In accordance with the present invention, stable electroosmotic flow systems and methods for designing the same are disclosed. The invention provides electroosmotic flow systems comprising electroosmotic flow elements, including bridge elements, that have matching flux ratios, i.e., when two or more elements of an electroosmotic flow system are in fluidic and electrical communication at a junction, the flux ratio for each of the elements is selected so that the difference in flux ratios of any two elements is less than a target value. The invention also provides methods for designing such systems. Also disclosed is a novel design for the terminal portions of electroosmotic flow (EOF) and bridge elements and for junctions in electroosmotic flow systems, whereby the elements are designed so that the terminal current flux is much smaller than the element current flux.