scholarly journals (In)compressibility and parameter identification in phase field models for capillary flows

2017 ◽  
Vol 44 (2) ◽  
pp. 189-214 ◽  
Author(s):  
M. Dehsara ◽  
H. Fu ◽  
S.Dj Mesarovic ◽  
D.P. Sekulic ◽  
M. Krivilyov
Keyword(s):  
Phase Field ◽  
Triple Line ◽  
Slip Boundary Condition ◽  
Diffuse Interface ◽  
Slip Boundary ◽  
Phase Field Models ◽  
Capillary Flows ◽  
Wide Range ◽  
Mobility Parameter ◽  
Wetting Process

Phase field (diffuse interface) models accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. We consider two commonly used classes of phase field models: the compositionally compressible (CC) model with compressibility limited to the fluid mix within the diffuse interface, and the incompressible (IC) model. First, we show that the CC model applied to fluids with dissimilar mass densities exhibits the computational instability leading to the breakup of the triple line. We provide a qualitative physical explanation of this instability and argue that the compositional compressibility within the diffuse interface is inconsistent with the global incompressible flow. Second, we derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. Third, we benchmark the IC model against sharp interface theory and experimental kinetics. The triple line kinetics is well represented by the triple line mobility parameter. Finally, we investigate the effects of the bulk phase field diffusional mobility parameter on the kinetics of the wetting process and find that within a wide range of magnitudes the bulk mobility does not affect the flow.

scholarly journals Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

2018 ◽  
Vol 849 ◽  
pp. 805-833 ◽  
Author(s):  
Xianmin Xu ◽  
Yana Di ◽  
Haijun Yu
Keyword(s):  
Boundary Condition ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Slip Boundary Condition ◽  
Sharp Interface ◽  
Navier Slip ◽  
Slip Boundary ◽  
Moving Contact ◽  
Moving Contact Lines

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for binary fluids with moving contact lines are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter on the boundary condition are considered. In asymptotic analysis, we consider both the cases that the mobility number is proportional to the Cahn number and the square of the Cahn number, and derive the sharp-interface limits for several set-ups of the boundary relaxation parameter. It is shown that the sharp-interface limit of the phase-field model is the standard two-phase incompressible Navier–Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters.

scholarly journals Calibration of material parameters based on 180$$^\circ $$ and 90$$^\circ $$ ferroelectric domain wall properties in Ginzburg–Landau–Devonshire phase field models

2020 ◽  
Vol 90 (12) ◽  
pp. 2755-2774
Author(s):  
Moritz Flaschel ◽  
Laura De Lorenzis
Keyword(s):  
Domain Wall ◽  
Phase Field ◽  
Domain Walls ◽  
Ferroelectric Domain ◽  
Ginzburg Landau ◽  
Closed Form Solutions ◽  
Material Parameters ◽  
Phase Field Models ◽  
Mobility Parameter ◽  
The Relationship

Abstract Ferroelectric phase field models based on the Ginzburg–Landau–Devonshire theory are characterized by a large number of material parameters with problematic physical interpretation. In this study, we systematically address the relationship between these parameters and the main properties of ferroelectric domain walls. A variational approach is used to derive closed form solutions for the polarization fields at the phase transition regions as well as for the propagation velocities of the domain walls. Introducing a modified set of material parameters, which appropriately scales different contributions to the free energy, we are able to accurately calibrate these parameters based on domain wall thickness and energy of both 180$$^\circ $$ ∘ and 90$$^\circ $$ ∘ domain walls. Moreover, the mobility parameter appearing in the Ginzburg–Landau evolution equation can be accurately calibrated based on the propagation velocity of the domain walls.

Unifying binary fluid diffuse-interface models in the sharp-interface limit

2013 ◽  
Vol 736 ◽  
pp. 5-43 ◽  
Author(s):  
David N. Sibley ◽  
Andreas Nold ◽  
Serafim Kalliadasis
Keyword(s):  
Phase Field ◽  
Outer Region ◽  
Mobility Model ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Binary Fluids ◽  
Sharp Interface Limit ◽  
Binary Fluid ◽  
Phase Field Models

AbstractRecent results published by Gugenberger et al. on surface diffusion (Phys. Rev. E, vol. 78, 2008, 016703), show that the sharp-interface limit of the phase field models often adopted in the literature fails to produce the appropriate boundary conditions. With this knowledge, we consider the sharp-interface limit of phase field models for binary fluids, obtained carefully, where hydrodynamic equations are coupled to phase field evolution based on Cahn–Hilliard or Allen–Cahn theories, in a variety of guises, and unify and contrast their forms and behaviours in the sharp-interface limit. In particular, a tensorial mobility model is analysed, which allows the bulk fluids in the outer region to satisfy classical Navier–Stokes type equations to all orders in the Cahn number.

scholarly journals Improved phase-field models of melting and dissolution in multi-component flows

