Two-Phase Binary Fluids and Immiscible Fluids Described by an Order Parameter

“…The last velocity interface boundary condition is exactly the Beavers-Joseph-SaffmanJones interface boundary condition [10,12,14,15,60,61,62,63,64,65] with the slip coefficient β equal to the Beavers-Joseph-Saffman-Jones coefficient α BJSJ . The Cahn-Hilliard-Stokes system can be viewed as the low Reynolds number approximation of the better-known Cahn-Hilliard-Navier-Stokes system for two phase flow [28,35,34,36,40,66,67,68,69,70]. The derivation above indicates that the interface boundary conditions (except for the three obtained via conservation of mass consideration) are in fact variational interface boundary conditions.…”

Section: Application Of Onsager's Extremum Principlementioning

confidence: 99%

“…In the diffuse-interface approach (or phase-field method) that we have adopted here, we approximate the separating boundary between two (macroscopically) immiscible fluid phases using an order parameter φ (phase field variable) that continuously, and usually monotonically, varies from one value in phase A (water for instance), say φ = +1, to another value in phase B (oil for instance), say φ = −1, in a transition layer of small, but finite, thickness (see Fig. 2 for an illustration) [34,35,36,37]. This idea can be traced back to van der Waals and Lord Rayleigh [38,39].…”

Section: Introductionmentioning

confidence: 99%

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Two‐phase flows in karstic geometry

Han

Sun

Wang

2013

Math Methods in App Sciences

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Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications.In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. Despite the importance of the subject, little work has been done on multi-phase flows in karstic geometry.In this paper we present a family of phase field (diffusive interface) models for two phase flow in karstic geometry. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws. Uniquely solvable first and second order in time numerical schemes that preserve the associated energy law are presented as well.

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Computational Phase‐Field Modeling

Gómez

Zee

2017

Encyclopedia of Computational Mechanics Second Edition

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Phase-field modeling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domain motions are also unknowns. The computational treatment of these problems requires moving meshes and is very difficult when the moving domains undergo topological changes. Phase-field modeling may be understood as a methodology to reformulate interface problems as equations posed on fixed domains. In some cases, the phase-field model may be shown to converge to the moving-boundary problem as a regularization parameter tends to zero, which shows the mathematical soundness of the approach. However, this is only part of the story because phase-field models do not need to have a moving-boundary problem associated and can be rigorously derived from classical thermomechanics. In this context, the distinguishing feature is that constitutive models depend on the variational derivative of the free energy. In all, phase-field models open the opportunity for the efficient treatment of outstanding problems in computational mechanics, such as, the interaction of a large number of cracks in three dimensions, cavitation, film and nucleate boiling, tumor growth or fully three-dimensional air-water flows with surface tension. In addition, phase-field models bring a new set of challenges for numerical discretization that will excite the computational mechanics community.

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Two-Phase Binary Fluids and Immiscible Fluids Described by an Order Parameter

Cited by 528 publications

References 22 publications

Computation of multiphase systems with phase field models

Computation of multiphase systems with phase field models

Two‐phase flows in karstic geometry

Computational Phase‐Field Modeling

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