Cilia are micro-scale (usually under 25 micron) hair-like structures that cover many eukaryotic cells, from single-celled protozoa to mammalian epithelial surfaces. Previous numerical studies of cilia focused primarily on the performance of fluid transport and pumping by the cilia while the other functions such as sensing, particle capture and fluid mixing are less well understood. We developed 3D numerical simulations with beating kinematics from experiment to study the fluid mechanics and effects of the beating pattern in the process of fluid mixing and particle capture. Depending on the function, we found that the accordance and sometimes lack of accordance between the beatings of cilia can greatly improve the performance of the cilia. Our studies shed new lights on the mechanisms of the multi-function roles of cilia in biological systems and may help the design of artificial cilia.