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Linear stability analysis of a horizontal phase boundary separating two miscible liquids

Linear stability analysis of a horizontal phase boundary separating two miscible liquids
Linear stability analysis of a horizontal phase boundary separating two miscible liquids
The evolution of small disturbances to a horizontal interface separating two miscible liquids is examined. The aim is to investigate how the interfacial mass transfer affects development of the Rayleigh-Taylor instability and propagation and damping of the gravity-capillary waves. The phase-field approach is employed to model the evolution of a miscible multiphase system. Within this approach, the interface is represented as a transitional layer of small but nonzero thickness. The thermodynamics is defined by the Landau free energy function. Initially, the liquid-liquid binary system is assumed to be out of its thermodynamic equilibrium, and hence, the system undergoes a slow transition to its thermodynamic equilibrium. The linear stability of such a slowly diffusing interface with respect to normal hydro- and thermodynamic perturbations is numerically studied. As a result, we show that the eigenvalue spectra for a sharp immiscible interface can be successfully reproduced for long-wave disturbances, with wavelengths exceeding the interface thickness. We also find that thin interfaces are thermodynamically stable, while thicker interfaces, with the thicknesses exceeding an equilibrium value, are thermodynamically unstable. The thermodynamic instability can make the configuration with a heavier liquid lying underneath unstable.We also find that the interfacial mass transfer introduces additional dissipation, reducing the growth rate of the Rayleigh Taylor instability and increasing the dissipation of the gravity waves. Moreover, mutual action of diffusive and viscous effects completely suppresses development of the modes with shorter wavelengths.
1539-3755
022404-[15pp]
Kheniene, Abdesselem
63a0b16b-ea45-475c-8d8f-3872f6cf74fa
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Kheniene, Abdesselem
63a0b16b-ea45-475c-8d8f-3872f6cf74fa
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01

Kheniene, Abdesselem and Vorobev, Anatoliy (2013) Linear stability analysis of a horizontal phase boundary separating two miscible liquids. Physical Review E, 88 (2), 022404-[15pp]. (doi:10.1103/PhysRevE.88.022404).

Record type: Article

Abstract

The evolution of small disturbances to a horizontal interface separating two miscible liquids is examined. The aim is to investigate how the interfacial mass transfer affects development of the Rayleigh-Taylor instability and propagation and damping of the gravity-capillary waves. The phase-field approach is employed to model the evolution of a miscible multiphase system. Within this approach, the interface is represented as a transitional layer of small but nonzero thickness. The thermodynamics is defined by the Landau free energy function. Initially, the liquid-liquid binary system is assumed to be out of its thermodynamic equilibrium, and hence, the system undergoes a slow transition to its thermodynamic equilibrium. The linear stability of such a slowly diffusing interface with respect to normal hydro- and thermodynamic perturbations is numerically studied. As a result, we show that the eigenvalue spectra for a sharp immiscible interface can be successfully reproduced for long-wave disturbances, with wavelengths exceeding the interface thickness. We also find that thin interfaces are thermodynamically stable, while thicker interfaces, with the thicknesses exceeding an equilibrium value, are thermodynamically unstable. The thermodynamic instability can make the configuration with a heavier liquid lying underneath unstable.We also find that the interfacial mass transfer introduces additional dissipation, reducing the growth rate of the Rayleigh Taylor instability and increasing the dissipation of the gravity waves. Moreover, mutual action of diffusive and viscous effects completely suppresses development of the modes with shorter wavelengths.

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Published date: 19 August 2013
Organisations: Engineering Science Unit

Identifiers

Local EPrints ID: 355990
URI: http://eprints.soton.ac.uk/id/eprint/355990
ISSN: 1539-3755
PURE UUID: ee4e48da-346e-4dda-af26-7f9db5490222
ORCID for Anatoliy Vorobev: ORCID iD orcid.org/0000-0002-6458-9390

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Date deposited: 09 Sep 2013 15:19
Last modified: 24 Sep 2019 00:43

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