The pressure driven flow of power-law fluids in Y-shape microchannel is calculated by the fourth-order compact difference scheme. The governing equations are established by the complete Poisson-Boltzmann equation

modified Cauchy momentum equation and continuity equation. The distribution of the electric double layer potential

the pressure

the apparent viscosity and the velocity profiles of different parameters are obtained by the simulation. The results of the simulation are discussed. Furthermore

the effects of the electric double layer on the velocity profile were investigated. The results show that with the decrease of the powerlaw index

the velocity peak of the flow is larger in the microchannel

the effects of the electric double layer are more obvious. Compared the shear thickening and Newtonian fluids

the shear thinning fluids are much more sensitive to the other parameters. The recirculation generating conditions are studied. The recirculation generating critical pressure decrease with enlarging the branching angle or decreasing the power-law index. The pressure

the power-law index and the branching angle have significant influence on the flow separation when fixing the other parameters. Increasing the pressure

decreasing the power-law index or enlarging the branching angle also can extend the region of the flow separation.