Electroosmotic flow (EOF) is the motion of liquid, generated as result of the interaction of an externally applied electric field with the net surplus of charged mobile ions in the diffuse part of an electrical double layer (EDL). For a uniform surface charge distribution, EOF is characterized by a uniform, plug-like, velocity profile, making it a useful tool for dispersion-free transport at the microscale. However, more realistic surfaces are often non-homogeneously charged, either due to manufacturing limitations, or by intended design. Applying external electric field in a heterogeneous channel results in induced internal pressure gradients and non-uniform flows within the bulk. We present a theoretical and numerical study of electroosmotic flow generated by non-uniform surface charge patterning, confined to a narrow gap between two parallel flat plates. Applying the lubrication approximation and assuming a thin EDL regime, we obtain a set of the Hele-Shaw equations relating the velocity and pressure to the surface zeta potential distribution. We demonstrate the use of our model for prediction of flow patterns obtained from non-uniform charge distribution, as well as the ability to obtain the necessary surface distribution for a desired flow pattern. We believe this method could be useful for future on-chip devices, allowing flow control without the need for mechanical components.
