Numerical analysis of electro-osmotic flows through elliptic microchannels

This work presents a comprehensive numerical analysis of electro-osmotically driven flows inside microchannels characterized by an elliptic cross-section. The mathematical model takes into account the presence of an opposing pressure gradient to correctly reproduce the operating conditions of pumps. The dynamical features are analyzed for isothermal flows in the fully developed region. Characteristic curves that relate the volumetric flow rate and the pressure head are presented with respect to all the non-dimensional parameters that influence the behavior of combined electroosmotic/ pressure-driven flows, i.e., the aspect ratio of the cross-section, the electrokinetic diameter, the non-dimensional zeta-potential and the ratio of the pressure force to the electric force. Such numerical results are also compared with two existing correlations for microchannels with rectangular or trapezoidal cross-sections, that assess both volumetric flow rate and pressure head. The comparison highlights that the correlation for the volumetric flow rate works perfectly also for this kind of geometry, while a correction is proposed for the pressure head estimate, in order to extend the validity of the original correlation to elliptic microchannels.