Peculiar properties of density wave formation in a two-layer system of reacting miscible liquids
DOI:
https://doi.org/10.7242/1999-6691/2018.11.3.23Keywords:
density wave, chemoconvective instability, neutralization reaction, concentration-dependent diffusion, miscible liquidsAbstract
The emergence of an internal density wave in a two-layer miscible system consisting of acid and base placed in a vertically Hele-Shaw cell is studied theoretically and experimentally. When the solutions come in contact, an exothermic neutralization reaction A+B→C starts, which is accompanied by the release of the reaction product - salt. This process is associated with a strong dependence of the diffusion coefficients of the reagents concentration that leads to the appearance of a local density pocket in which cellular convection develops. Under certain concentrations, the low density pocket collapses, and no previously observed chemoconvective regime that is characterized by the formation of a shock-like density wave. It has been experimentally shown that the wave movement is accompanied by an effective mixing of the reactants and continuous reaction product withdrawal, which ensures a high reaction rate. The emergence of a shock-like density wave is confirmed and studied in detail for various combinations of pairs of the acid (HNO3) and alkali (LiOH, NaOH, KOH) that confirms the universality of the instability mechanism. It is shown that the previously proposed dimensionless parameter, which is the ratio of the density of the reaction zone to the density of the upper reagent, is a similarity criterion for all the combinations of reagent pairs studied and determines the boundary for the chemoconvective regime appearance. We propose a mathematical model for the phenomenon, which under certain assumptions can be reduced to the Saint-Venant equations for the surface gravitational waves in the shallow water approximation, which allow for shock-wave type solutions. Numerical simulations of the density wave dynamics for different values of the control parameter are presented. The transition from diffusion-controlled solution to the shock-wave-like solution when the governing parameter is varied is investigated. Comparison of numerical calculations with experimental data is given.
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