Abstract
Chemoconvective structures in a system of two reacting miscible liquids, placed in a cylindrical Hele-Shaw cell rotated uniformly around the symmetry axis have been investigated. Previously, the formation of structures under similar conditions has been studied by the authors experimentally and theoretically in the static gravity field. The radial inertial field, formed by the centrifugal force, is varied in space (along the radius) and can be tuned by changing the rotation frequency, which gives the system new degrees of freedom. The initial configuration of the system includes two concentric layers of aqueous solutions, initially separated in space by an infinitely thin diffusion zone. The acid and base solutions are located closer to the rotation axis and the cell periphery, respectively. The concentrations of reactants are chosen so as to guarantee the initial stability of the system with respect to Rayleigh–Taylor perturbations. After bringing liquids into contact, a neutralization reaction, accompanied by the production of salt, begins. The functional dependence of the diffusion coefficients of reagents on their concentration in the solution plays an important role in this process, which results in a nonlinearity of the corresponding transport equations even in the ground reaction–diffusion state. As in the case of static force field, a density potential well, which determines the nonlinear dynamics of the system, arises near the reaction front. A system of nonlinear equations describing the liquid motion is obtained. A complete nonlinear problem has been numerically simulated. It is shown that cellular convection develops in the potential well at a certain ratio of the initial concentrations and the values of centrifugal Rayleigh numbers. With an increase in the rotation speed, the structure periodicity is increasingly violated due to the instability of the diffusion layer formed near the rotation axis and the action of the inertial field, which ejects some cells from the potential well.
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Funding
The derivation and analysis of the equations of motion of rotational convection were supported by the Ministry of Science and Higher Education of the Russian Federation (grant no. FSNM-2020-0026). The statement of the CDD problem, analysis of the ground state, writing of an original program, and numerical nonlinear-dynamics calculations were supported by the Russian Science Foundation (grant no. 19-11-00133).
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Translated by Yu. Sin’kov
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Utochkin, V.Y., Siraev, R.R. & Bratsun, D.A. Chemoconvective Structures in a Rotating System of Reacting Liquids. J Appl Mech Tech Phy 62, 1132–1144 (2021). https://doi.org/10.1134/S0021894421070191
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DOI: https://doi.org/10.1134/S0021894421070191