Three-dimensional phase field modeling of inhomogeneous gas-liquid systems using the PeTS equation of state

Diewald, Felix; Heier, Michaela; Horsch, Martin; Kuhn, Charlotte; Langenbach, Kai; Hasse, Hans; Müller, Ralf

doi:10.1063/1.5035495

Cited by 16 publications

(21 citation statements)

References 60 publications

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“…The Phase Field (PF) model used in this work couples the Navier-Stokes equations with the static PF model described in [1]. The coupling is done via the capillary stress tensor described by Korteweg in 1901, see e.g.…”

Section: Phase Field Modelmentioning

confidence: 99%

“…The free energy per particle a = a(ρ, T ) is taken from the PeTS equation of state [3] and the constant κ is set to κ = 2.7334 [1]. The free energy per particle a = a(ρ, T ) is taken from the PeTS equation of state [3] and the constant κ is set to κ = 2.7334 [1].…”

Section: Phase Field Modelmentioning

confidence: 99%

“…The temperature is set to T = 0.7, at which the surface tension between the liquid and the vapor phase is γ lv = 0.581 [1]. A droplet is initialized with a radius of r ini = 5 with its center h ini = 12.5 above the bottom of the structured surface.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…, trace tr, dyadic product ⊗, and viscosity η. The free energy per particle a = a(ρ, T ) is taken from the PeTS equation of state [3] and the constant κ is set to κ = 2.7334 [1]. The Lennard-Jones dimensions are used for all physical quantities.…”

Section: Phase Field Modelmentioning

confidence: 99%

See 3 more Smart Citations

A Navier‐Stokes‐Korteweg Model for Dynamic Wetting based on the PeTS Equation of State

Diewald

Heier

Lautenschläger

et al. 2019

Proc Appl Math and Mech

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Dynamic wetting of component surfaces can be investigated by finite element phase field simulations. Often these models use a double-well potential or the van der Waals equation to define the local part of the free energy density at a point of the computational domain. In order to give the present model a stronger physical background the molecular dynamics based perturbed Lennard-Jones truncated and shifted (PeTS) equation of state is used instead. This results in phase field liquid-vapor interfaces that agree with the physical density gradient between the two phases. In order to investigate dynamic scenarios, the phase field description is coupled to the compressible Navier-Stokes equations. This coupling requires a constitutive equation that complies with the surface tension of the liquid-vapor interface resulting from the PeTS equation of state and is comparable to the so-called Korteweg tensor. Phase Field ModelThe Phase Field (PF) model used in this work couples the Navier-Stokes equations with the static PF model described in [1]. The coupling is done via the capillary stress tensor described by Korteweg in 1901, see e.g. [2]. Therefore, the model can be classified as a Navier-Stokes-Korteweg model. A central component of Navier-Stokes-Korteweg models is the equation of state that formulates the free energy density of the bulk phases as well as the transition zone between them. Instead of applying the commonly used van der Waals equation of state, the present model utilizes the PeTS equation of state [3] which provides an accurate energy density formulation for the Lennard-Jones truncated and shifted fluid.For a domain B that is bounded by ∂B the mass and momentum balanceṡare solved for particle density ρ( x, t) and velocity v( x, t). Position in space and time and gravitational acceleration are denoted by x, t and g. The material time derivative is denote by( ·) = d(·) dt . The boundary conditions read v = 0 on ∂B ,The outer normal to the boundary and the part of ∂B that is given by a solid surface are given by n and ∂B s . With ϕ = ρ−ρ ′′ ρ ′ −ρ ′′ , where ρ ′ and ρ ′′ are the liquid and vapor bulk densities, (4) ensures a specified contact angle Θ for a droplet that is in contact with ∂B s , see also [4,5]. The solid-liquid and solid-vapor surface tensions are denoted by γ sl and γ sv . The temperature T is assumed to be constant (T = const.). The stress tensor σ readsand ∇ s (·) = 1 2 (∇(·) + (∇(·)) T ), trace tr, dyadic product ⊗, and viscosity η. The free energy per particle a = a(ρ, T ) is taken from the PeTS equation of state [3] and the constant κ is set to κ = 2.7334 [1]. The Lennard-Jones dimensions are used for all physical quantities. They are nondimensionalized by using the convention σ LJ = ε LJ = M LJ = 1 for the size parameter, the energy parameter, and the mass per particle. Second derivatives in the weak form of the momentum balance (2) are avoided by using the chemical potential µ as an additional degree of freedom. For the finite element implementation, v is discretized with quadratic s...

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Section: Phase Field Modelmentioning

confidence: 99%

Section: Phase Field Modelmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Phase Field Modelmentioning

confidence: 99%

See 2 more Smart Citations

A Navier‐Stokes‐Korteweg Model for Dynamic Wetting based on the PeTS Equation of State

Diewald

Heier

Lautenschläger

et al. 2019

Proc Appl Math and Mech

Self Cite

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“…The lower computational effort of the PF simulations compared to MD simulations enables the model to simulate wetting scenarios on the microscale. The present phase field (PF) model represents a coupling of the static PF model described in [1] with the compressible Navier-Stokes equations, cf. [2].…”

mentioning

confidence: 99%

Phase Field Simulations of Wetting Based on Molecular Simulations

Diewald

Heier

Lautenschläger

et al. 2021

Proc Appl Math and Mech

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Manufacturing techniques that can produce surfaces with a defined microstructure are in the focus of current research efforts. The ability to manufacture such surfaces gives rise to the need for numerical models that can predict the wetting properties of a given microstructure and can help to optimize these surfaces with respect to certain wetting properties. The present phase field (PF) model for wetting is linked to molecular dynamics (MD) simulations by the usage of the MD based perturbed Lennard‐Jones truncated and shifted (PeTS) equation of state as well as a MD based viscosity correlation. The lower computational effort of the PF simulations compared to MD simulations enables the model to simulate wetting scenarios on the microscale.

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Full Field Model Describing Phase Front Propagation, Transformation Strains, Chemical Partitioning, and Diffusion in Solid–Solid Phase Transformations

Pohjonen

2023

Advcd Theory and Sims

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A novel mathematical formulation is presented for describing growth of phase in solid-to-solid phase transformations and it is applied for describing austenite to ferrite transformation. The formulation includes the effects of transformation eigenstrains, the local strains, as well as partitioning and diffusion. In the current approach the phase front is modeled as diffuse field, and its propagation is shown to be described by the advection equation, which reduces to the level-set equation when the transformation proceeds only to the interface normal direction. The propagation is considered as thermally activated process in the same way as in chemical reaction kinetics. In addition, connection to the Allen-Cahn equation is made. Numerical tests are conducted to check the mathematical model validity and to compare the current approach to sharp interface partitioning and diffusion model. The model operation is tested in isotropic 2D plane strain condition for austenite to ferrite transformation, where the transformation produces isotropic expansion, and also for austenite to bainite transformation, where the transformation causes invariant plane strain condition. Growth into surrounding isotropic austenite, as well as growth of the phase which has nucleated on a grain boundary are tested for both ferrite and bainite formation.

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Three-dimensional phase field modeling of inhomogeneous gas-liquid systems using the PeTS equation of state

Cited by 16 publications

References 60 publications

A Navier‐Stokes‐Korteweg Model for Dynamic Wetting based on the PeTS Equation of State

A Navier‐Stokes‐Korteweg Model for Dynamic Wetting based on the PeTS Equation of State

Phase Field Simulations of Wetting Based on Molecular Simulations

Full Field Model Describing Phase Front Propagation, Transformation Strains, Chemical Partitioning, and Diffusion in Solid–Solid Phase Transformations

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