Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

Abstract

Gradients of concentration and temperature across exothermic chemical fronts propagating in free-surface solution layers can initiate Marangoni-driven convection. We investigate here the dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and Marangoni-driven flows. To this end, we numerically integrate the incompressible Navier-Stokes equations coupled through the tangential stress balance to evolution equations for the concentration of the autocatalytic product and for the temperature. A solutal and a thermal Marangoni numbers measure the coupling between reaction-diffusion processes and surface-driven convection. In the case of an isothermal system, the asymptotic dynamics is characterized by a steady fluid vortex traveling at a constant speed with the front, deforming and accelerating it [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)]. We analyze here the influence of the reaction exothermicity on the dynamics of the system in both cases of cooperative and competitive solutal and thermal effects. We show that exothermic fronts can exhibit new unsteady spatio-temporal dynamics when the solutal and thermal effects are antagonistic. The influence of the solutal and thermal Marangoni numbers, of the Lewis number (ratio of thermal diffusivity over molecular diffusivity), and of the height of the liquid layer on the spatio-temporal front evolution are investigated. As a chemical reaction induces changes in the temperature and in the composition of the reactive medium, it can modify the properties of the solution (density, viscosity, surface tension) and thereby trigger convective motions, which in turn affect the reaction. Such a coupling can typically be observed around reactive interfaces in liquid solutions. Two classes of convective flows are then commonly developing in solutions open to air, namely Marangoni flows arising from surface tension gradients and buoyancy flows driven by density gradients. As both flows can be induced by compositional changes as well as thermal changes and in turn modify them, the resulting experimental dynamics are often complex. The purpose of our study is to gain insight into these intricate dynamics thanks to the theoretical analysis of model systems where only one type of convective flow is present. We address here the dynamics of an exothermic autocatalytic front propagating in the presence of Marangoni flows, when the density remains uniform. The surface tension gradient across the front has both a thermal component linked to the exothermicity of the reaction and a solutal component arising from the change in the chemical composition during the reaction. We show that the thermal effects modify the properties of the isothermal system and that new dynamics such as oscillations of the concentration field can be observed when the solutal and thermal effects act antagonistically on the surface tension, provided that they act on different length scales