Objective: In this article, a numerical study is conducted on mixing of two fluids in the liquid phase with two different concentrations of a chemical species in the electro-osmotic flow. Methods: The base liquid is an electrolyte which flows in a two-dimensional micro-channel having electrically charged walls. Lorentz electric force, which is used as stimulating flow factor, is created by applying an external electric field on the electric double layer (EDL) aroused by adjacency of electrolyte and charged wall. Results: To ensure the convergence of the results obtained from the computer program, equations are solved iteratively until the residual amount after solving each equation is less than machine error and independence of results from the number and location of network nodes is verified for an experimental flow. To increase the mixing efficiency, some square and triangle shaped obstacles are embedded on the micro channel wall. Herein, the fundamental principles for passive mixing as well as the effect of frequency and height of the barriers on mixing efficiency are studied. The obtained results from numerical solving of electro-osmotic flow in micro-channel are compared with the theoretical results and a very good agreement is observed.