Propagating fronts in fluids with solutal feedback

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 squareroot 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.

The fluid dynamics of propagating fronts with solutal and thermal coupling

“…For intermediate values of η the trend suggests a transition between these two regimes of small and large heat release. A similar trend is observed for propagating fronts with only solutal feedback (Ra s / = 0, η = 0, Ra T < Ra T,c ), where Ū varies linearly for small values of Ra s and transitions to square root scaling for large values of Ra s although the flow structure for purely solutal feedback is a single convection roll that travels with the front (Mukherjee & Paul 2020).…”

“…This event repeats periodically and results in a time dependence for the cusp region (see supplementary movie 1 available at https:// doi.org/10.1017/jfm.2022.375). We point out that this flow field is quite different than what occurs when only solutal coupling is included, which results in a single large convection roll that travels with the front (for example, see figure 2 of Mukherjee & Paul 2020).…”

“…The extended leading edge of the front is steady in time and yields the linear shape on the right-hand side of the reaction zone. In the absence of solutal or thermal feedback, the front propagates with a constant velocity, which would yield a solid yellow-green line from the upper left to the lower right of the space-time plot, as shown in Mukherjee & Paul (2020). However, the space-time plot of figure 7 shows repeating features in the reaction zone.…”

“…For Ra s > 0, solutal coupling alone will generate a large clockwise convection roll that propagates with an extended front (cf. Rongy et al 2007;Mukherjee & Paul 2020). Also, for η > 0, the heat release from the reaction generates a convection roll with clockwise rotation that travels with the leading edge of the front, as shown in figure 2(d).…”

“…As the flow complexity increased, with the introduction of smaller scale features in the flow field, the front velocity increased. Mukherjee & Paul (2020) conducted a detailed study of the propagation of a front through a cellular flow field with solutal coupling and without heat release by the reaction. The scaling properties of the front-induced fluid velocity, front velocity and mixing length were determined for a wide range of parameters.…”