Front instabilities in the presence of convection due to thermal and compositional gradients

Reaction fronts separate fluids of different densities due to thermal and compositional gradients that may lead to convection. The stability of convectionless flat fronts propagating in the vertical direction depends not only on fluid properties but also in the dynamics of a front evolution equation. In this work, we analyze fronts described by the Kuramoto-Sivashinsky (KS) equation coupled to hydrodynamics. Without density gradients, the KS equation has a flat front solution that is unstable to perturbations of long wavelengths. Buoyancy enhances this instability if a fluid of lower density is underneath a denser fluid. In the reverse situation, with the denser fluid underneath, the front can be stabilized with appropriate thermal and compositional gradients. However, in this situation, a different instability develops for large enough thermal gradients. We also solve numerically the nonlinear KS equation coupled to the Navier-Stokes equations to analyze the front propagation in two-dimensional rectangular domains. As convection takes place, the reaction front curves, increasing its velocity.