Propagating Fronts in Fluids with Solutal Feedback

TL;DR

This study numerically investigates how reacting fronts propagate in a fluid layer with solutal feedback and convection, revealing scaling laws, complex geometries, and oscillations influenced by solutal and thermal effects.

Contribution

It introduces a detailed numerical analysis of reacting front dynamics in fluid with solutal feedback and convection, highlighting new scaling behaviors and complex front geometries.

Findings

Front velocity scales quadratically with solutal Rayleigh number at low values.

At high solutal Rayleigh numbers, front shape becomes self-similar and asymmetric.

Counter-rotating convection rolls affect front speed and mixing length.

Abstract

We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counter-rotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit square-root scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counter-rotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Lastly, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.