Displacement of a two-dimensional immiscible droplet in a channel

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Lattice Boltzmann methods for multiphase flow and phase-change heat transfer (2015, background): “[279, 280] have extended Martys and Chen’s ρ − based fluid-solid interaction to the D2Q9 lattice model.”
Lattice Boltzmann method for microfluidics: models and applications (2011, methodology): “8 Simulated concentration patterns under an applied electrical field in a microchannel with heterogeneous surface potential (Kang et al. 2008). Reprinted with kind permission of Springer Science and Business Media 18 Microfluid Nanofluid (2011) 10:1–28”
A level-set approach for simulations of flows with multiple moving contact lines with hysteresis (2005, background): “[17]) do not track the contact angle in time.”
A lattice Boltzmann model for multiphase flows with large density ratio (2006, unknown): “The pressure jump is plotted as a function of the curvature in Fig. 2. It can be easily observed that like the work of Kang et al. [ 13 ], the relationship is linear as the Laplace law.”
Lattice‐Boltzmann simulation of two‐phase flow in porous media (2004, methodology): “Note that the fluid-solid interaction force Ff s k exists only on the fluid-solid interface, so it does not affect the macroscopic fluid equations [Kang et al., 2002].”