In this study, we use the lattice Boltzmann method to perform 2D and 3D numerical simulations to investigate the electrokinetic effect on the fluid flow and mixing in a rectangular microchannel. Zeta-potential serves as the main factor representing the electrokinetic effect. The numerical simulations in particular aim at evaluation of the mixing performance of two new designs of electrode distribution in the microchannel. One uses the periodically distributed rectangular electrodes on lateral walls of the microchannel, for which 2D and 3D simulations were implemented with time-periodic application of the electric potential on the electrodes. In another model, a periodic array of trapezoidal electrodes with a constant electric potential on them was attached on the bottom walls, for which 3D simulation was carried out. Through the parametric studies for both designs, it was shown that there exists an optimum parameter value leading to the best mixing performance.