Analysis of self-heating in electrosprays operating in the cone-jet mode

Abstract

The electrohydrodynamic processes taking place in a cone jet cause ohmic and viscous dissipation, and ultimately self-heating of the liquid. Despite this, previous analyses have modelled cone jets as isothermal systems. To investigate the validity of this assumption, this work applies the leaky-dielectric model to cone jets, while also requiring conservation of energy to reproduce the variation of temperature caused by dissipation and temperature-dependent liquid properties. The main goals are to determine whether there exist electrospraying conditions for which the isothermal assumption is inaccurate, and quantify the temperature field under such conditions. The work confirms that self-heating and thermal effects are important in liquids with sufficiently high conductivities, which is a significant limit because these electrical conductivities are needed to produce jets and droplets with radii of tens of nanometres or smaller. The numerical solution provides accurate expressions for evaluating the dissipation and the temperature increase in cone jets, and confirms that thermal effects cause the apparent breakdown of the traditional scaling law for the current of cone jets of highly conducting liquids.