A phase-field-based lattice Boltzmann model for ternary fluid flows is proposed, where the conservative Allen-Cahn equation for ternary fluids is used to track the interface of fluids. A time derivative term is introduced into the lattice Boltzmann equation for the conservative Allen-Cahn equation and a forcing distribution function is used in the lattice Boltzmann equation for the Navier-Stokes equations. The computational accuracy and capability of the proposed model are verified by benchmark cases related to stationary droplets, spreading of a liquid lens, and phase separation of a ternary fluid mixture. Moreover, a wetting boundary scheme based on the framework of the lattice Boltzmann method applicable to ternary fluid flows is developed. This model performs well in eliminating the undesired numerical artifact after consideration of the wettability effect. Typical wettability problems are simulated to verify the applicability of the wetting boundary scheme, including the spreading of binary droplets and compound droplets on a surface. The numerical results for static contact angles and spreading length show a good fit of the data to the theoretical results within the scope of permissible error. Furthermore, the reliability of this wetting boundary condition for the dynamic case is verified by our modeling the motion of compound droplets subjected to shear flow on a substrate. This boundary scheme performs well for the motion of ternary fluids with a small density ratio and a large density ratio. In conclusion, the phase-field-based lattice Boltzmann model for ternary fluid flows considering the wetting effect has good applicability for modeling ternary fluid flows with a density ratio of 1000.

提出了一种用于三元流体流动的基于相场的晶格 Boltzmann 模型，其中三元流体的保守 Allen-Cahn 方程用于跟踪流体的界面。对于保守的 Allen-Cahn 方程，在格子 Boltzmann 方程中引入了时间导数项，在 Navier-Stokes 方程的格子 Boltzmann 方程中使用了强迫分布函数。所提出模型的计算精度和能力通过与静止液滴、液体透镜的扩散和三元流体混合物的相分离相关的基准案例验证。此外，基于适用于三元流体流动的格子 Boltzmann 方法的框架开发了润湿边界方案。在考虑润湿性影响后，该模型在消除不需要的数值伪影方面表现良好。模拟典型的润湿性问题以验证润湿边界方案的适用性，包括二元液滴和复合液滴在表面上的扩散。静态接触角和铺展长度的数值结果表明，在允许误差范围内，数据与理论结果拟合良好。此外，我们通过模拟复合液滴在基材上受到剪切流的运动来验证动态情况下这种润湿边界条件的可靠性。这种边界方案对于小密度比和大密度比的三元流体运动表现良好。综上所述，