Efficient energy stable numerical schemes for a phase field moving contact line model

Shen, Jie; Yang, Xiaofeng; Yu, Haijun

doi:10.1016/j.jcp.2014.12.046

Cited by 111 publications

(104 citation statements)

References 45 publications

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“…The results are qualitatively similar to those reported in the literature (see [42,43] for example and the references therein).…”

Section: Droplet Spreadingsupporting

confidence: 91%

“…Observe that this choice of surface potential is not exactly the same as the one in [12,16,17,26,43,44] where a cubic surface potential is considered (and thus assumption (1.5) is not satisfied). As explained above, our construction retains the main qualitative properties required for f s so that it gives satisfactory numerical results (see Sect.…”

Section: Presentation Of the System Of Equationsmentioning

confidence: 99%

“…To our knowledge, there is only few available contributions concerning the discretization of the Cahn−Hilliard/Navier−Stokes phase field model with dynamic boundary conditions. From a computational point of view, some recent works propose numerical schemes for such kind of models and give various simulations (see [12,16,17,32,43,44] and the references therein), but without precise mathematical analysis. We also mention [42] which is concerned with a slightly different model but gives a thorough stability analysis for a conforming finite element discretization.…”

Section: Introductionmentioning

confidence: 99%

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A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions

Boyer

Nabet

2017

ESAIM: M2AN

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Abstract. In this paper we propose a "Discrete Duality Finite Volume" method (DDFV for short) for the diffuse interface modelling of incompressible two-phase flows. This numerical method is, conservative, robust and is able to handle general geometries and meshes. The model we study couples the Cahn−Hilliard equation and the unsteady Stokes equation and is endowed with particular nonlinear boundary conditions called dynamic boundary conditions. To implement the scheme for this model we have to derive new discrete consistent DDFV operators that allows an energy stable coupling between both discrete equations. We are thus able to obtain the existence of a family of solutions satisfying a suitable energy inequality, even in the case where a first order time-splitting method between the two subsystems is used. We illustrate various properties of such a model with some numerical results.Mathematics Subject Classification. 35K55, 65M08, 65M12, 76D07, 76M12, 76T10.

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“…The results are qualitatively similar to those reported in the literature (see [42,43] for example and the references therein).…”

Section: Droplet Spreadingsupporting

confidence: 91%

Section: Presentation Of the System Of Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions

Boyer

Nabet

2017

ESAIM: M2AN

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“…In the authors consider the viscous Cahn–Hilliard equations coupled with the Navier–Stokes equations and endowed with different boundary conditions and they prove the well‐posedness of the model and provide the numerical analysis for some semi‐discrete and fully discrete schemes. For the numerical studies of the CHNS model with different types of dynamic boundary conditions, we cite .…”

Section: Setting Of the Problemmentioning

confidence: 99%

“…We propose an energy stable numerical scheme for . As in , our method requires that the second derivative of F ( ϕ ) to be bounded, which is not the case for the Ginzburg–Landau potential. It was proved in that as we are only interested in ϕ ∈ [−1, 1], we can replace the Ginzburg–Landau potential by a truncated version that has a quadratic growth at infinity, more exactly we consider the following potential:

\overset{true^}{F} (ϕ) = \frac{1}{4} \{\begin{matrix} left \\ 4 {((), ϕ + 1)}^{2}, & on ϕ < - 1, \\ {((), ϕ^{2} - 1)}^{2}, & on - 1 \leq ϕ \leq 1, \\ 4 {((), ϕ - 1)}^{2}, & on ϕ > 1, \end{matrix}

and

\overset{true^}{f} (ϕ) = {\overset{F}{true}}^{'} (ϕ)

.…”

Section: The Time‐discretization Schemementioning

confidence: 99%

Energy stable numerical scheme for the viscous Cahn–Hilliard–Navier–Stokes equations with moving contact line

Cherfils

Petcu

2019

Numerical Methods Partial

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In the present article we study the numerics of the viscous Cahn–Hilliard–Navier–Stokes model, endowed with dynamic boundary conditions which allow us to take into account the interaction between the fluids interface and the moving walls of the physical domain. In what follows, we propose an energy stable temporal scheme for the problem and we prove the stability and the unconditional solvability of the discretization proposed. We also propose a fully discrete scheme for which we prove the stability and the unconditional solvability. Numerical simulations are presented to illustrate the theoretical results.

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Wetting Effect on Patterned Substrates

Wang

Nestler

2023

Advanced Materials

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A droplet deposited on a solid substrate leads to the wetting phenomenon. A natural observation is the lotus effect, known for its superhydrophobicity. This special feature is engendered by the structured microstructure of the lotus leaf, namely, surface heterogeneity, as explained by the quintessential Cassie-Wenzel theory (CWT). In this work, recent designs of functional substrates are overviewed based on the CWT via manipulating the contact area between the liquid and the solid substrate as well as the intrinsic Young's contact angle. Moreover, the limitation of the CWT is discussed. When the droplet size is comparable to the surface heterogeneity, anisotropic wetting morphology often appears, which is beyond the scope of the Cassie-Wenzel work. In this case, several recent studies addressing the anisotropic wetting effect on chemically and mechanically patterned substrates are elucidated. Surface designs for anisotropic wetting morphologies are summarized with respect to the shape and the arrangement of the surface heterogeneity, the droplet volume, the deposition position of the droplet, as well as the mean curvature of the surface heterogeneity. A thermodynamic interpretation for the wetting effect and the corresponding open questions are presented at the end.

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Efficient energy stable numerical schemes for a phase field moving contact line model

Cited by 111 publications

References 45 publications

A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions

A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions

Energy stable numerical scheme for the viscous Cahn–Hilliard–Navier–Stokes equations with moving contact line

Wetting Effect on Patterned Substrates

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