In recent years, the gradual minimization of continuous-flow chemical reactors, which is stimulated by the interests of pharmaceutical production, has led to the emergence of a new generation of microreactors. A decrease in the thickness of the channels where the species contact and react, forces to search for new, non-mechanical, mechanisms for mixing the initial solutions. In this work, we consider the efficiency of mixing the reactants induced by electro-osmotic flow in a Hele-Shaw configuration with non-uniform zeta potential distribution. We consider the neutralization reaction, which has simple but non-linear kinetics, as a test reaction. The reaction occurs between two miscible solutions, which are initially separated in space and come into contact in a continuous-flow microreactor. The reaction proceeds frontally, which prevents the efficient mixing of the reactants due to diffusion. We show numerically that the mixing of solutions can be effectively controlled by specifying special forms of the zeta potential, which make it possible to lengthen the reaction front by an order of magnitude and increase the yield of the reaction product by several times.