We demonstrate how miniature diodes embedded into microfluidic channel walls can provide locally distributed pumping or mixing functions powered by a global external field. The millimeter-sized diodes attached to the walls rectify the voltage induced between their electrodes from external alternating electric field. The resulting electroosmotic flux localized on the surface of diodes pumps fluids in the microfluidic channel in the direction of either the cathode or the anode depending on their surface charge. The flow velocity linearly increases with applied voltage, but does not depend on the frequency of the applied field. This could eliminate intrinsic problem with vortices in areas of non-uniform field that occur in conventional AC electrohydrodynamic pumps. The localized electroosmotic flow between diodes could also be used to construct microfluidic mixers. Theoretical analysis and numerical simulations of the microfluidic pumping and mixing provided by the diodes on a chip were in excellent agreement with the experimental data. The combined application of AC and DC fields in our microfluidic chips allows decoupling the velocity of the particles and the liquid. By precisely and independently adjusting the magnitude of the AC and DC fields particles with small differences in their charges or sizes could be efficiently separated. The technique can be used in "smart", dynamically reconfigurable, microfluidic chips.