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In this work, a model is developed that provides a general framework for the modelling of electroosmotic flow and pressure-driven flow in porous media of different geometries. This model is found to be compatible with standard theory, but incorporates viscous shear stresses into the model which enables the modelling of fluid flow in both porous and open channels. The model is based upon the generalized porous medium equations devised for pressure-driven flow, and thus reduces to the Navier-Stokes equations in the case of an open channel. The model is used to solve for the volume-averaged flow profile in a 2D channel with adjacent open and porous segments with mismatched zeta potentials. The flow profile in the open segment deviates substantially from the flat profile one would normally expect with electroosmotic flow. The deviation from the typical flat flow profile in the porous segment is much less severe.