When two species are initially separated and react according to a second-order reaction scheme, $\mathrm{A}+\mathrm{B}\to \mathrm{C}$, a dynamical reaction zone or $\mathit{reaction}\mathit{front}$ forms. In horizontally oriented layers filled with liquid miscible mixtures, natural convection plays a crucial role. In particular, when the three chemical species (A, B, and C) involved in the reaction affect the surface tension at the air-liquid interface, currents due to Marangoni forces emerge and couple to the preexisting reaction-diffusion dynamics of the front. The system dynamics is then described by coupling the reaction-diffusion-convection equations of the three species to the incompressible Navier-Stokes equations subject to Marangoni stresses at the air-liquid interface. In this work, we analyze the surface tension profiles and the structure of the flows that result from this coupling, such as the number of convective rolls, their rotational direction and relative size, in the general scheme when all the species diffuse at different rates. We show how differential diffusion effects induce and control complex Marangoni-driven convective patterns in solution. We connect the structure of the reactive flows to the surface tension profiles and their monotonic properties. Independently of the model parameters, we find that the number of extrema $\left(m\right)$ and of convective rolls $\left(n\right)$ are related as $n\le m+1$ for all times, with $n$ and $m$ defined as positive integers. The analysis is simplified when the monotonic properties of the surface tension profiles are conserved in time, for which we show that $n=m+1$ for all times. By varying the layer thickness with differential diffusion, more complex convective structures also generically emerge.

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• Interfacial flows
• Laminar reacting flows
• Marangoni convection
• Nonlinear dynamics in fluids