Electroosmotic flow in micro/nanochannels with surface potential heterogeneity: An analysis through the Nernst–Planck model with convection effect

A complete two-dimensional model is discussed to analyze the electroosmotic flow near a step jump in surface charge distribution of a micro- or nanochannel. The present model does not require the core neutrality of the fluid and it can handle electrolyte of arbitrary ionic valence as well. The governing equations consists of the flow field, mass transfer and electric potential equations. A pressure correction-based iterative algorithm (SIMPLE) is employed for computation. An analytic solution is obtained near the surface heterogeneity based on the Debye–Hückel approximation. The EOF is investigated both for weak and strong electrolytes at different channel heights. The form of the vortical flow near the potential patch and the dependence of the vortex strength on the patch overpotential is analyzed. A linear pressure drop is observed above the vortex. Average streamwise velocity overshoots the Helmholtz–Smoluchowski velocity. A comparison of the present model with the model based on the equilibrium Boltzmann distribution of ions is made. The results due to the two models differ significantly in the region where the convection effect is strong.