Linear stability of a horizontal phase boundary subjected to shear motion

Kheniene, Abdesselem; Vorobev, Anatoliy

doi:10.1140/epje/i2015-15077-4

Cited by 4 publications

(10 citation statements)

References 39 publications

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“…The increase of the Cahn number increases the surface tension effect, which makes the interface less prone to deformations, and this reduces the amplitude of the waves and the amplitude of the hydrodynamic motion in the layer. Similar observations were earlier achieved with the help of the linear stability analysis [26].…”

Section: Numerical Resultssupporting

confidence: 88%

“…Stronger viscous and diffusion effects should result in a closure of the zone of the Holmboe instability, although such cases are not modelled in the present work. Similar stability diagrams were earlier reported by other researchers [11,12,26]. In particular, figure 6a is adopted from our earlier work [26], where this diagram is obtained by using the linear stability analysis for an interface that separates two semiinfinite domains of two miscible liquids.…”

Section: Numerical Resultssupporting

confidence: 53%

“…Similar stability diagrams were earlier reported by other researchers [11,12,26]. In particular, figure 6a is adopted from our earlier work [26], where this diagram is obtained by using the linear stability analysis for an interface that separates two semiinfinite domains of two miscible liquids. Figures 6b-d are obtained with the help of the numerical solution of the full equations.…”

Section: Numerical Resultssupporting

confidence: 53%

“…The linear stability of a phase boundary in a heterogeneous binary system is investigated in work [26], where the boundaries of the Kelvin-Helmholtz and Holmboe instabilities are determined. It is found that the zones of instability are larger for thinner interfaces.…”

Section: Introductionmentioning

confidence: 99%

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Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

2019

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The stability of a shear flow imposed along a diffusive interface that separates two miscible liquids (a heavier liquid lies underneath) is studied using direct numerical simulations. The phase-field approach is employed for description of a thermo-and hydrodynamic evolution of a heterogeneous binary mixture. The approach takes into account the dynamic interfacial stresses at a miscible interface and uses the extended Fick's law for setting the diffusion transport (the diffusion flux is proportional to the gradient of chemical potential). The shear flow is unstable to two kinds of instabilities: (i) the Kelvin-Helmholtz instability, with an immovable vortex formed in the middle of an interface (in the vertical direction), and (ii) the Holmboe instability, with travelling waves along the interfacial boundary. The development of the Holmboe instability results in a stronger enhancement of molecular mixing between the mixture components. Earlier, the boundaries of these instabilities were determined using the linear stability analysis and employing the concept of a 'frozen interface'. In the current work, through the solution of full equations, we obtain the stability boundaries for several sets of governing parameters, showing a greater variety of the possible shapes of the stability diagrams. The Kelvin-Helmholtz instability always occurs at lower gravity effects (lower density contrasts), while the Holmboe instability occurs when gravity is stronger. We show that for some parameters these two instabilities are separated by a zone where the shear flow is stable, and this zone disappears for the other sets of parameters.

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Section: Numerical Resultssupporting

confidence: 88%

Section: Numerical Resultssupporting

confidence: 53%

Section: Numerical Resultssupporting

confidence: 53%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

2019

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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: 82%

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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Modelling of the rise and absorption of a fluid inclusion

Vorobev

Khlebnikova

2018

International Journal of Heat and Mass Transfer

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The buoyancy-driven rise of a small single fluid inclusion in a viscous liquid that is enclosed in a container of the cylindrical shape is numerically modelled. It is additionally assumed that the inclusion is slowly absorbed by the surrounding liquid. The phase-field approach is used as a physics-based model for the description of the thermo-and hydrodynamic evolution of a miscible heterogeneous binary mixture. The interplay of the effects of absorption and inclusion's motion are investigated. We found that the dissolution of a nearly spherical inclusion does not occur evenly over its surface. The interfacial diffusion is stronger at the inclusion's top cap. The matter absorbed by the liquid does not quickly penetrate into the bulk of the ambient phase, it accumulates behind the inclusion forming a concentration wake. We found that during the rise the inclusion's speed grows. The speed and the acceleration of the inclusion strongly depend on the absorption rate, so the inclusion rises faster at the higher absorption rates. This effect is explained by the action of the Marangoni stress that is developed due to non-uniform mixture composition along the inclusion's surface. We also found that the rise of the inclusion in a closed container is accompanied by the recirculation flow that is developed near the inclusion and that rises upwards with the inclusion. In the limit of negligible absorption (higher Peclet numbers) the convergence to a constant terminal speed of an immiscible inclusion is observed.

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Linear stability of a horizontal phase boundary subjected to shear motion

Cited by 4 publications

References 39 publications

Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

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

Modelling of the rise and absorption of a fluid inclusion

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