Modelling and scaling laws of the ion emission regime in Taylor cones

Abstract

This article presents a first-principles model for electrosprays operating in the ion emission regime. The model considers ion emission from a Taylor cone anchored on a tubular emitter, including the fluid dynamics as well as the electrostatic interaction between the liquid, the electrodes and the ion beam. The model accounts for the self-heating of the liquid due to ohmic and viscous dissipation, and the associated variation of the viscosity and electrical conductivity with temperature. The numerical solution reproduces the experimental phenomenology of the ion emission regime (e.g. current levels, the high sensitivity to the ion solvation energy, the proportionality between the emitted current and emitter potential, etc.), and other aspects of the underlying physics such as the coupling between ion emission and self-heating of the liquid. The numerical solution is also used to validate a simpler analytical model that yields scaling laws for the emitted current, and for the characteristic length, current density and electric field of the emission region. The analytical model also provides liquid-dependent criteria for the onset of the ion emission regime.