With the development of microfluidics, electro-osmotic (EO) driven flow has gained intense research interest as a result of its unique flow profile and the corresponding benefits in its application in the transportation of sensitive samples. Challenges occur when the EO driven mechanism encounters complex rheology and vital questions such as "Can the zeta potential still be assumed to be constant when dealing with fluids with complex rheology?", "Does the shear thinning effect enhances electroosmotic driven flow?" need to be answered. Experiments were conducted via using current monitoring and microscopy fluorescent methods, and a analytical model was developed by coupling a generalized Smoluchowski approach with the power-law constitutive model. The zeta potential was calculated. The shear thinning effect is also addressed via experimental data and theoretical calculations. The mathematical model for the two immiscible layers of electro-osmotic driven flow in the parallel microchannel was proposed. One layer is a conducting non-Newtonian power-law fluid driven by electro-osmotic force. The other layer is a nonconducting Newtonian layer driven by interface shear. The effects of Debye-Hueckel parameter xhi, interfacial zeta potential If/ I , the Newtonian viscosity 1'2' the non-Newtonian fluid consistency coefficient m & flow behavior index n were discussed. The complex flow behavior, namely fluid consistent coefficient and flow behavior index, play important roles in the velocity distributions. The shear thinning effect is also analyzed. The results show that the shear thinning fluid is not only ideal for direct electro-osmotic driving but also for hybrid driving. A flow-focusing geometry in a microfluidic device was studied for the formation of uniform droplets and we qualitatively illustrated aspects of controlling the droplet I