於兩相流研究中，藉由模擬液珠於不同構造與材質之表面上的行為，可以提供材料科學與微流道設計作為資料庫。於此篇論文中，我們利用Zheng等人所建立的三維晶格波茲曼兩相流模型配合Briant等人發展出的部分沉浸邊界條件，模擬液珠置於平面與微結構上的接觸角度，並且藉由與Yoshimitsu等人所發表的實驗數值相互比較，驗證此兩相流模型的可靠度。於微結構平面模擬中，由於邊界條件複雜，因此我們實施三種不同的邊界處理方式，利用實驗數值跟理論數值驗證何者為最佳。另一方面，為了改善計算效率，我們採用簡化擴散項的Allen-Cahn方程式，並結合Zheng等人與Takada等人所提出的兩相流模組，藉由表面濕潤性控制模擬，審視此方法之可行性。

In two-phase flow field, the present researches of the droplet behavior simulation on the different structured-surface and different material provide the helpful information for the material research and micro-fluidic channel design. In this thesis, the three dimensional lattice Boltzmann model based on Zheng et al., which is for high density ratio, with partial wetting boundary condition by Briant et al. is adopted. This method is used to simulate a droplet on a partial wetting surface with given contact angle, and the results are compared with the experiment by Yoshimitsu et al. to verify the accuracy. Three different strategies which focus on dealing with the complicated boundary conditions on edges and corners are implemented, and the most appropriate approach is found out by contrasting the apparent contact angles with the experimental values. On the other hand, in order to improve the computational efficiency, Allen-Cahn equation is also considered and implemented due to simpler diffusion term. The 3D lattice Boltzmann model based on Zheng et al. and Takada et al. cooperating with Allen-Cahn equation is implemented and scrutinized for applicability.

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