2026 年 21 巻 1 号 p. JFST0003
We developed a numerical method for simulating a stationary droplet with a high density ratio on a solid surface using an improved lattice Boltzmann method (LBM) for incompressible two-phase flows. This method uses the phase-field model and wettability of a solid surface is determined from the wetting boundary condition based on a solid surface free energy density. We first reviewed existing solid surface free energy densities from both physical and numerical viewpoints. We then proposed a new one as a cosine power form, which was derived by improving drawbacks in the existing forms. We next implemented a new wetting boundary condition in the LBM based on the proposed density function form. Using the developed method, we conducted three-dimensional simulations of a stationary droplet on a flat solid surface and investigated the range of static contact angles θ that can be computed with the numerical stability. As a result, we successfully demonstrated stable simulations over a wide range of θ, including the superhydrophobic (θ > 150◦) and superhydrophilic (θ < 30◦) surfaces. Furthermore, the simulated contact angles showed good agreement with the theoretical values predicted by Young’s equation within the range of 30◦ ≲ θ ≲ 150◦, confirming the validity of the proposed approach.
