Microfluidic and Lab-on-a-chip devices have attracted great interest over the last decade due to the advantages such as increased efficiency, throughput, portability, reduced analysis time, reagent consumption and cost. Comparing with a number of techniques (e.g., pressure, centrifuge, and thermal gradient driven flow), electroosmosis has been used to induce electroosmotic flow to transport, separate, and mix samples. This thesis addresses the following four topics: (1) Three-fluid flow in straight microchannels based on the combined effect of hydrodynamic and electroosmosis with planar interface; (2) Modeling of tunable optofluidic lens based on the combined effect of hydrodynamic and electroosmosis; (3) Semi-analytical model of mixed electroosmotic/pressure-driven two immiscible fluids with curved interface ; (4) The linear stability of two-fluid flow in a During my study at Nanyang Technological University, lots of professors, staff and friends helped me in various ways. I wish to express my sincere gratitude to these friends. Firstly and foremost, I wish to express my sincere gratitude and hearty thanks to my supervisor Associate Professor Wong Teck Neng. During my study and research work, Prof. Wong provides excellent guidance, patient encouragement and support. I would like to express my sincere gratitude and hearty thanks to Associate Professor Nguyen Nam-Trung for his kind help in my whole research work. I wish to express my deep gratitude to Mr. Yuan Kee Hock for the valuable assistance of my experiment. I am also grateful to the graduate and FYP students, my friends in the Thermal and Fluid Research Lab for their help whenever needed. During my PhD study, my wife Liu Haili has been very supportive. Her unconditional support has given me the strength to finish my study. I am much indebted to my wife for all her love and support. I also would like to acknowledge the Research Scholarship provided by Nanyang Technological University.