Influence of Marangoni flows on the dynamics of isothermal A + B → C reaction fronts

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.