Effect of shear flow on the stability of domains in two-dimensional phase-separating binary fluids

Frischknecht, Amalie L.

doi:10.1103/physreve.56.6970

Cited by 20 publications

(13 citation statements)

References 26 publications

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“…The goal of this paper is to explore the stabilization of cylindrical domains by an imposed shear flow. It is a sequel to my previous work on the stabilization by shear flow of a two-dimensional, lamellar domain in phaseseparating binary fluids [15]. In that paper it was shown that a lamellar domain at rest with diffuse interfaces is unstable towards a "varicose" instability.…”

Section: Introductionmentioning

confidence: 85%

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Stability of cylindrical domains in phase-separating binary fluids in shear flow

Frischknecht

1998

Phys. Rev. E

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The stability of a long cylindrical domain in a phase-separating binary fluid in an external shear flow is investigated by linear stability analysis. Using the coupled Cahn-Hilliard and Stokes equations, the stability eigenvalues are derived analytically for long-wavelength perturbations, for arbitrary viscosity contrast between the two phases. The shear flow is found to suppress and sometimes completely stabilize both the hydrodynamic Rayleigh instability and the thermodynamic instability of the cylinder against varicose perturbations, by mixing with nonaxisymmetric perturbations. The results are consistent with recent observations of a ''string phase'' in phase-separating fluids in shear. ͓S1063-651X͑98͒15909-3͔

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Section: Introductionmentioning

confidence: 85%

“…consider a cylindrical domain in a solid binary alloy) a cylindrical domain in the two-phase state is still unstable. This is due to the Gibbs-Thomson effect, in which the chemical potential depends on the curvature [15,16]. The higher curvature at the necks will drive a diffusive flux towards the bulges, also leading to instability.…”

Section: Introductionmentioning

confidence: 99%

Stability of cylindrical domains in phase-separating binary fluids in shear flow

Frischknecht

1998

Phys. Rev. E

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“…26 for an approximate concentration profile. Figure 2 shows the results of numerical simulation of Eq.…”

Section: Instability In the Absence Of Flowmentioning

confidence: 99%

“…26 We seek solutions of Eqs. ͑13͒ in the form of asymptotic series in powers of small wavenumbers k appropriate for the long-wave limit,…”

Section: ͑12͒mentioning

confidence: 99%

Stability of a two-layer binary-fluid system with a diffuse interface

et al. 2008

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The phase separation of a binary fluid can lead to the creation of two horizontal fluid layers with different concentrations resting on a solid substrate and divided by a diffuse interface. In the framework of the Cahn-Hilliard equation, it is shown analytically and numerically that such a layered system is subject to a transverse instability that generates a slowly coarsening multidomain structure. The influence of gravity, solutocapillary effect at the free boundary, and Korteweg stresses inside the diffuse interface on the stability of the layers is studied using the coupled system of the hydrodynamic equations and the nonlinear equation for the concentration ͑H model͒. The parameter regions of long-wave instabilities are found.

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“…In [39][40][41], the thermodynamic stability of an equilibrium interface (also called a kink solution) was studied. It was found that such an interface is stable in respect to normal perturbations with the decay rate growing as k 3 .…”

Section: Introductionmentioning

confidence: 99%

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

Kheniene

Vorobev

2013

Phys. Rev. E

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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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Effect of shear flow on the stability of domains in two-dimensional phase-separating binary fluids

Cited by 20 publications

References 26 publications

Stability of cylindrical domains in phase-separating binary fluids in shear flow

Stability of cylindrical domains in phase-separating binary fluids in shear flow

Stability of a two-layer binary-fluid system with a diffuse interface

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

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