Influence of a simple magnetic bar on buoyancy-driven fingering of traveling autocatalytic reaction fronts

Abstract

Magnetic fields have been shown experimentally to modify convective dynamics developing around traveling chemical fronts in presence of unfavorable density gradients. To understand the conditions in which such magnetic fields affect autocatalytic fronts, we study theoretically the influence of a simple magnetic bar on buoyancy-driven density fingering of a chemical front by numerical simulations of a reaction-diffusion-convection system. The model couples Darcy’s law for the flow velocity to an evolution equation for the concentration of the autocatalytic product, which affects both the density of the solution and the magnetic force. The solutions of both products and reactants are assumed to be diamagnetic (i.e., negative magnetic susceptibility) and the magnetization is oriented perpendicularly to the plane in which the front travels. We show that, when aligned along the direction of front propagation, the magnetic force is able to suppress or enhance the convective instability depending on the value of the magnetic Rayleigh number of the problem. If the magnetic force is oriented transversely to the front propagation direction, tilted drifting convective patterns are obtained.