In recent years there has been considerable intrerest in fabricating electrophoretic separation systems on microchips. In this study the boundary element method is used to numerically model both the electrical charge density and the electrokinetically driven fluid flow velocity field in two‐dimensional micro‐channels containing an arbitrary configuration of circular flow obstacles. An estimate of both the average velocity and the resolution has been determined for various obstacle configurations, obstacle sizes, area fractions, surface line lengths per unit area and for different values of the thickness of the electrical double layer. Based on the results, an optimal microchannel design is suggested. In addition, the recently observed phenomenon of recirculated flow in an open region of an otherwise packed electrochromatography column has been confirmed with the numerical model.