Nonlinear development of convective patterns driven by a neutralization reaction in immiscible two-layer systems

Abstract

This article provides the results of a theoretical and experimental study of buoyancy-driven instabilities triggered by a neutralization reaction in an immiscible two-layer system placed in a vertical Hele–Shaw cell. Flow patterns are predicted by a reaction-induced buoyancy number K ρ , which we define as the ratio of densities of the reaction zone and the lower layer. In experiments, we observed the development of cellular convection ( K ρ ≤ 1 ), the fingering process with an aligned line of fingertips at a slightly denser reaction zone ( K ρ ≥ 1 ) and the typical Rayleigh–Taylor convection for K ρ > 1 . A mathematical model includes a set of reaction–diffusion–convection equations written in the Hele–Shaw approximation. The model’s novelty is that it accounts for the water produced during the reaction, a commonly neglected effect. The persisting regularity of the fingering during the collapse of the reaction zone is explained by the dynamic release of water, which compensates for the heavy fluid falling and stabilizes the pattern. Finally, we present a stability map on the plane of the initial concentrations of solutions. Good agreement between the experimental data and theoretical results is observed. This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.