In this work, wetting boundary schemes in a modified phase-field lattice Boltzmann (LB) method are developed to simulate the contact-line motion and contact angle hysteresis of binary fluids with large density ratios. In the modified phase-field LB method, two multiple-relaxation-time (MRT) LB equations are utilized, one with a nondiagonal relaxation matrix used to solve the conserved Allen-Cahn (A-C) equation and the other with a modified discrete source term used to solve the incompressible Navier-Stokes (N-S) equations. Based on the idea of geometric formulation, two wetting boundary schemes corresponding to the modified phase-field LB model are proposed. In the first scheme, a layer of virtual nodes is utilized to realize the geometric formulation. The values of the order parameter at the virtual nodes are determined by the central difference method. In the second scheme, the geometric formulation is realized through a local scheme for the gradient terms of the order parameter where the nonequilibrium parts of the distribution function are utilized. Compared with the first wetting boundary scheme and some previous models, the second wetting boundary scheme does not require the virtual nodes and simplifies the numerical implementation. The developed two schemes are validated through a series of benchmark simulations, including droplet spreading on idea substrate, capillary intrusion and droplet shearing on nonideal substrate. It is found that satisfactory accuracy can be achieved by both two schemes, and the second scheme can obtain better stability while the first scheme shows better performance in simulating contact angle hysteresis.

在这项工作中，开发了改进的相场晶格玻尔兹曼（LB）方法中的润湿边界方案，以模拟具有大密度比的二元流体的接触线运动和接触角滞后。在改进的相场 LB 方法中，使用了两个多重松弛时间 (MRT) LB 方程，一个具有用于求解守恒 Allen-Cahn (AC) 方程的非对角松弛矩阵，另一个具有改进的离散源项用于求解不可压缩的 Navier-Stokes (NS) 方程。基于几何公式的思想，提出了两种与修正相场LB模型对应的润湿边界方案。在第一种方案中，利用一层虚拟节点来实现几何公式化。虚拟节点的顺序参数值由中心差分法确定。在第二种方案中，几何公式是通过使用分布函数的非平衡部分的顺序参数的梯度项的局部方案来实现的。与第一种润湿边界方案和之前的一些模型相比，第二种润湿边界方案不需要虚拟节点，简化了数值实现。所开发的两种方案通过一系列基准模拟得到验证，包括在理想基板上的液滴扩散、毛细管侵入和在非理想基板上的液滴剪切。发现两种方案都可以达到满意的精度，