Many biomedical, chemical, and industrial processes involve mixtures of three or more liquid components. In spite of the importance of three-phase flows, most studies of three-phase systems do not consider hydrodynamical interactions between the components. There have been few theoretical and numerical studies of flows containing three or more components compared to the large body of research for two-phase flows. This is partly due to the difficulties in dealing with hydrodynamics associated with interfaces and triple junctions. In the frame work of an ALE finite method, we have developed a novel adaptive numerical method to model accurately this type of flow. One example is shown in Fig.1 where a lighter than water oil droplet breaks through an air-water interface and finally forms a floating lens. This method can be easily adapted for moving contact line problems on a curved solid surface, which are, despite centuries of research, active research topics nowadays.