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Rayleigh-Taylor instability of a miscible interface in a confined domain

Rayleigh-Taylor instability of a miscible interface in a confined domain
Rayleigh-Taylor instability of a miscible interface in a confined domain
On the basis of the phase-field approach we investigate the simultaneous diffusive and convective evolution of an isothermal binary mixture of two slowly miscible liquids that are confined in a horizontal plane layer. We assume that two miscible liquids are brought into contact so the binary system is thermodynamically unstable and the heavier liquid is placed on top of the lighter liquid so the system is gravitationally unstable. Our model takes into account the non-Fickian nature of the interfacial diffusion and the dynamic interfacial stresses at a boundary separating two miscible liquids. The numerical results demonstrate that the classical growth rates that characterise the initial development of the Rayleigh-Taylor instability can be retrieved in the limit of the higher Peclet numbers (weaker diffusion) and thinner interfaces. The further nonlinear development of the Rayleigh-Taylor instability, characterised e.g. by the size of the mixing zone, is however limited by the height of the plane layer. On a longer time scale the binary system approaches the state of thermodynamic and hydrodynamic equilibrium. In addition, a novel effect is found. It is commonly accepted that the interface between the miscible liquids slowly smears in time due to diffusion. We however found when the binary system is subject to hydrodynamic transformations the interface boundary stretches so its thickness changes (the interface becomes thinner) on a much faster convective time scale. The thickness of the interface is inversely proportional to the surface tension, and the stronger surface tension limits the development of the Rayleigh-Taylor instability.
Rayleigh-Taylor instability, miscible liquids, phase-field approach
1070-6631
Lyubimova, Tatiana
ea977036-7fca-4d61-abf5-1da0a94c9b35
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Prokopev, S.
b5f7d4d7-1414-4153-b4e9-61df5eea2186
Lyubimova, Tatiana
ea977036-7fca-4d61-abf5-1da0a94c9b35
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Prokopev, S.
b5f7d4d7-1414-4153-b4e9-61df5eea2186

Lyubimova, Tatiana, Vorobev, Anatoliy and Prokopev, S. (2019) Rayleigh-Taylor instability of a miscible interface in a confined domain. Physics of Fluids, 31 (1). (doi:10.1063/1.5064547).

Record type: Article

Abstract

On the basis of the phase-field approach we investigate the simultaneous diffusive and convective evolution of an isothermal binary mixture of two slowly miscible liquids that are confined in a horizontal plane layer. We assume that two miscible liquids are brought into contact so the binary system is thermodynamically unstable and the heavier liquid is placed on top of the lighter liquid so the system is gravitationally unstable. Our model takes into account the non-Fickian nature of the interfacial diffusion and the dynamic interfacial stresses at a boundary separating two miscible liquids. The numerical results demonstrate that the classical growth rates that characterise the initial development of the Rayleigh-Taylor instability can be retrieved in the limit of the higher Peclet numbers (weaker diffusion) and thinner interfaces. The further nonlinear development of the Rayleigh-Taylor instability, characterised e.g. by the size of the mixing zone, is however limited by the height of the plane layer. On a longer time scale the binary system approaches the state of thermodynamic and hydrodynamic equilibrium. In addition, a novel effect is found. It is commonly accepted that the interface between the miscible liquids slowly smears in time due to diffusion. We however found when the binary system is subject to hydrodynamic transformations the interface boundary stretches so its thickness changes (the interface becomes thinner) on a much faster convective time scale. The thickness of the interface is inversely proportional to the surface tension, and the stronger surface tension limits the development of the Rayleigh-Taylor instability.

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Accepted/In Press date: 25 December 2018
e-pub ahead of print date: 15 January 2019
Published date: January 2019
Keywords: Rayleigh-Taylor instability, miscible liquids, phase-field approach

Identifiers

Local EPrints ID: 427240
URI: https://eprints.soton.ac.uk/id/eprint/427240
ISSN: 1070-6631
PURE UUID: 432addf2-1b3a-4bf6-a6d6-db486e81e49a
ORCID for Anatoliy Vorobev: ORCID iD orcid.org/0000-0002-6458-9390

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Date deposited: 09 Jan 2019 17:30
Last modified: 15 Jul 2019 16:46

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