Modeling soft interface dominated systems: A comparison of phase field and Gibbs dividing surface models

Lamorgese, Andrea; Mauri, Roberto; Sagis, Leonard M.C.

doi:10.1016/j.physrep.2017.01.002

Cited by 46 publications

(49 citation statements)

References 362 publications

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“…The Cahn number Ch sets the thickness of the interfacial layer where φ undergoes a smooth transition between the two bulk values φ = ±1 following the hyperbolic tangent profile. A mean-field approximation [26] is adopted in the description of the interface: the interfacial thickness (set with the Cahn number) is much larger than that of a real interface (molecular scale). The description of all the scales, from the problem scale down to the molecular scale, would require computational resources currently unavailable and, thus, the adoption of a mean-field approximation.…”

Section: Classic Phase Field Methods Formulationmentioning

confidence: 99%

Mass-conservation-improved phase field methods for turbulent multiphase flow simulation

2018

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The phase field method has emerged as a powerful tool for the simulation of multiphase flow. The method has great potential for further developments and applications: it has a sound physical basis, and when associated with a highly refined grid, physics is accurately rendered. However, in many cases, especially when dealing with turbulent flows, the available computational resources do not allow for a complete resolution of the interfacial phenomena and some undesired effects such as shrinkage, coarsening and misrepresentation of surface tension forces and thermo-physical properties can affect the accuracy of the simulations. In this paper, we present two improved phase field method formulations (profile-corrected and flux-corrected), specifically developed to overcome the previously mentioned drawbacks, and we benchmark their performance versus the classic one. The formulations are first tested considering the rise of a bubble in a quiescent fluid and the interaction of two droplets in laminar shear flow; then, their performances are compared in the simulation of a droplet-laden turbulent flow. The aim of this work is to review and benchmark the different phase field method formulations, with the final goal of laying down useful guidelines for the accurate simulation of turbulent multiphase flow with the phase field method.

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Section: Classic Phase Field Methods Formulationmentioning

confidence: 99%

Mass-conservation-improved phase field methods for turbulent multiphase flow simulation

2018

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“…In the absence of any external field, i. e., when ψ 12 = 0, and considering eqs. (15) and 19, we obtain…”

Section: Constitutive Relationsmentioning

confidence: 92%

“…where ρ is the mixture molar density (which is constant), t is time, q is the source of internal energy per unit volume (generally referred to as heat source), and, according to the local equilibrium hypothesis, J q is the diffusive flux of internal energy (i. e., the heat flux) while J ϕ is the diffusive material flux. Imposing that the total energy is conserved (i. e., the total energy source is zero) we find that q = −J ϕ ⋅ ∇ψ 12 [8,9,15] (see, in particular, eq. (7.43) in Mauri [9]), with ψ 12 = ψ 1 − ψ 2 , where ψ k is the potential acting on component k. Such a potential ψ k is defined to express any conservative body force (per unit mole) F exerted on the mixture (see Section 7.4 in Mauri [9]) as…”

Section: Entropy Equation In Non-equilibrium Thermodynamicsmentioning

confidence: 99%

“…where we defined p ὔ = −ψ 2 . Here, the ∇p ὔ term can be omitted since any force that can be represented as the gradient of a scalar can be reabsorbed within the pressure term, and here it has no effect since the mixture is incompressible (see the second footnote in Lamorgese et al [15]). An example of potential ψ k of a conservative force field is reported in the appendix.…”

Section: Entropy Equation In Non-equilibrium Thermodynamicsmentioning

confidence: 99%

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Constitutive Relations of Thermal and Mass Diffusion

Bertei

Lamorgese

Mauri

2020

Journal of Non-Equilibrium Thermodynamics

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Non-equilibrium thermodynamics provides a general framework for the description of mass and thermal diffusion, thereby including also cross-thermal and material diffusion effects, which are generally modeled through the Onsager coupling terms within the constitutive equations relating heat and mass flux to the gradients of temperature and chemical potential. These so-called Soret and Dufour coefficients are not uniquely defined, though, as they can be derived by adopting one of the several constitutive relations satisfying the principles of non-equilibrium thermodynamics. Therefore, mass diffusion induced by a temperature gradient and heat conduction induced by a composition gradient can be implicitly, and unexpectedly, predicted even in the absence of coupling terms. This study presents a critical analysis of different formulations of the constitutive relations, with special focus on regular binary mixtures. It is shown that, among the different formulations presented, the one which adopts the chemical potential gradient at constant temperature as the driving force for mass diffusion allows for the implicit thermo-diffusion effect to be strictly absent while the resulting Dufour effect is negligibly small. Such a formulation must be preferred to the other ones since cross-coupling effects are predicted only if explicitly introduced via Onsager coupling coefficients.

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“…For systems that are not in equilibrium, the force is nonzero and is responsible for the strong convection observed when the mixture is separated, and is not present in the system where the chemical potential is uniform. Like the Gibbs fractal surface model, the diffuse reflection interface model has been widely used in the mixing and delamination of binary mixtures, buoyancy-driven separation of droplets, droplet breakage and coalescence, Marangoni effect and flow of nanometer and microchannels (Lamorgese et al, 2017). Diffuse interface models resolve the steep but smooth transition of an order parameter for a two-phase system at the fluid interface.…”

Section: Phase Filed Model Coupled With Equation Of Statementioning

confidence: 99%

Review on Dynamic Van der Waals Theory in two-phase flow

Tao

Kou

Sun

2017

Adv. Geo-Energ. Res.

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In this paper we review the Dynamic Van der Waals theory, which is a recent developed method to study phase separation and transition process in multiphase flow. Gradient contributions are included in the entropy and energy functions, and it's particularly useful and non-trivial if we consider problems with temperature change. Using this theory, we can simulate that, a droplet in an equilibrium liquid will be attracted to the heated wall(s) which was initially wetted, which is the main cause of the famous hydrodynamic phenomena-Leidonfrost Phenomena. After more than ten years development, this theory has been widely used to study the fluid flow in vaporing and boiling process, e.g. droplet motion. Furthermore, this theory has been combined with phase field model, which could be extended to solid-liquid phase transition. There has also been researches about constructing LBM scheme to extend to the Dynamic Van der Waals theory, using Chapman-Enskog analyze. In all, due to its rigorous thermodynamic derivation, this theory has now become the fundamental theoretical basis in the heated multiphase flow.

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Modeling soft interface dominated systems: A comparison of phase field and Gibbs dividing surface models

Cited by 46 publications

References 362 publications

Mass-conservation-improved phase field methods for turbulent multiphase flow simulation

Mass-conservation-improved phase field methods for turbulent multiphase flow simulation

Constitutive Relations of Thermal and Mass Diffusion

Review on Dynamic Van der Waals Theory in two-phase flow

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