Sharp-interface limit of the Cahn–Hilliard model for moving contact lines

By Pengtao Yue, Chunfeng Zhou, James J. Feng. Journal of Fluid Mechanics, 2010

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Pore-Scale Simulations of Gas Displacing Liquid in a Homogeneous Pore Network Using the Lattice Boltzmann Method (2013, methodology): “…the volume-of-fluid (VOF) (Hirt and Nichols 1981; Rider and Kothe 1998; Gueyffier et al. 1999), the level set (LS) (Osher and Sethian 1988; Sussman et al. 1998; Osher and Fedkiw 2003), and the phase-field (PF) methods (Anderson and McFadden 1998; Jacqmin 2000; Yue et al. 2010) are commonly used.”
The sharp-interface limit of the Cahn–Hilliard/Navier–Stokes model for binary fluids (2013, background): “…by the incompressible Navier–Stokes equations coupled to the phase field by the surface tension term proportional to ∇Φ (see, e.g., Jacqmin 2000; Yue et al. 2010), leading to the complete system ∇ ·u= 0, (2.4a) ∂u ∂t + u ·∇u=−∇p+ 1 Re ∇2u+ 3 2 √ 2 1 WeCn (Φ3 −Φ − Cn2∇2Φ)∇Φ, (2.4b) ∂Φ ∂t + u…”
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer (2015, background): “liquid droplet in a porous media with wetting boundaries. Some numerical results can be found in Fig. 13. Besides the linear form of the surface energy density, some other forms can be found in Refs. [331, 332, 333]. For example, a quadratic form surface energy density and a cubic form surface energ”