Análisis de estabilidad de frentes químicos en reacciones exotérmicas

Abstract

Buoyancy-driven convection is a phenomenon that appears in a wide range of natural processes, from atmospheric and oceanic flows to the Earth’s core inner dynamics. In particular, convective flows are ubiquitous in systems of chemical substances reacting at an interface known as a reaction front. Autocatalytic reaction fronts allow for different types of instabilities due to gradients in chemical composition and the exothermicity of the reaction. In order to study the effects of thermal gradients in such systems, we develop a model for thin-front propagation in two-dimensional tubes. Temperature and front evolution are coupled to two different descriptions of the system’s hydrodynamics: Darcy’s law and the Navier-Stokes equations for viscous flows. We study the stability of the convectionless flat front by carrying out a linear stability analysis. The regimes for which convection arises will depend on a control parameter, called the thermal Rayleigh number, which measures the strength of thermal gradients in the system. We vary this parameter between positive and negative values and analyze its effects on the stability of the fronts.