In this thesis, a three-dimensional lattice Boltzmann two-phase model which is capable of dealing large liquid and gas density ratio and partial wetting surface with a given contact angle is investigated. The LBM model is based on Zheng et al. model of high density ratio with partial wetting boundary condition of Briant et al.

In the present work, a droplet rests on a partial wetting surface with given contact angle is simulated. The results of three-dimensional droplets at different partial wetting condition at equilibrium state are in well agreement with the analytical solutions. High density ratio may cause spurious velocity oscillation because of the interfacial force imbalance. Cases of different contact angle and viscosity ratio are examined. The results show that the spurious velocity is about the order of 10^{-6} in each case. The effect of gravitational force on droplet shape is also discussed in terms of Bond number.

The present model has lots of applications. First, it is applied to simulate liquid lens cases. The simulation result shows good agreement with the experiment done by Hsieh et al. Secondly, phenomena influenced by different wetting surfaces are presented, such as a droplet on heterogeneous surface. Finally, the droplet can be moved by giving gradient of wettability, where the droplet speed is proportional to the gradient. To control the droplet speed, different width of wetting zones are also examined in the study.

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