The motivation of the present study is to generate vortical flow by introducing channel wall roughness in the form of a wall mounted block that has a step-jump in $\zeta $-potential on the upper face. The characteristics for the electrokinetic flow are obtained by numerically solving the Poisson equation, the Nernst–Planck equation, and the Navier–Stokes equations, simultaneously. A numerical method based on the pressure correction iterative algorithm (SIMPLE ) is adopted to compute the flow field and mole fraction of the ions. The potential patch induces a strong recirculation vortex, which in turn generates a strong pressure gradient. The strength of the vortex, which appears adjacent to the potential patch, increases almost linearly with the increase in $\zeta $-potential. The streamlines follow a tortuous path near the wall roughness. The average axial flow rate over the block is enhanced significantly. We found that the ionic distribution follow the equilibrium Boltzmann distribution away from the wall roughness. The solutions based on the Poisson–Boltzmann distribution and the Nernst–Planck model are different when the inertial effect is significant. The combined effects due to geometrical modulation of the channel wall and heterogeneity in $\zeta $-potential is found to produce a stronger vortex, and hence a stronger mixing, compared with either of these. Increase in $\zeta $-potential increases both the transport rate and mixing efficiency. A novelty of the present configuration is that the vortex forms above the obstacle even when the patch potential is negative.