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Vibrational convection in a heterogeneous binary mixture. Part I. Time-averaged equations

Vibrational convection in a heterogeneous binary mixture. Part I. Time-averaged equations
Vibrational convection in a heterogeneous binary mixture. Part I. Time-averaged equations
High-frequency vibrations of a container filled with a fluid generate the pulsation flows that however are barely visible with the naked eye, and induce the slow but large-amplitude averaged flows that are important for various practical applications. In this work we derive a theoretical model that gives the averaged description of the influence of uniform high-frequency vibrations on an isothermal mixture of two slowly miscible liquids. The miscible multiphase system is described within the framework of the phase-field approach. The full Cahn-Hillard-Navier-Stokes equations are split into the separate systems for the quasi-acoustic, pulsating and averaged flow fields, eliminating the need for the resolution of the short time-scale pulsation motion and thus making the analysis of the long-term evolution much more efficient. The resultant averaged model includes the effects of concentration diffusion and barodiffusion, the dynamic interfacial stresses, and the generation of the hydrodynamic flows by non-homogeneities of the concentration field (when they are combined with the effects of gravity and vibrations). The resultant model for the vibrational convection in a heterogeneous mixture of two fluids separated by diffusive boundaries could be used for the description of processes of mixing/de-mixing, solidification/melting, polymerisation, etc. in the presence of vibrations.
0022-1120
543-562
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 I. Time-averaged equations. Journal of Fluid Mechanics, 870, 543-562. (doi:10.1017/jfm.2019.282).

Record type: Article

Abstract

High-frequency vibrations of a container filled with a fluid generate the pulsation flows that however are barely visible with the naked eye, and induce the slow but large-amplitude averaged flows that are important for various practical applications. In this work we derive a theoretical model that gives the averaged description of the influence of uniform high-frequency vibrations on an isothermal mixture of two slowly miscible liquids. The miscible multiphase system is described within the framework of the phase-field approach. The full Cahn-Hillard-Navier-Stokes equations are split into the separate systems for the quasi-acoustic, pulsating and averaged flow fields, eliminating the need for the resolution of the short time-scale pulsation motion and thus making the analysis of the long-term evolution much more efficient. The resultant averaged model includes the effects of concentration diffusion and barodiffusion, the dynamic interfacial stresses, and the generation of the hydrodynamic flows by non-homogeneities of the concentration field (when they are combined with the effects of gravity and vibrations). The resultant model for the vibrational convection in a heterogeneous mixture of two fluids separated by diffusive boundaries could be used for the description of processes of mixing/de-mixing, solidification/melting, polymerisation, etc. in the presence of vibrations.

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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: 429882
URI: http://eprints.soton.ac.uk/id/eprint/429882
ISSN: 0022-1120
PURE UUID: 6c9db08a-389e-4f93-976b-e243adf0a486
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 06:51

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Author: Tatyana Lyubimova

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