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Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases
Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases
The stability of a shear flow imposed along a diffusive interface that separates two miscible liquids (a heavier liquid lies underneath) is studied using direct numerical simulations. The phase-field approach is employed for description of a thermo- and hydrodynamic evolution of a heterogeneous binary mixture. The approach takes into account the dynamic interfacial stresses at a miscible interface and uses the extended Fick's law for setting the diffusion transport (the diffusion flux is proportional to the gradient of chemical potential). The shear flow is unstable to two kinds of instabilities: (i) the Kelvin-Helmholtz instability, with an immovable vortex formed in the middle of an interface (in the vertical direction), and (ii) the Holmboe instability, with travelling waves along the interfacial boundary. The development of the Holmboe instability results in a stronger enhancement of molecular mixing between the mixture components. Earlier, the boundaries of these instabilities were determined using the linear stability analysis and employing the concept of a 'frozen interface'. In the current work, through the solution of full equations, we obtain the stability boundaries for several sets of governing parameters, showing a greater variety of the possible shapes of the stability diagrams. The Kelvin-Helmholtz instability always occurs at lower gravity effects (lower density contrasts), while the Holmboe instability occurs when gravity is stronger. We show that for some parameters these two instabilities are separated by a zone where the shear flow is stable, and this zone disappears for the other sets of parameters.
2470-0045
1-11
Zagvozkin, Timofey
dcd8774d-869f-4473-979e-731eea770e38
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Lyubimova, T.
5c021d17-a1c6-49a6-97ce-3ea583eaed4b
Zagvozkin, Timofey
dcd8774d-869f-4473-979e-731eea770e38
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Lyubimova, T.
5c021d17-a1c6-49a6-97ce-3ea583eaed4b

Zagvozkin, Timofey, Vorobev, Anatoliy and Lyubimova, T. (2019) Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases. Physical Review E, 100 (2), 1-11. (doi:10.1103/PhysRevE.100.023103).

Record type: Article

Abstract

The stability of a shear flow imposed along a diffusive interface that separates two miscible liquids (a heavier liquid lies underneath) is studied using direct numerical simulations. The phase-field approach is employed for description of a thermo- and hydrodynamic evolution of a heterogeneous binary mixture. The approach takes into account the dynamic interfacial stresses at a miscible interface and uses the extended Fick's law for setting the diffusion transport (the diffusion flux is proportional to the gradient of chemical potential). The shear flow is unstable to two kinds of instabilities: (i) the Kelvin-Helmholtz instability, with an immovable vortex formed in the middle of an interface (in the vertical direction), and (ii) the Holmboe instability, with travelling waves along the interfacial boundary. The development of the Holmboe instability results in a stronger enhancement of molecular mixing between the mixture components. Earlier, the boundaries of these instabilities were determined using the linear stability analysis and employing the concept of a 'frozen interface'. In the current work, through the solution of full equations, we obtain the stability boundaries for several sets of governing parameters, showing a greater variety of the possible shapes of the stability diagrams. The Kelvin-Helmholtz instability always occurs at lower gravity effects (lower density contrasts), while the Holmboe instability occurs when gravity is stronger. We show that for some parameters these two instabilities are separated by a zone where the shear flow is stable, and this zone disappears for the other sets of parameters.

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More information

Accepted/In Press date: 1 July 2019
e-pub ahead of print date: 5 August 2019
Published date: August 2019

Identifiers

Local EPrints ID: 432343
URI: http://eprints.soton.ac.uk/id/eprint/432343
ISSN: 2470-0045
PURE UUID: d21ecc50-0b04-485d-8164-170770ddc2a3
ORCID for Anatoliy Vorobev: ORCID iD orcid.org/0000-0002-6458-9390

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Date deposited: 11 Jul 2019 16:30
Last modified: 22 Nov 2021 02:56

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Contributors

Author: Timofey Zagvozkin
Author: T. Lyubimova

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