Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling

Jacqmin, David

doi:10.1006/jcph.1999.6332

Cited by 1,366 publications

(1,147 citation statements)

References 23 publications

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“…In f mix , λ is the mixing energy density, is the capillary width and the ratio λ/ produces the interfacial tension σ [23,24]. f bulk is the Frank energy with a single elastic constant K, n being the director, regularized to permit defects where |n| deviates from unity over a small region of size δ [25,26].…”

Section: Theoretical Model and Numerical Methodsmentioning

confidence: 99%

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Yue

Feng

et al. 2005

Journal of Colloid and Interface Science

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Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.  2005 Elsevier Inc. All rights reserved.

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Section: Theoretical Model and Numerical Methodsmentioning

confidence: 99%

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Yue

Feng

et al. 2005

Journal of Colloid and Interface Science

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“…(Here, we have assumed arbitrarily that the composite material is relaxed at a reference temperature, and assumed an operation temperature of 1000 • above the reference temperature.) We chose the elastic constants of GDC to be isotropic (λ 11 − λ 12 = 2λ 44 [77]. As in Section 5.1, we again use domain parameters to indicate the GDC phase (ψ 1 = 1 inside the GDC and ψ 1 = 0 outside the GDC) and the LSC phase (ψ 2 = 1 inside the LSC and ψ 2 = 0 outside the LSC).…”

Section: Thermal Stressmentioning

confidence: 99%

“…For an isotropic solid, the Young's moduli are related to Lame constants by E = λ 12 (1 + ν)(1 − 2ν)/ν, where ν is the Poisson's ratio; the shear modulus is given by λ 44 = λ 12 (1 − 2ν)/2ν, and the elastic constant λ 11 is given by λ 11 = λ 12 + 2λ 44 . The pair, λ 12 and ν, forms the set of Lame constants.…”

Section: H Mechanical Equilibrium Equation Solvermentioning

confidence: 99%

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries

Chen

Thornton

2012

Modelling Simul. Mater. Sci. Eng.

109

113

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In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction-diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelled droplet.

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“…Currently, the phase-field approach is mostly used as a numerical tool for tracing immiscible 30 interfaces [2,3,4,5]. In the current work, however, this approach is used as a comprehensive physical model capable of describing the thermo-and hydrodynamic evolution of multiphase binary mixtures with undergoing phase transformations.…”

mentioning

confidence: 99%

“…105 Figure 1a shows the 2D concentration fields in a single capillary for the concentration-dependent diffusion coefficient (2). We assume that the capillary is initially saturated with the solute and then the solvent penetrates from the open ends.…”

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confidence: 99%

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

Xie

Vorobev

2016

Journal of Colloid and Interface Science

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Mixing of miscible liquids is essential for numerous processes in industry and nature. Mixing, i.e. interpenetration of molecules through the liquid/liquid boundary, occurs via interfacial diffusion.Mixing can also involve externally or internally driven hydrodynamic flows, and can lead to de- approach that is used as a physics-based model for the thermo-and hydrodynamic evolution of binary mixtures. Within this approach, the diffusion flux is defined through the gradient of chemical potential, and, in particular, includes the effect of barodiffisuon. The dynamic interfacial stresses at the miscible interface are also taken into account. The simulations showed that such an approach can accurately reproduce the shape of the solute/solvent boundary, and some aspects of the diffusion dynamics. Nevertheless, all experimentally-observed features of the diffusion motion of the solute/solvent boundary, were not reproduced.

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Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling

Cited by 1,366 publications

References 23 publications

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries

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

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