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

Kheniene, Abdesselem; Vorobev, Anatoliy

doi:10.1103/physreve.88.022404

Cited by 14 publications

(16 citation statements)

References 47 publications

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“…These results, including appearance of the cloudy regions near the droplet's ends, are is in agreement with the experimental pictures [22]. Figure 2 depicts the results of the numerical simulations of the droplet's time evolution obtained for the 4 In [37,38], the influence of the interface thickness on the stability of a phase boundary has been studied. It has been found that if the interface thickness is smaller than the thickness that corresponds to the thermodynamic equilibrium value δ 0 (21), then the thickness of the transition zone quickly adjusts to the thermodynamic equilibrium value, i.e.…”

Section: Numerical Resultssupporting

confidence: 73%

Phase-field modelling of a miscible system in spinning droplet tensiometer

Vorobev

Boghi

2016

Journal of Colloid and Interface Science

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The spinning drop tensiometry is used for measurements of surface tension coefficients, especially, when interfaces are characterised by low and ultra-low interfacial stresses. A droplet of lighter liquid is introduced into a rotating capillary that was initially saturated with another heavier liquid. The tube is subject to axial rotation that results in droplet's elongation along the tube's axis. The equilibrium shape of the droplet is used to determine the surface tension coefficient. In this work, the evolution of a slowly miscible droplet introduced into a spinning capillary is investigated. This technique is frequently employed for studies of the dynamics of miscible systems, even despite the fact that a strict equilibrium is never achieved in a mixture of fully miscible liquids. The numerical modelling of a miscible droplet is fulfilled on the basis of the phase-field (Cahn-Hilliard) approach. The numerical results are compared against the experimental data pursuing two objectives: (i) to verify the use of the phase-field approach as a consistent physics-based approach capable of accurate tracking of the short-and long-term evolution of miscible systems, and (ii) to estimate the values of the phenomenological parameters introduced within the phase-field approach, so making this approach a practical tool for modelling of thermohydrodynamic changes in miscible systems within various configurations.

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Section: Numerical Resultssupporting

confidence: 73%

Phase-field modelling of a miscible system in spinning droplet tensiometer

Vorobev

Boghi

2016

Journal of Colloid and Interface Science

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“…The linear stability of such an interface was studied in ref. [1], where it was shown that the interfacial diffusion slows down the development of hydrodynamic modes. From the other hand, in [1], it was also shown that thick interfaces, with the thicknesses exceeding the thickness of a thermodynamically equilibrium phase boundary, are prone to the new thermodynamic instability.…”

Section: Introductionmentioning

confidence: 99%

“…[1], where it was shown that the interfacial diffusion slows down the development of hydrodynamic modes. From the other hand, in [1], it was also shown that thick interfaces, with the thicknesses exceeding the thickness of a thermodynamically equilibrium phase boundary, are prone to the new thermodynamic instability. Thus, the thick interface would be thermodynamically unstable, and development of the instability would inevitably be accompanied by hydrodynamic motion, even if the lighter liquid lies over the heavier liquid.…”

Section: Introductionmentioning

confidence: 99%

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Linear stability of a horizontal phase boundary subjected to shear motion

Kheniene

Vorobev

2015

Eur. Phys. J. E

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Abstract. We investigate the stability of slowly smearing phase boundary that appears at the contact of two miscible liquids. A hydrodynamic flow is imposed along the boundary. The aim is to find out whether the slow diffusive smearing of a boundary can be overrun by faster mixing. The phase-field approach is used to model the evolution of the binary mixture. The linear stability in respect to 2D perturbations is studied. If the heavier liquid lies above the lighter liquid, the interface is unconditionally unstable due to the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The imposed flow accelerates the growth of the long-wave modes and suppresses the growth of the short-wave perturbations. Viscosity, diffusivity and capillarity reduce the growth of perturbations. If the heavier liquid underlies the lighter one, the interface can be stable. The stability boundaries are defined by the strength of gravity (density contrast) and the intensity of the imposed flow. Thinner interfaces are usually characterised by larger zones of instability. The thermodynamic instability, identified for the thicker interfaces with the thicknesses greater than the thickness of a thermodynamically equilibrium phase boundary, makes such interfaces unconditionally unstable. The zones of instability are enlarged by diffusive and capillary terms. Viscosity plays its stabilising role. PACS

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“…On macroscopic scales, the interface between two liquids is infinitely sharp, and the limit of δ → 0 is of the primary interest for the phase-field approach. As shown in [8], the limit of the sharp interface is not easy to obtain, as both the interface thickness and the surface tension coefficients depend on Ca, and both values would decrease if Ca tends to zero. Hence, a single decrease in the values of the capillary number would make the interface thinner, but a thinner interface would be also endowed with smaller surface tension.…”

Section: Governing Equations: Phase-field Approachmentioning

confidence: 99%

Phase-field modelling of gravity-capillary waves on a miscible interface

2017

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Abstract. Using the approach of direct numerical simulations we investigate the gravity-capillary waves induced on a horizontal interface between two slowly miscible liquids. It is assumed that the liquids are just brought into contact, and thus the interface is slowly smeared by the action of interfacial diffusion. It is also assumed that the initial shape of the interface is distorted by harmonic perturbations, which results in the development of the gravity-capillary surface waves. The evolution of the binary mixture is modelled on the basis of the phase-field method. Our results show that in the limiting case of negligible diffusion the classical dispersion relations for immiscible interfaces can be reproduced. Although, for the waves with shorter wavelengths such an agreement is more difficult to obtain. The interfacial diffusion brings an additional dissipation to the fluid system, strongly damping the development of the shorter waves. We also show that the mixing (or the transition of a binary system to the state of thermodynamic equilibrium) is intensified by the presence of the surface waves, and this effect is more important when the liquids are slowly miscible, i.e. when the interfacial diffusion is weak.

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

Cited by 14 publications

References 47 publications

Phase-field modelling of a miscible system in spinning droplet tensiometer

Phase-field modelling of a miscible system in spinning droplet tensiometer

Linear stability of a horizontal phase boundary subjected to shear motion

Phase-field modelling of gravity-capillary waves on a miscible interface

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