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Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations
Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations
We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.
1050-2947
056312-[10pp]
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01

Vorobev, Anatoliy (2010) Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. Physical Review A, 82 (5), 056312-[10pp]. (doi:10.1103/PhysRevE.82.056312).

Record type: Article

Abstract

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

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Published date: November 2010
Organisations: Thermofluids and Superconductivity

Identifiers

Local EPrints ID: 169633
URI: http://eprints.soton.ac.uk/id/eprint/169633
ISSN: 1050-2947
PURE UUID: f80d2951-f50b-4698-bdbc-d9dec3421f2b
ORCID for Anatoliy Vorobev: ORCID iD orcid.org/0000-0002-6458-9390

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Date deposited: 22 Dec 2010 12:13
Last modified: 14 Mar 2024 02:53

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