Steady Marangoni flow traveling with chemical fronts

Abstract

When autocatalytic chemical fronts propagate in thin layers of solution in contact with air, they can induce capillary flows due to surface tension gradients across the front (Marangoni flows). We investigate here such an interplay between autocatalytic reactions, diffusion, and Marangoni effects with a theoretical model coupling the incompressible Navier-Stokes equations to a conservation equation for the autocatalytic product concentration in the absence of gravity and for isothermal conditions. The boundary condition at the open liquid/air interface takes the surface activity of this product into account and introduces the solutal Marangoni number M representing the intensity of the coupling between hydrodynamics and reaction-diffusion processes. Positive and negative Marangoni numbers correspond, respectively, to the cases where the product decreases or increases surface tension behind the front. We show that, in both cases, such coupled systems reach an asymptotic dynamics characterized by a steady fluid vortex traveling at a constant speed with the front and deforming it, with, however, an asymmetry between the results for positive and negative M. A parametric study shows that increased propagation speed, front deformation, and possible transient oscillating dynamics occur when the absolute value of M is increased.