The effect of natural convection on the gas-phase Sal'nikov reaction in a closed vessel

Abstract

In an exothermic, gas-phase reaction in a closed vessel, natural convection develops once the Rayleigh number has risen to ∼10³. The subsequent evolution of the reaction depends on a complex interaction between chemical kinetics, diffusion of heat and mass, and also convection. In this paper, we analyse the interaction between these three processes for Sal'nikov's reaction of two first-order steps in series: P → A → B for a purely gaseous system in a batch reactor. Here, the first step is assumed to be thermoneutral, with an activation energy of zero. The second step is exothermic and has a positive activation energy; these properties make such a mechanism one of the simplest to explain thermokinetic oscillations, such as cool flames. We show theoretically that the system's behaviour depends on the relative magnitude of the time scales for chemical reaction, diffusion and natural convection. We calculate these time scales in terms of the chemical and physical parameters of the system. A new three-dimensional diagram is proposed; it enables the different regimes of behaviour for thermokinetic systems to be delineated. Our theoretical predictions are verified by numerical simulation.