接触角迟滞（CAH）是液滴在固体表面常见的现象，低毛细数下对液滴的形态和运动起重要作用。已有模拟液滴的格子Boltzmann方法（LBM）中尚未包含CAH模型。本项目拟发展含CAH模型的新型LBM，并将其用于研究壁面附近的液滴。具体包括：将CAH模型加入基于相场的LBM，开发含CAH模型、适用较宽参数（如密度比和粘性比、毛细数等）范围的二维、轴对称及三维LBM程序；研究CAH对液滴和接触线运动的影响及有CAH时各参数的影响；针对壁面浸润性梯度驱动的液滴，研究有CAH时如何最优控制壁面浸润性以实现对其的快速输运；在LBM框架内比较不同CAH模型或模拟的研究和相关理论及实验结果，阐明其之间的关系、各自的适用性和优缺点。含CAH的液滴模拟属多相流模拟的前沿课题，引入CAH后的LBM可更准确模拟实际情形下液滴在基底上的运动，为重要应用如微流体芯片上的生化分析等提供更具价值的参考。

Contact angle hysteresis (CAH) is a commonly seen phenomenon for droplets on solid surfaces. Under small capillary numbers, CAH plays an important role in determining the shape and motion of droplets. Till now, the existing lattice Boltzmann methods (LBMs) have not included any CAH model. The aim of this project is to develop a newly improved LBM with explicit CAH model and to apply it to study near-wall droplets. The main tasks include: to add suitable CAH models into a phase-field based LBM, and to develop two-dimensional, axisymmetric and three-dimensional LBM codes with CAH model that are applicable for a wide range of parameters (e.g., the density ratio, viscosity ratio, and capillary number, etc.); to investigate the effects of CAH on the motions of droplet and contact line, and the effects of various parameters in the presence of CAH; to simulate a droplet driven by the wettability gradient of a surface and study how to control the surface wettability optimally in order to achieve rapid transport of the droplet when CAH exists; within the LBM framework, to compare different methods to model or simulate CAH, and also to compare their numerical outcome with relevant theoretical and experimental results, so as to uncover their relationship, their respective applicability, pros and cons. Droplet simulations with CAH are among the forefront topics in multiphase flow simulation; with CAH introduced, one can capture droplet motions on substrates much more precisely by using LBM, thus providing more valuable references for important applications like biochemical analyses on microfluidic chips.