Double-diffusive instabilities of autocatalytic chemical fronts

Abstract

Convective instabilities of an autocatalytic propagating chemical front in a porous medium are studied. The front creates temperature and concentration gradients which then generate a density gradient. If the front propagates in the direction of the gravity field, adverse density stratification can lead to Rayleigh–Taylor or Rayleigh–Bénard instabilities. Differential diffusivity of mass and heat can also destabilize the front because of the double-diffusive phenomena. We compare the stability boundaries for the classical hydrodynamic case of a bounded layer without reaction and for the chemical front in the parameter space spanned by the thermal and solutal Rayleigh numbers. We show that chemical reactions profoundly affect the stability boundaries compared to the non-reactive situation because of a delicate coupling between the double-diffusive and Rayleigh–Taylor mechanisms with localized density perturbations driven by the reaction. In the reactive case, a linear stability analysis identifies three distinct stationary branches of the instability. They bound a region of stability that shrinks with increasing Lewis number, in marked contrast to the classical double-diffusive layer. In particular a region of global and local stable stratification is susceptible to a counter-intuitive mechanism of convective instability driven by chemistry and double-diffusion. The other two regions display an additional contribution of localized Rayleigh–Taylor instabilities. Displaced-particle arguments are employed in support of and to elucidate the entire stability boundary.