Slow Discharge Theory and Calculation of the Potential Drop across the Compact Layer at High Electrode Voltages

A novel approach presented in this work allows one to calculate the potential drop across the compact layer in electrostatic atomization with high voltages applied at the electrode. Ionic conductor liquids employed in electrostatic atomization have a low dielectric constant, which causes almost all of the potential drop across the double layer to occur inside the compact layer. In the previous article of this group (Sankarn, A., et al. Langmuir 2017, 33, 1375-1384), it was shown that faradaic reactions in the kinetics-limited regime are responsible for liquid electrification in electrostatic atomization. Here, we apply the Frumkin slow discharge theory to calculate the electric potential at the interface of the compact and diffuse layers. The electric potential value at the interface of the compact and diffuse layers is required in computational models accounting for the discharge of counterions due to faradaic reactions when solving the ionic transport equations. The activation energy of the electron transfer reaction is calculated through the Marcus theory. Knowing the counterion flux value at the electrode surface from the concurrent experimental measurements, the ionic concentration and net charge distribution across the polarized diffuse layer are also found from the numerical simulations. Considering canola oil to be the ionic conductor liquid, two different examples are used to demonstrate the application of this approach to calculate the electric potential at the interface of compact and diffuse layers.