An electrokinetic pump achieves high and low flow rates without producing significant gaseous byproducts and without significant evolution of the pump fluid. A first feature of the pump is that the electrodes in the pump are capacitive with a capacitance of at least 10.sup.-4 Farads/cm.sup.2. A second feature of the pump is that it is configured to maximize the potential across the porous dielectric material. The pump can have either or both features.