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200508
Author(s):  
Eric W. Hester ◽  
Louis-Alexandre Couston ◽  
Benjamin Favier ◽  
Keaton J. Burns ◽  
Geoffrey M. Vasil
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Second Order ◽  
Diffuse Interface ◽  
Benchmark Problems ◽  
First Order ◽  
Phase Field Models ◽  
Arbitrary Geometries ◽  
Second Order Convergence ◽  
Fluid Solid Interaction

We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretizations that track the moving phase boundary. However, standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework, we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid–solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.

scholarly journals High-resolution simulations of the flow around an impulsively started cylinder using vortex methods

1995 ◽  
Vol 296 ◽  
pp. 1-38 ◽  
Author(s):  
P. Koumoutsakos ◽  
A. Leonard
Keyword(s):  
High Resolution ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
The Body ◽  
Navier Stokes ◽  
Rectilinear Motion ◽  
Vortex Methods ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Wide Range

The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier–Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot–Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented high-resolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.

Development of an Anti-Trapping Current for Phase Field Models Using Arbitrary CALPHAD Thermodynamics

2018 ◽  
Vol 941 ◽  
pp. 2337-2342
Author(s):  
Andrew M. Mullis ◽  
Peter C. Bollada ◽  
Peter K. Jimack
Keyword(s):  
Phase Field ◽  
Lattice Models ◽  
Diffuse Interface ◽  
Solidification Velocity ◽  
Solute Partitioning ◽  
Interface Width ◽  
Phase Field Models ◽  
Growth Metrics ◽  
Ideal Solutions ◽  
Tip Radius

Unless corrected by so called anti-trapping currents, phase field models of solidification display a dependence upon the diffuse interface width, δ, used in the simulation. This is most commonly manifest as a reduction in solute partitioning, which is both growth velocity and interface width dependent, resulting in a serious impediment to quantitative simulation. However, such anti-trapping currents are often restricted to very simple materials thermodynamics, appropriate only to dilute ideal solutions. Here we propose a form of the anti-trapping current which can be implemented for arbitrary thermodynamics, including both Redlich-Kister solution phases and sub-lattice models for intermetallic growth. The effect of the new anti-trapping current is illustrated with respect to Pb dendrites growing from a Pb-Sn melt containing either 25% or 30% Sn. The new anti-trapping current is shown to render the solutions independent of the diffuse interface width both with regard to solute partitioning and other growth metrics such as solidification velocity and dendrite tip radius.

Rarefied transitional flow through diverging nano and microchannels: A TRT lattice Boltzmann study

2018 ◽  
Vol 29 (12) ◽  
pp. 1850117 ◽  
Author(s):  
Soroush Fallah Kharmiani ◽  
Ehsan Roohi
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Pressure Ratio ◽  
Slip Boundary Condition ◽  
Divergence Angle ◽  
Slip Boundary ◽  
Wide Range ◽  
Flow Through ◽  
Slip Coefficients ◽  
Bounce Back

Rarefied isothermal gaseous flow through long diverging micro and nanochannels is investigated in this paper using the two-relaxation-time (TRT) lattice Boltzmann method (LBM). The simulations are performed over a wide range of Knudsen number, pressure ratio, and divergence angle. The Bounce-Back Specular Reflection (BSR) slip boundary condition is applied and is connected to the second-order slip boundary condition coefficients by means of the antisymmetric relaxation time and the bounce-back portion parameter. The effects of the slip coefficients on the wall and centerline Mach numbers, as well as the mass flow rates, are investigated. The numerical results are validated with those of the direct simulation Monte Carlo (DSMC) reported in the literature. The results show that the local pressure distributions are almost independent of the slip coefficients with excellent agreements with DSMC over a wide range of the divergence angle. Our results demonstrate that there is a specific divergence angle at each pressure ratio where the local unbounded Knudsen and, as a result, Mach numbers remain constant along the channel. This observation is almost independent of the slip coefficients, and the underlying reason is that the pressure drop is compensated by an increase in the channel area.

scholarly journals Combining phase field approach and homogenization methods for modelling phase transformation in elastoplastic media

2009 ◽  
pp. 485-523
Author(s):  
Kais Ammar ◽  
Benoît Appolaire ◽  
Georges Cailletaud ◽  
Samuel Forest
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Diffuse Interface ◽  
Field Approach ◽  
Phase Field Models ◽  
Nonlinear Mechanical ◽  
Finite Element Calculations ◽  
Homogenization Methods ◽  
Elastoplastic Media

A general constitutive framework is proposed to incorporate linear and nonlinear mechanical behaviour laws into a standard phase field model. In the diffuse interface region where both phases coexist, two mixture rules for strain and stress are introduced, which are based on the Voigt/Taylor and Reuss/Sachs well-known homogenization schemes and compared to the commonly used mixture rules in phase field models. Finite element calculations have been performed considering an elastoplastic precipitate growing in an elastic matrix in order to investigate the plastic accommodation processes.

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