Fluid flow was driven within a network of intersecting capillaries integrated on a glass chip using electroosmotic pumping. Potentials could be applied to several capillaries simultaneously to quantitatively control the amount of each reagent stream delivered to an intersection of capillaries. An example of a simple dilution of sample with buffer is shown. Kirchhoffs rules for resistive networks were found to predict the currents and fluid flow within the capillaries. Leakage of sample from one channel to another at an intersection was shown to arise from both diffusive and hydrodynamic effects. Application of potentials to the intersecting channels could fully arrest such leakage. These phenomena were evaluated both qualitatively from photomicrographs of the fluid flow in the channels and quantitatively from measurements of electrophoretic separations of amino acids and fluoresceins.