Numerical investigation of ionic conductor liquid charging at low to high voltages

A numerical modeling of electrification and ion transport in ionic conductor liquids (oils) is conducted while allowing for the Frumkin-Butler-Volmer kinetics responsible for the ion transfer at metal electrode surfaces. The numerically predicted near-electrode polarized layer is validated against a boundary layer analytical solution for low voltages also developed in this paper. Another benchmark related to microchannels with dielectric walls with a non-zero ζ-potential is used to validate the implementation of the Coulombic body force responsible for the electro-osmotic flow. Finally, the case of an electrohydrodynamic flow in a microchannel (a model for the flow and charging inside an electrostatic atomizer) with two metal electrodes of opposite polarity attached is considered aiming at the prediction of the resulting net charge at the channel exit. The charging electrodes occupy only a fraction of the channel walls, which are otherwise insulated. It is shown that the considered channel length does not play a role in determining the available net charge achieved at the exit. Indeed, the value of the spray current practically does not vary along the exit section of the channel (behind the electrode part), which means that irrespective of the exit location, the spray current would be the same. Moreover, it is shown that in the present case, the role of the Smoluchowski slip near the electrodes is negligibly small compared to the viscous scraping of the polarized layer under any realistic values of the imposed longitudinal electric field.