Stability of convective patterns in reaction fronts: A comparison of three models

Abstract

Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three different models for front propagation. We use a model based on a reaction-diffusion-advection equation coupled to the Navier-Stokes equations to account for fluid flow. A second model replaces the reaction-diffusion equation with a thin front approximation where the front speed depends on the front curvature. We also introduce a new low-dimensional model based on a finite mode truncation. This model allows a complete analysis of all stable and unstable fronts. © 2010 American Institute of Physics. ͓doi:10.1063/1.3467858͔Chemical fronts propagating in vertical cylinders exhibit flat, nonaxisymmetric, and axisymmetric fronts. The different types of fronts are determined by convection. In the case of flat fronts, there is no convection. For nonaxisymmetric fronts, fluid rises on one side and falls on the opposite side of the tube. For axisymmetric fronts, fluid rises in the middle of the tube and falls on the sides. In this work we model the transition between different fronts using a two-dimensional domain. We compared three different models of front propagation, one based on a reaction-diffusion-advection equation, the other on a front propagation equation, and finally a low-dimensional model. We study the stability of different solutions.

Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains

“…(2009) for results on FitzHugh–Nagumo reaction kinetics. There have also been a number of works which have focused on travelling reaction fronts in reaction–diffusion–advection systems under Poiseuille flow (Edwards 2002; Spangler & Edwards 2003; Koptyug, Zhivonitko & Sagdeev 2008; Vasquez & Coroian 2010). The modification of wave fronts in the Kuramoto–Sivashinsky equation due to a Couette flow was considered in Vilela & Vasquez (2014).…”

“…See also Stucchi & Vasquez (2013 for similar results on the cubic autocatalytic reaction kinetics, Ayodele, Raabe & Varnik (2015) for results on a two-species Gray-Scott model with advection, Kuptsov, Satnoianu & Daniels (2005) for results on Lengyel-Epstein reaction kinetics for the chlorite-iodide-malonic acid-starch reaction, Liu et al (2016) for results on the chlorite-trithionate reaction and Ermakova et al (2009) for results on FitzHugh-Nagumo reaction kinetics. There have also been a number of works which have focused on travelling reaction fronts in reaction-diffusion-advection systems under Poiseuille flow (Edwards 2002;Spangler & Edwards 2003;Koptyug, Zhivonitko & Sagdeev 2008;Vasquez & Coroian 2010). The modification of wave fronts in the Kuramoto-Sivashinsky equation due to a Couette flow was considered in Vilela & Vasquez (2014).…”