Electroosmotic flow and dispersion in open and closed packed beds were investigated using Nuclear Magnetic Resonance (NMR) spectroscopy and pore-scale simulation. A series of NMR spectroscopy experiments were conducted to measure the effect of electroosmotic pressure on dispersion in packed spheres as a function of diameter and electric field strength. The experiments confirm earlier observations by others of superdiffusive transport in closed media. However, superdiffusive behavior is observed even at small pore sizes, contrary to earlier results and simulations in fixed sphere packs, and is conjectured to result from pressure-induced rearrangement of the particles. Simulations also support the existence of pore size-independent velocity distributions in closed media. The distribution of reverse velocities is also similar, apart from a difference in sign, to pressure-driven flow in open porous media.