Asymptotic structure of steady nonlinear reaction-diffusion-Marangoni convection fronts

Chemical fronts propagating in horizontal liquid layers with a free surface can induce localized steady Marangoni flow. Numerical integration of the Stokes equations coupled to a reaction-diffusion-convection equation for the concentration of the surface-active reaction product shows that the system reaches an asymptotic dynamic state characterized by a deformed front surrounded by a steady convection roll traveling at a constant speed. To understand the basic balances determining this steady dynamics, we present here an asymptotic analysis of the system based on the numerically obtained scalings at high Marangoni numbers M quantifying the interaction between reaction-diffusion processes and Marangoni convection. M is positive (negative) when the product decreases (increases) the surface tension behind the front. We obtain a semianalytical solution for the product concentration for large M > 0, showing that the key balances are between reaction, convection, and vertical (rather than axial) diffusion. For M < 0, we present evidence of a multiscale structure of the front resulting from more complex balances. (c) American Institute of Physics.