Amongst the processes that have been implemented in microfluidic devices, electrophoretic transport of charged molecules, along microfluidic channels, is one of the most commonly found. However, less work has been done about continuous, pressure gradient driven flow systems where an electric field is applied orthogonally with respect to the microchannel walls. The perspective applications of this technique, include continuous flow separation and concentration of analyte molecules, and the kinetic control of surface reactions. In order to dimensioning and optimizing such a device, a mathematical model has been formulated and analyzed both with numeric and analytic methods. The given solutions let the designer of microfluidic devices able to estimate the concentration profiles along the microchannel length, as a function of the main system parameters. As a practical example of application which could be of great interest in biotechnology applications, the results relative to the simulation of the electrostatic induced cross flow of single strand DNA oligonucleotides of about 20 bases has been reported.