The nonlinear dynamics of A + B → C fronts is analyzed both numerically and theoretically in the presence of Marangoni flows, i.e., convective motions driven by surface tension gradients. We consider horizontal aqueous solutions where the three species A, B, and C can affect the surface tension of the solution, thereby driving Marangoni flows. The resulting dynamics is studied by numerically integrating the incompressible Navier-Stokes equations coupled to reaction-diffusion-convection (RDC) equations for the three chemical species. We show that the dynamics of the front cannot be predicted solely on the basis of the one-dimensional reaction-diffusion profiles as is the case for buoyancy-driven convection around such fronts. We relate this observation to the structure of Marangoni flows which lead to more complex and exotic dynamics. We find in particular the surprising possibility of a reversal of the front propagation direction in time for some sets of Marangoni numbers, quantifying the influence of each chemical species concentration on the solution surface tension. We explain this reversal analytically and propose a new classification of the convective effects on A + B → C reaction fronts as a function of the Marangoni numbers. The influence of the layer thickness on the RDC dynamics is also presented. Those results emphasize the importance of flow symmetry properties when studying convective front dynamics in a given geometry.

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This work describes a new mechanism for the emergence of oscillatory dynamics driven by the interaction of hydrodynamic flows and reaction-diffusion processes with no autocatalytic feedback nor prescribed hydrodynamic instability involved. To do so, we study the dynamics of an A+ B → C reaction-diffusion front in the presence of chemically-driven Marangoni flows for arbitrary initial concentrations of reactants and diffusion coefficients of all species. All the species are assumed to affect the solution surface tension thereby inducing Marangoni flows at the air-liquid interface. The system dynamics is studied by numerically integrating the incompressible Navier-Stokes equations coupled to reaction-diffusion-convection equations for the three chemical species. We report spatial and temporal oscillations of surface tension triggered by differential diffusion effects of surfactant species coupled to the chemically-induced Marangoni effect. Such oscillations are related to the discontinuous traveling of the front along the surface leading to the progressive formation of local extrema in the surface tension profiles as time evolves.

Pattern interaction has so far been restricted to systems with relatively complex reaction schemes, such as activator-inhibitor systems, that lead to rich spatio-temporal dynamics. Surprisingly, a simple second-order chemical reaction is capable of generating similar complex phenomena, such as attractive or repulsive interaction modes between the localized reaction zones (or fronts). We illustrate the latter statement both analytically and numerically with two initially separated A + B → C reaction-diffusion fronts when the solution of B is initially confined between two solutions of A. The nature of the front-front interaction changes from an attractive type to a repulsive one above a critical distance separating the two fronts initially. The complexity of the pattern dynamics emerges here due to finite-size effects. A scaling law relating the critical distance d c above which the repulsion occurs and kinetic parameters gives insights into (i) extracting those parameters from experiments for bimolecular reactions and (ii) the control strategy of periodic patterns.

When bimolecular fronts form in solutions, their dynamics is likely to be affected by chemically driven convection such as buoyancy- and Marangoni-driven flows. It is known that front dynamics in the presence of buoyancy-driven convection can be predicted solely on the basis of the one-dimensional reaction–diffusion concentration profiles but that those predictions fail for Marangoni-driven convection. With a two-dimensional reaction–diffusion–Marangoni convection model, we analyze here convective effects on the time scalings of the front properties, together with the influence of reaction reversibility and of the ratio of initial reactants’ concentrations on the front dynamics. The effect of buoyancy forces is here neglected by assuming the reactive system to be in zero-gravity condition and/or the solution density to be spatially homogenous. This article is part of the theme issue ’New trends in pattern formation and nonlinear dynamics of extended systems’.