Thermal effects on chemically induced Marangoni convection around A + B → C reaction fronts

Abstract

Chemical reactions can induce Marangoni flows by changing the surface tension of a solution open to the air, either by changing the composition and/or by modifying the temperature. We consider the case of a simple A + B → C reaction front propagating in a thin horizontal system open to air. The effect of the three chemical species on the surface tension of the aqueous solution is quantified by three solutal Marangoni numbers, while the effect of temperature changes is determined by the thermal Marangoni number. By integrating numerically the incompressible Navier–Stokes equations coupled to reaction-diffusion-convection equations for the chemical concentrations and temperature taking into account the Lewis number (ratio between heat and mass diffusivities), we emphasize the importance of thermal changes occurring due to the heat of reaction on the dynamics of chemically induced Marangoni convection. Based on the reaction-diffusion profiles of concentrations and temperature, asymptotic analytical solutions for the surface tension profiles are obtained and classified as a function of the Marangoni numbers and the Lewis number. This new classification allows for the prediction of the convective patterns in thermo-solutal Marangoni flows. The analytical predictions are further confirmed by numerical results and additional extrema in surface tension profiles induced by the thermal effects are found to affect the nonlinear dynamics.