The influence of natural convection on the temporal development of the temperature and concentration fields for Sal’nikov’s reaction, P A B, occurring batchwise in the gas-phase in a closed vessel

Sal'nikov's chemical reaction is very simple; it consists of two consecutive first-order steps, yielding a product B from a precursor P via an active intermediate A, in P→A→B. The first of these steps is assumed here to be thermoneutral, with zero activation energy, whilst the second step is taken to be exothermic with a positive activation energy. These properties make this reaction one of the simplest to display thermokinetic oscillations, such as characterise cool flames. This study considers Sal'nikov's reaction occurring batchwise in the gas-phase in a closed spherical reactor, whose wall is held at a constant temperature. Natural convection becomes significant once the temperature in the reactor has risen sufficiently for the Rayleigh number to reach ~ 10 3. The behaviour of the system is governed by the interaction between three phenomena: natural convection, diffusion of both heat and matter, and chemical reaction. Recent studies of such a system revealed that when natural convection is significant, the oscillations in the temperature are not always in anti-phase with those in the local concentration of the intermediate A, as was previously thought. Instead, the phase difference between the oscillations in the temperature and the concentration of A depends on the position and conditions in the reactor. The shift of this phase difference is studied here using a full numerical solution of the governing equations for a system in which the first step of the reaction is much slower than the second. The phase behaviour is found to depend on the ratio of the characteristic timescales for step 2 of the reaction,  Step 2 , and natural convection,  Convection. When  Step 2 /  Convection < 10, the temperature and the concentration oscillate in anti-phase, but when  Step 2 /  Convection is increased above ~ 15, i.e. when natural convection is relatively fast, there is, near the axis in the bottom of the 3 reactor, no phase difference between these oscillations. This shift in the phase difference results from a surprisingly complex interaction between chemical kinetics and heat and mass transport, by both natural convection and diffusion.