Extended classification of the buoyancy-driven flows induced by a neutralization reaction in miscible fluids. Part 2. Theoretical study

摘要

The buoyancy-driven chemoconvection induced by a neutralization reaction is theoretically studied for a system consisting of nitric acid and sodium hydroxide aqueous solutions placed in a vertically oriented Hele-Shaw cell. This pair of reactants is a representative case of reacting miscible acid-base systems investigated experimentally in Part 1 of this work (Mizev et al., J. Fluid Mech., vol. 916, 2021, A22.). We showed that the list of the possible instabilities in this system is much richer than previously thought. A new scenario for pattern formation depends on a single parameter denoted by, the reaction-induced buoyancy number defined in Part 1. In this paper, the theoretical analysis complementing the experimental observations provides the conceptual insights required for a full understanding of the mechanisms of the observed phenomena. The mathematical model we develop consists of a system of reaction-diffusion-advection equations governing the evolution of concentrations coupled to the Navier-Stokes equation. The system dynamics is examined through transient linear stability analysis and numerical simulation. If 1$]]＞, then a statically stable potential well appears adjacent to the reaction front. As a result, a Rayleigh-Benard-like cellular pattern can arise in this depleted density region. If, then a potential well collapses, and a shock-wave-like structure with an almost planar front occurs. This wave propagates fast compared with the diffusion time and acts as a turbulent bore separating immobile fluid and an area of intense convective mixing. Finally, we determine the place of the above instabilities in an extended classification of known instability types.