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Vibrational convection in a heterogeneous binary mixture. Part II. Frozen waves

Vibrational convection in a heterogeneous binary mixture. Part II. Frozen waves
Vibrational convection in a heterogeneous binary mixture. Part II. Frozen waves
The action of high-frequency vibrations on a heterogeneous binary mixture that fills in a closed container is numerically modelled to validate the theoretical model obtained in the first part of the work, and to investigate the role of interfacial stresses in the evolution of miscible boundaries. Only weightlessness conditions are considered. A recent experimental study reports the threshold ignition of the frozen waves at a miscible interface even under weightlessness conditions, which cannot be explained on the basis of the classical approach that represents a binary mixture as a single phase fluid with impurity. This effect, however, can be well explained on the basis of the phase-field equations that are derived in the first part of our work. In particular, we found that when the vibrational forcing is sufficiently strong (the vibrational forcing is primarily determined by the amplitude of the vibrational velocity), above a certain threshold value, then the interface becomes shaped into a 'frozen' (time-independent to the naked eye) structure of several pillars (the frozen waves) with the axes perpendicular to the directions of vibrations. The threshold level of vibrations is determined by the interfacial stresses that need to be associated with miscible interfaces. The time needed for setting up the frozen pattern is relatively small, determined by hydrodynamic processes, however this time grows exponentially near the threshold. The frozen pattern remains stable either indefinitely long (if liquids are partially miscible) or until the interface becomes invisible due to diffusive smearing (if liquids are miscible in all proportions). A further increase of the vibrational forcing alters the number of the pillars, which happens discretely when the intensity of the vibrations surpasses a sequence of further critical levels. Correlation of the results with the previous experimental and theoretical studies validate the new approach making it a useful tool for tracing thermo- and hydrodynamic changes in heterogeneous mixtures.
0022-1120
563-564
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Lyubimova, Tatyana
ea977036-7fca-4d61-abf5-1da0a94c9b35
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Lyubimova, Tatyana
ea977036-7fca-4d61-abf5-1da0a94c9b35

Vorobev, Anatoliy and Lyubimova, Tatyana (2019) Vibrational convection in a heterogeneous binary mixture. Part II. Frozen waves. Journal of Fluid Mechanics, 870, 563-564. (doi:10.1017/jfm.2019.305).

Record type: Article

Abstract

The action of high-frequency vibrations on a heterogeneous binary mixture that fills in a closed container is numerically modelled to validate the theoretical model obtained in the first part of the work, and to investigate the role of interfacial stresses in the evolution of miscible boundaries. Only weightlessness conditions are considered. A recent experimental study reports the threshold ignition of the frozen waves at a miscible interface even under weightlessness conditions, which cannot be explained on the basis of the classical approach that represents a binary mixture as a single phase fluid with impurity. This effect, however, can be well explained on the basis of the phase-field equations that are derived in the first part of our work. In particular, we found that when the vibrational forcing is sufficiently strong (the vibrational forcing is primarily determined by the amplitude of the vibrational velocity), above a certain threshold value, then the interface becomes shaped into a 'frozen' (time-independent to the naked eye) structure of several pillars (the frozen waves) with the axes perpendicular to the directions of vibrations. The threshold level of vibrations is determined by the interfacial stresses that need to be associated with miscible interfaces. The time needed for setting up the frozen pattern is relatively small, determined by hydrodynamic processes, however this time grows exponentially near the threshold. The frozen pattern remains stable either indefinitely long (if liquids are partially miscible) or until the interface becomes invisible due to diffusive smearing (if liquids are miscible in all proportions). A further increase of the vibrational forcing alters the number of the pillars, which happens discretely when the intensity of the vibrations surpasses a sequence of further critical levels. Correlation of the results with the previous experimental and theoretical studies validate the new approach making it a useful tool for tracing thermo- and hydrodynamic changes in heterogeneous mixtures.

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Accepted/In Press date: 29 March 2019
e-pub ahead of print date: 14 May 2019
Published date: 10 July 2019

Identifiers

Local EPrints ID: 429881
URI: http://eprints.soton.ac.uk/id/eprint/429881
ISSN: 0022-1120
PURE UUID: 63f6b285-ca7a-47ff-95a4-2a36e76f7fd7
ORCID for Anatoliy Vorobev: ORCID iD orcid.org/0000-0002-6458-9390

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Date deposited: 08 Apr 2019 16:30
Last modified: 26 Nov 2021 05:14

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Author: Tatyana Lyubimova

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