On Rayleigh-Bénard Mechanism of Alignment of Salt Fingers in Reactive Immiscible Two-Layer Systems

Abstract

The stability of a front of chemoconvective finger structures being spontaneously formed in a two-layer system of fluids filling a vertical Hele-Shaw cell, each of them containing a reactant of an exothermic A + B → S reaction is examined. If the configuration consists of more dense acid (or salt) on top of less dense base in the presence of gravity, the development of the Rayleigh- Taylor instability leads to the standard scenario of density fingering. Despite the widespread perception of fingering as an irregular process, we show that, at least in some cases, the exact balance between the instabilities involved can result quasi-regular fingering pattern formation. In the case of immiscible fluids, we demonstrate that the Rayleigh-Benard mechanism associated with intensive heat release during the reaction performs fine-tuning of the envelope of salt fingers. The mathematical model we develop consists in a set of reaction-diffusion-convection equations governing the evolution of concentrations and temperature coupled to Navier-Stokes and energy equations, written in a Hele-Shaw approximation. The results of linear stability analysis and direct numerical simulations of the fully nonlinear system are presented.