Electrokinetic modelling of cone-jet electrosprays

The physics of electrospray has been subject to an intense debate for three decades regarding the ultimate electrokinetics that determines the electric current and the size of the emitted droplets in the steady Taylor cone-jet mode (TCJ). In order to solve with a high degree of accuracy the complete electrokinetic structure of the TCJ, in this work, we have used the full Poisson-Nernst-Planck model electrokinetic equations, which have been solved using a high accuracy numerical scheme. We consider a formulation with no interfacial adsorption of ions, as in Mori & Young (J. Fluid Mech., vol. 855, 2018, pp. 67-130). Our simulations corroborate Mori and Young's conclusion that the classical leaky dielectric model (LDM) recovers the electrodiffusion theory for weak electrolytes when disregarding ion adsorption at the interface. However, for strong electrolytes, our results differ drastically from those provided by the LDM. In this case, we observe that the ion distribution, and consequently the conductivity in the bulk, can be strongly non-homogeneous. Given the rather universal validity of the LDM experimentally observed so far, we postulate that ion interfacial adsorption must be considered in the case of strong, highly dissociated electrolytes to retrieve the LDM limit, mostly for a cone jet operating in the vicinity of the minimum flow rate.