Interacting length scales in the reactive-infiltration instability

The reactive-infiltration instability, which develops when a porous matrix is dissolved by a flowing fluid, contains two important length scales. Here we outline a linear stability analysis that simultaneously incorporates both scales. We show that the commonly used thin-front model is a limiting case of a more general theory, which also includes convection-dominated dissolution as another special case. The wavelength of the instability is bounded from below and lies in the range 1 mm to 1 km for physically reasonable flow rates and reaction rates. We obtain a closed form for the growth rate when the change in porosity is small.