scholarly journals Fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities

2020 ◽  
Vol 83 ◽  
pp. 614-639 ◽  
Author(s):  
Guangpu Zhu ◽  
Huangxin Chen ◽  
Aifen Li ◽  
Shuyu Sun ◽  
Jun Yao
Keyword(s):  
Contact Line ◽  
Phase Field ◽  
Discrete Energy ◽  
Line Model ◽  
Fully Discrete ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Energy Stable ◽  
Energy Stable Scheme ◽  
Stable Scheme

scholarly journals Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants

2019 ◽  
Vol 879 ◽  
pp. 327-359 ◽  
Author(s):  
Guangpu Zhu ◽  
Jisheng Kou ◽  
Bowen Yao ◽  
Yu-shu Wu ◽  
Jun Yao ◽  
...  
Keyword(s):  
Contact Line ◽  
Phase Field ◽  
Surfactant Adsorption ◽  
Line Model ◽  
Droplet Dynamics ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Soluble Surfactants ◽  
Flow States ◽  
Contact Line Dynamics

Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a challenging task to model and simulate the moving contact line dynamics with soluble surfactants. In this work, we present a derivation of the phase-field moving contact line model with soluble surfactants through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle. The derived thermodynamically consistent model consists of two Cahn–Hilliard type of equations governing the evolution of interface and surfactant concentration, the incompressible Navier–Stokes equations and the generalized Navier boundary condition for the moving contact line. With chemical potentials derived from the free energy functional, we analytically obtain certain equilibrium properties of surfactant adsorption, including equilibrium profiles for phase-field variables, the Langmuir isotherm and the equilibrium equation of state. A classical droplet spread case is used to numerically validate the moving contact line model and equilibrium properties of surfactant adsorption. The influence of surfactants on the contact line dynamics observed in our simulations is consistent with the results obtained using sharp interface models. Using the proposed model, we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface. It is observed that droplets will form three typical flow states as a result of different surfactant bulk concentrations and defect strengths, specifically the coalescence mode, the non-coalescence mode and the detachment mode. In addition, a phase diagram for the three flow states is presented. Finally, we study the unbalanced Young stress acting on triple-phase contact points. The unbalanced Young stress could be a driving or resistance force, which is determined by the critical defect strength.

scholarly journals A phase-field moving contact line model with soluble surfactants

2020 ◽  
Vol 405 ◽  
pp. 109170 ◽  
Author(s):  
Guangpu Zhu ◽  
Jisheng Kou ◽  
Jun Yao ◽  
Aifen Li ◽  
Shuyu Sun
Keyword(s):  
Contact Line ◽  
Phase Field ◽  
Line Model ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Soluble Surfactants

A phase-field-based lattice Boltzmann method for moving contact line problems on curved stationary boundaries in two dimensions

2019 ◽  
Vol 30 (06) ◽  
pp. 1950044
Author(s):  
Weifeng Zhao
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Two Dimensions ◽  
Curved Boundaries ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method

In this work, we propose a phase-field-based lattice Boltzmann method to simulate moving contact line (MCL) problems on curved boundaries. The key point of this method is to implement the boundary conditions on curved solid boundaries. Specifically, we use our recently proposed single-node scheme for the no-slip boundary condition and a new scheme is constructed to deal with the wetting boundary conditions (WBCs). In particular, three kinds of WBCs are implemented: two wetting conditions derived from the wall free energy and a characteristic MCL model based on geometry considerations. The method is validated with several MCL problems and numerical results show that the proposed method has utility for all the three WBCs on both straight and curved boundaries.

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