Two dimensional, time-independent and time-dependent electroosmotic flows driven by a uniform electric field in rectangular cavities with uniform and non-uniform zeta potential distributions along the cavities’ walls are investigated theoretically. The time-independent flow fields are computed with the aid of Fourier series. The series’ convergence is accelerated so that highly accurate solutions are obtained with just a few (<10) terms in the series. The analytic solution is used to compute flow patterns for various distributions of the zeta potential along the cavities’ boundaries. It is demonstrated that by time-wise periodic modulation of the zeta potentials, one can induce chaotic advection in the cavities. Such chaotic flows may be used to stir and mix fluids in microfluidic devices.