An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

Shen, Lingyue; Huang, Huaxiong; Lin, Ping; Song, Zilong; Xu, Shixin

doi:10.1016/j.jcp.2019.109179

Cited by 13 publications

(11 citation statements)

References 77 publications

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“…which is proposed in [27] from a wall functional. Here, g w (φ) is an interpolation function satisfying g w (±1) = ±1 and g w (±1) = 0, and we choose g w (φ) = sin π 2 φ , like [51,6,25,52]. Another choice of g w (φ) is the Hermite polynomial, i.e., g w (φ) = 1 2 φ(3 − φ 2 ), used, e.g., in [27,14,67,61].…”

Section: Two-phase Modelmentioning

confidence: 99%

“…Such an additional effect can drive the contact line to move even though the no-slip boundary condition is assigned [49,27]. One commonly used procedure to derive the contact angle boundary conditions for the Phase-Field models is in the context of wall energy relaxation [27,45,14,6,52], where the wall energy is minimized by the L 2 gradient flow. Such a procedure has been extended to include surfactant [68], contact angle hysteresis [61], three fluid phases [53,51,67], and N (N 2) fluid phases [15].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

Huang,

Lin,

Ardekani

2021

Preprint

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In the present work, a general formulation is proposed to implement the contact angle boundary conditions for the second-order Phase-Field models, which is applicable to N -phase (N 2) moving contact line problems. To remedy the issue of mass change due to the contact angle boundary condition, a Lagrange multiplier is added to the original second-order Phase-Field models, which is determined by the consistent and conservative volume distribution algorithm so that the summation of the order parameters and the consistency of reduction are not influenced. To physically couple the proposed formulation to the hydrodynamics, especially for large-density-ratio problems, the consistent formulation is employed. The reduction-consistent conservative Allen-Cahn models are chosen as examples to illustrate the application of the proposed formulation. The numerical scheme that preserves the consistency and conservation of the proposed formulation is employed to demonstrate its effectiveness. Results produced by the proposed formulation are in good agreement with the exact and/or asymptotic solutions. The proposed method captures complex dynamics of moving contact line problems having large density ratios.

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Section: Two-phase Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

Huang,

Lin,

Ardekani

2021

Preprint

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“…The energy dissipative law [7,30,22] states that without external force acting on the system, the changing rate of total energy equals the dissipation d dt E total = −∆.…”

Section: Model Derivationmentioning

confidence: 99%

“…In this paper, a thermal-dynamical consistent diffusive model is first proposed by using energy variational method [22], which starts from two functionals for the total energy and dissipation, together with the kinematic equations based on physical laws of conservation. The key is to modify the diffusion coefficient as a function of φ and interface permeability K. The restricted diffusion only means that the changing rate of energy near the interface follows a specific dissipation rate functional.…”

Section: Introductionmentioning

confidence: 99%

A phase field model for mass transport with semi-permeable interfaces

Qin,

Huang,

Zhu

et al. 2021

Preprint

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In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using energy variation method. We consider a restricted diffusion problem where the flux across the interface depends on its conductance and the difference of the concentration on each side. The diffusive interface phase-field framework used in here has several advantages over the sharp interface method. First of all, explicit tracking of the interface is no longer necessary. Secondly, the interfacial condition can be incorporated with a variable diffusion coefficient. A detailed asymptotic analysis confirms the diffusive interface model converges to the existing sharp interface model as the interface thickness goes to zero. A decoupled energy stable numerical scheme is developed to solve this system efficiently. Numerical simulations first illustrate the consistency of theoretical results on the sharp interface limit. Then a convergence study and energy decay test are conducted to ensure the efficiency and stability of the numerical scheme. To illustrate the effectiveness of our phase-field approach, several examples are provided, including a study of a two-phase mass transfer problem where drops with deformable interfaces are suspended in a moving fluid.

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“…This involves considering a moving contact line problem. The first goal of this paper thus is to derive a thermodynamically consistent phase-field model for vesicles' motion and shape transformation in a closed spatial domain by using an energy variational method [61,72,74,27]. All the physics taken into consideration are introduced through definitions of energy functionals and dissipation functional, together with the kinematic assumptions of laws of conservation.…”

Section: Introductionmentioning

confidence: 99%

An Energy Stable $C^0$ Finite Element Scheme for A Phase-Field Model of Vesicle Motion and Deformation

Shen¹,

Xu²,

Lin³

et al. 2022

SIAM J. Sci. Comput.

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A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between vesicles and the wall of the fluid domain. A second-order accurate in both space and time C 0 finite element method is proposed to solve the model governing equations. Various numerical tests confirm the convergence, energy stability, and conservation of mass and surface area of cells of the proposed scheme. Vesicles with different mechanical properties are also used to explain the pathological risk for patients with sickle cell disease.

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An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

Cited by 13 publications

References 77 publications

Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

A phase field model for mass transport with semi-permeable interfaces

An Energy Stable $C^0$ Finite Element Scheme for A Phase-Field Model of Vesicle Motion and Deformation

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