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

Xu, Xianmin; Di, Yana; Yu, Haijun

doi:10.1017/jfm.2018.428

Cited by 58 publications

(39 citation statements)

References 68 publications

(96 reference statements)

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“…To reduce the computational effort, the inclination angle of the plate, see Figure 1, is set to zero and the simulation is already stopped at t = 0.2. As expected for b = O( ) and r = O(1), see [29], the rate of convergence for 0.005 5 × 10 −6 0.2097 Table 6: Position of the contact line for a receding droplet (similar to the sliding droplet case with inclinication angle set to zero) obtained with different values of on a very fine mesh h min = 0.0002 (τ = 0.001, θ = 150 • , r = 0.35, l = 140). The decoupled/nonlinear solution scheme is used.…”

Section: Resultssupporting

confidence: 76%

“…To the best of our knowledge, there is no consent yet which combinations of bulk energy potential and contact line energy are most appropriate from both a physical and numerical point of view. From an analytical point of view, all combinations are reasonable that lead to the correct sharp interface limit, see [29] for results on formal sharp interface asymptotics. Here, the authors use the combination of W poly and ϑ poly .…”

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 97%

“…Common choices for ϑ contain the sine function ϑ sin (ϕ) := 1 2 sin( π 2 ϕ), for example proposed in [7,Sec. 4], or a cubic polynomial ϑ poly (ϕ) = 1 4 (3ϕ−ϕ 3 ), for example proposed in [29]. An alternative is given in [34].…”

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 99%

“…However, this topic is subject to future work. Further note, that using the notation from [29] we are in the setting L d = O( ), and V s = O(1).…”

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 99%

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Comparison of energy stable simulation of moving contact line problems using a thermodynamically consistent Cahn–Hilliard Navier–Stokes model

Bonart

Kahle

Repke

2019

Journal of Computational Physics

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Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. To model this situation, we use a phase field approach. The bulk model is given by the thermodynamically consistent Cahn-Hilliard Navier-Stokes model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22 (3), 2012]. To model the contact line dynamics we apply the generalized Navier boundary condition for the fluid and the dynamically advected boundary contact angle condition for the phase field as derived in [Qian et al., J. Fluid Mech., 564, 2006]. In recent years several schemes were proposed to solve this model numerically. While they widely differ in terms of complexity, they all fulfill certain basic properties when it comes to thermodynamic consistency. However, an accurate comparison of the influence of the schemes on the moving contact line is rarely found. Therefore, we thoughtfully compare the quality of the numerical results obtained with three different schemes and two different bulk energy potentials. Especially, we discuss the influence of the different schemes on the apparent contact angles of a sliding droplet.

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Section: Resultssupporting

confidence: 76%

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 97%

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 99%

“…However, this topic is subject to future work. Further note, that using the notation from [29] we are in the setting L d = O( ), and V s = O(1).…”

Section: Remark 1 (Nonlinear Density and Viscosity)mentioning

confidence: 99%

See 2 more Smart Citations

Comparison of energy stable simulation of moving contact line problems using a thermodynamically consistent Cahn–Hilliard Navier–Stokes model

Bonart

Kahle

Repke

2019

Journal of Computational Physics

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“…Furthermore, A has a linear dependence on the value of γ. It was showed by Magaletti et al [37] and Xu et al [46] that the phase-field Cahn-Hilliard-Navier-Stokes model for binary fluids has a fast convergence with respect to ε when the phenomenological mobility γ ∼ O(ε 2 ). When coupled with hydrodynamics, what is a proper choice for the mobility γ in the Allen-Cahn model is an interesting question.…”

Section: )mentioning

confidence: 99%

Energy-stable second-order linear schemes for the Allen–Cahn phase-field equation

Wang

2019

Communications in Mathematical Sciences

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Phase-field model is a powerful mathematical tool to study the dynamics of interface and morphology changes in fluid mechanics and material sciences. However, numerically solving a phase field model for a real problem is a challenge task due to the non-convexity of the bulk energy and the small interface thickness parameter in the equation. In this paper, we propose two stabilized second order semi-implicit linear schemes for the Allen-Cahn phase-field equation based on backward differentiation formula and Crank-Nicolson method, respectively. In both schemes, the nonlinear bulk force is treated explicitly with two second-order stabilization terms, which make the schemes unconditional energy stable and numerically efficient. By using a known result of the spectrum estimate of the linearized Allen-Cahn operator and some regularity estimates of the exact solution, we obtain an optimal second order convergence in time with a prefactor depending on the inverse of the characteristic interface thickness only in some lower polynomial order. Both 2-dimensional and 3-dimensional numerical results are presented to verify the accuracy and efficiency of proposed schemes.

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A dual resolution phase‐field solver for wetting of viscoelastic droplets

Bazesefidpar

Brandt

Tammisola

2022

Numerical Methods in Fluids

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We present a new and efficient phase‐field solver for viscoelastic fluids with moving contact line based on a dual‐resolution strategy. The interface between two immiscible fluids is tracked by using the Cahn‐Hilliard phase‐field model, and the viscoelasticity incorporated into the phase‐field framework. The main challenge of this approach is to have enough resolution at the interface to approach the sharp‐interface methods. The method presented here addresses this problem by solving the phase field variable on a mesh twice as fine as that used for the velocities, pressure, and polymer‐stress constitutive equations. The method is based on second‐order finite differences for the discretization of the fully coupled Navier–Stokes, polymeric constitutive, and Cahn–Hilliard equations, and it is implemented in a 2D pencil‐like domain decomposition to benefit from existing highly scalable parallel algorithms. An FFT‐based solver is used for the Helmholtz and Poisson equations with different global sizes. A splitting method is used to impose the dynamic contact angle boundary conditions in the case of large density and viscosity ratios. The implementation is validated against experimental data and previous numerical studies in 2D and 3D. The results indicate that the dual‐resolution approach produces nearly identical results while saving computational time for both Newtonian and viscoelastic flows in 3D.

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

Cited by 58 publications

References 68 publications

Comparison of energy stable simulation of moving contact line problems using a thermodynamically consistent Cahn–Hilliard Navier–Stokes model

Comparison of energy stable simulation of moving contact line problems using a thermodynamically consistent Cahn–Hilliard Navier–Stokes model

Energy-stable second-order linear schemes for the Allen–Cahn phase-field equation

A dual resolution phase‐field solver for wetting of viscoelastic droplets

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