A study of wall boundary conditions in pseudopotential lattice Boltzmann models

The effect of fluid–solid interactions on the hydrodynamics of non-ideal fluids and wettability of surfaces is investigated. We integrate the interaction forces, simulated by pseudopotentials, into two on-site boundary conditions: standard bounce-back (SBB) and Zou and He (ZH) [12] to determine the distribution functions of the boundary nodes. Three different interaction forces are tested: pseudopotential-based interaction (ψ), modified pseudopotential-based interaction (mψ), and a ZH-based interaction, which is proposed by this study based on the ZH method. Therefore, the schemes are ψ-SBB, mψ-SBB, mψ-ZH, and ZH-ZH. The first criterion is the achievement of macroscopic Poiseuille flow. The second criterion is the achievement of a wide range of contact angles. The main method of simulation is multipseudopotential interaction [30]. It is found that the scheme of ψ-SBB creates a relatively large fluctuation of density across the channel. Whilst, the schemes of mψ-SBB, mψ-ZH, and ZH-ZH generate much less density variation across the channel. Among them, ZH-ZH treatment is superior based on density fluctuation and the error associated with the resolution, relaxation time, and compressibility. We found that all four boundary conditions can form a wide of range of contact angles. The ψ-SBB scheme creates largest density fluctuation inside a drop on wettable surfaces. The schemes of mψ-SBB and mψ-ZH create almost the same density fluctuation which is larger than ZH-ZH. Moreover, mψ interaction generates spurious velocities as high as six times a free drop with SBB and eight times with ZH while spurious velocities in ψ-SBB and ZH-ZH are very close to the free drop. Therefore, ZH-ZH performs best, also, in wettability tests.