model, we predict the spatial scales over which transitions occur between reacted and unreacted media, revealing a spectrum spanning smooth reaction fronts to sharp (Stefan-like) reaction fronts. We document a complete regime diagram for these flows across a complete parameter space of Damkohler and a reaction-capacity number. We document the late time behaviour of the axisymmetric injection and its dependence on the Peclet number.