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Extended classification of the buoyancy-driven flows induced by a neutralization reaction in miscible fluids. Part 2. Theoretical study

Published online by Cambridge University Press:  12 April 2021

D.A. Bratsun Open the ORCID record for D.A. Bratsun [Opens in a new window] ,
A.I. Mizev Open the ORCID record for A.I. Mizev [Opens in a new window]  and
E.A. Mosheva
D.A. Bratsun*
Affiliation:
Perm National Research Polytechnic University, Perm614990, Russia
A.I. Mizev
Affiliation:
Perm National Research Polytechnic University, Perm614990, Russia Institute of Continuous Media Mechanics, Russian Academy of Science, Perm614013, Russia
E.A. Mosheva
Affiliation:
Perm National Research Polytechnic University, Perm614990, Russia Institute of Continuous Media Mechanics, Russian Academy of Science, Perm614013, Russia
*
†Email address for correspondence: [email protected]
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Abstract

The buoyancy-driven chemoconvection induced by a neutralization reaction is theoretically studied for a system consisting of nitric acid and sodium hydroxide aqueous solutions placed in a vertically oriented Hele-Shaw cell. This pair of reactants is a representative case of reacting miscible acid–base systems investigated experimentally in Part 1 of this work (Mizev et al., J. Fluid Mech., vol. 916, 2021, A22.). We showed that the list of the possible instabilities in this system is much richer than previously thought. A new scenario for pattern formation depends on a single parameter denoted by $K_{\rho }$, the reaction-induced buoyancy number defined in Part 1. In this paper, the theoretical analysis complementing the experimental observations provides the conceptual insights required for a full understanding of the mechanisms of the observed phenomena. The mathematical model we develop consists of a system of reaction–diffusion–advection equations governing the evolution of concentrations coupled to the Navier–Stokes equation. The system dynamics is examined through transient linear stability analysis and numerical simulation. If $K_{\rho }>1$, then a statically stable potential well appears adjacent to the reaction front. As a result, a Rayleigh–Bénard-like cellular pattern can arise in this depleted density region. If $K_{\rho }\leqslant 1$, then a potential well collapses, and a shock-wave-like structure with an almost planar front occurs. This wave propagates fast compared with the diffusion time and acts as a turbulent bore separating immobile fluid and an area of intense convective mixing. Finally, we determine the place of the above instabilities in an extended classification of known instability types.

JFM classification

Convection: Buoyancy-driven instability Low-Reynolds-number flows: Hele-Shaw flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A23
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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