ALIGNMENT OF FINGERING PATTERN INDUCED BY AN INTERFACIAL NEUTRALIZATION REACTION

Abstract

In this paper, we numerically study buoyancy-driven chemoconvective instabilities in a vertically oriented Hele-Shaw cell. At the beginning, the cavity is filled with a homogeneous aqueous solution of a strong inorganic alkali, and this system is statically stable. We assume that the upper boundary is free, and a fixed value of the concentration of a strong inorganic acid is set there. After bringing the reactants into contact, density stratification quickly becomes unstable due to a neutralization reaction, resulting in density fingering. The mathematical model includes the effect of producing a new amount of solvent (water). We show that this effect is a reason for the sudden alignment of salt fingers that we previously observed in experiments. In this work, we carry out a formal parametric study of the system with a change in the dimensionless parameter responsible for the intensity of water production. One can interpret this variation as a sequential consideration of substances from the homologous series of alkalis. We show that there exists a critical value of the parameter, crossing which one can observe a spontaneous transition from an irregular fingering pattern to cellular chemoconvection. The latter looks like a system of fingers tightly pressed against each other with tips aligned along a horizontal line. The lower boundary of the vortices uniformly moves down. We found that instead of the usual coarsening of the structure, one observes an increase in the aspect ratio of vortices. We investigate the dynamics of the lower boundary of the fingering pattern and changes in the pattern wavelength. Complex rearrangements of the reaction front, which include the processes of plume creation and coalescence, are illustrated using space-time diagrams.