Fingering instabilities of exothermic reaction-diffusion fronts in porous media

We consider the density fingering of exothermic autocatalytic fronts in vertically oriented Hele-Shaw cells with chemical reactions whose solutal and thermal contributions to density changes have opposite signs. Using the Darcy–Boussinesq equations we examine the influence of the competition between solutal and thermal density changes on the linear stability of traveling fronts and the fully nonlinear dynamics. Ascending fronts are characterized by standard Rayleigh–Taylor fingering dispersion curves and in the nonlinear stage of the instability they feature thermal plumes. Descending fronts on the other hand behave strikingly differently as they can feature for some values of the parameters Turing-type dispersion curves and stationary patterns with fingers of constant amplitude and wavelength.