Effects of zeta potential distribution and geometrical specifications on flow rate and mixing performance of electroosmotic flows in straight, converging, diverging, and converging-diverging microchannels are investigated by lattice Boltzmann method. Modified Navier-Stokes equations along with the Nernst-Planck equation for ionic distributions are solved and validated against the available electroosmotic flow solutions. The geometrical effects on flow patterns and mixing efficiencies in the presence of patched zeta potential distributions are examined in search for the simultaneously enhanced mixing performance and mass flow rate. Numerical results indicate that converging channel leads to a sizable increase in mixing efficiencies, while at the same time decreases the flow rate. In contrast, diverging channels increase the flow rate, where the mixing performance deteriorates. Thus, it is expected to achieve a balance between the mixing efficiency and mass flow rate using converging-diverging geometries. In this regard, the response surface methodology (RSM) is employed to maximize the mixing efficiency and flow rate of the converging-diverging microchannel. According to numerical results, the optimum parameters predicted by RSM are in excellent agreement with full numerical simulations. (C) 2018 Elsevier Ltd. All rights reserved.