SPONTANEOUS ORDERING OF CHEMOCONVECTIVE FINGERING NEAR AN INTERFACE IN A REACTING SOLUTION

Abstract

In this work, we develop a mathematical model of buoyancy-driven mass transfer in an aqueous alkali solution filling a Hele-Shaw cell. The upper boundary of the layer is free and nondeformable. The acid flux through the interface is determined by the constant value of the acid concentration set at the interface. Thus, the neutralization reaction proceeds near the interface and is accompanied by the formation of salt and water. We neglect the heat release of the exothermic reaction and the Marangoni effect, assuming that all substances do not exhibit surface activity. The ratio of the initial concentrations of acid and base is the control parameter of the system, which unambiguously determines the onset of various types of chemoconvection. The described model reproduces the main properties of a two-layer system of immiscible reacting liquids if the interface is impermeable to base and salt. Based on recent experimental observations, we modify the equation of solvent motion, introducing an integral term that describes the reaction-induced production of water. We demonstrate that such an assumption drastically changes the density distribution in the system because of the depletion of solutions in the reaction zone. In particular, this effect leads to spontaneous stabilization of fingering process in the parameter range, where numerical simulation of the standard model predicts the development of disordered Rayleigh-Taylor convection. Finally, we present a bifurcation diagram for the ratio of initial concentrations. The obtained results are in good agreement with the experimental data.