Reactive flows in porous media are characterised by the development of a moving reaction front separating reacted and unreacted regions. These fronts are observed in many geoscience settings, such as mantle dynamics and hydrous flow in crustal rock. The connection between reacted and unreacted regions can involve either a smooth or sudden near-interfacial transition, in each of porosity and reactant concentration. This thesis studies the contributions of transport and reaction to the control of the transition in fundamental geometries, and seeks to demonstrate the quantitative use of the resulting relationships in geoscience examples. This thesis presents generalised novel regime diagrams for the dynamics of reaction fronts in fundamental configurations.
The first of these configurations is the generation of a planar reaction front, supplied by a constant flux of fluid. A detailed mathematical study of its predictions to classify emergent regimes and their parametric controls is conducted.
The limiting late-time regimes are the sharp and the diffusionless regime, characterised by the separation of scales between the porosity and concentration transitions and by the controlling balance of transport respectively.
The second configuration is a reaction front supplied by a local point source, with a constant radial flux. A detailed asymptotic analysis of the emergent regimes and their parametric controls is performed. In this configuration the reaction front tends towards sharpness irrespective of the Pe number, with the Pe number instead controlling whether the front tends towards the 1D reaction front in a quasi constant-flux regime.
The third problem addressed in this thesis is to begin to understand the instability of planar reaction fronts. The conditions for the linear stability of planar reaction fronts in the sharp porosity transition limit are derived. The resultant dispersion relation is applied to geoscience applications, demonstrating scenarios for which the linear model can and cannot predict emergent instability.
