In this thesis, a lattice Boltzmann multiphase fluid model capable to deal with large density ratio and with partial wetting surface is introduced. Multiphase fluid behavior can be simulated using the the Navier-Stokes equation coupling with convective Cahn-Hilliard equation [1], where the latter equation is used to capture the interface of multiphase fluid in terms of chemical potential. By adopting the multiphase model and adding an additional
term describing surface energy, a droplet rests on a surface with given contact angle can be computed.

The capability of the present model, which is to compute two phase flows with wettability controllable surface, is validated by simulating a droplet that rests on a surface with given contact angle. The contact angles calculated from the results agree with theory. The effect of gravitational force on droplet shape is also discussed in terms of Bond number. Besides, phenomena caused by different wetting condition of the surface are presented in this thesis, such as droplet on heterogeneous surface and transient response of a droplet with changing wettability.

The present model is applied to simulate liquid lens cases. The simulation result shows good compatibility with the experiment done by Hsieh et al [58], where Bond number is about $0.05$. Further improvement of the lens fabrication technique is suggested with observations in the present work. Optical properties of the lens such as back focal length of the liquid lens can be changed by controlling Bond number to reach wider FOV or longer BFL, which are
important specifications in optics.

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