Buoyancy-driven convection around exothermic autocatalytic chemical fronts traveling horizontally in covered thin solution layers

摘要

Spatial variations of concentrations and temperature across exothermic chemical fronts can initiate buoyancy-driven convection. We investigate here theoretically the spatiotemporal dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and buoyancy-driven flows when an exothermic autocatalytic front travels perpendicularly to the gravity field in a thin solution layer. To do so, we numerically integrate the incompressible Stokes equations coupled to evolution equations for the concentration of the autocatalytic product and temperature through buoyancy terms proportional to, respectively, a solutal R_C and a thermal R_T Rayleigh number. We show that exothermic fronts can exhibit new types of dynamics in the presence of convection with regard to the isothermal system. In the cooperative case (R_C and R_T are of the same sign), the dynamics asymptotes to one vortex surrounding, deforming, and accelerating the front much like in the isothermal case. However, persistent local stratification of heavy zones over light ones can be observed at the rear of the front when the Lewis number Le )ratio of thermal diffusivity over molecular diffusion) is nonzero. When the solutal and thermal effects are antagonistic (R_C and R_T of opposite sign), temporal oscillations of the concentration, temperature, and velocity fields can, in some cases, be observed in a reference frame moving with the front. The various dynamical regimes are discussed as a function of R_C, R_T, and Le.