On the phase-field modelling of a miscible liquid/liquid boundary

Xie, Ruilin; Vorobev, Anatoliy

doi:10.1016/j.jcis.2015.11.026

Cited by 8 publications

(3 citation statements)

References 34 publications

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“…The approach correctly predicts the evolution of the shape of the droplet, predicting such experimentally-observed details of the process as the existence of the sharp phase boundary for the entire dissolution, non-negligible interfacial mass transfer during any stage of the process including the initial stage after the change the rotation speed when the droplet quickly accommodates to the new shape, the cloudy regions near the droplet's ends, the independence of interfacial stresses on the speed of the tube's rotation and the size of the immersed droplet, and some others [22,19,20]. This also confirms our earlier phasefield-based calculations fulfilled for the mixture of miscible liquids within a different geometry [39].…”

Section: Discussionsupporting

confidence: 85%

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: Discussionsupporting

confidence: 85%

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

Vorobev

Boghi

2016

Journal of Colloid and Interface Science

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“…In figure 1 one sees that function (8) coincides with the Landau function near the critical solution point, and this function defines a different behaviour when |C| → 1/2, where overshooting (non-physical values in the concentration field) are excluded by the logarithmic terms. Free energy function (8) was previously used in our other works where evolving heterogeneous binary systems were examined in the frameworks of other physical problems [34][35][36][37][38].…”

Section: Mathematical Modelmentioning

confidence: 99%

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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“…In other words we extend the usual expectations allowed for the values of a and b near In the presence of strong gravity-induced gradients in the field of concentration, or in the presence of strong flows, expression (2) becomes less convenient, as in these cases the numerically calculated values of the concentration can be outside of the range of concentrations that correspond to the pure components (±1/2). 1 In [39,40] the other free energy function is used,…”

Section: Governing Equations Phase-field Approachmentioning

confidence: 99%

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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On the phase-field modelling of a miscible liquid/liquid boundary

Cited by 8 publications

References 34 publications

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

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

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

Modelling of the rise and absorption of a fluid inclusion

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