The study delves into the enhancement of micro-mixing techniques for various neutral eluted species through the incorporation of surface heterogeneity within an electrokinetic framework. The primary objective is to predict the efficacy and precision of micro-mixing for rapid and accurate mixing. A computational investigation is conducted to assess the mixing efficiency of an electroosmotic micromixer, featuring a microchannel with a nozzle-diffuser configuration and a central microchamber. The numerical simulations employ the Poisson-Nernst-Planck-based Cauchy momentum equations, considering a non-Newtonian fluid adhering to the Carreau model. By analyzing the microchamber's design, surface heterogeneity, and the electric double layer's thickness, this study scrutinizes their impacts on the flow dynamics within the electroosmotic micromixer, aiming to establish optimal mixing conditions. Furthermore, the study highlights the superior mixing performance of shear-thickening fluids compared to shear-thinning fluids, a finding of significance in the advancement of innovative micromixer fabrication techniques.