Self-consistent modeling of laminar electrohydrodynamic plumes from ultra-sharp needles in cyclohexane

Abstract

This paper presents a self-consistent model of electrohydrodynamic (EHD) laminar plumes produced by electron injection from ultra-sharp needle tips in cyclohexane. Since the density of electrons injected into the liquid is well described by the Fowler-Nordheim field emission theory, the injection law is not assumed. Furthermore, the generation of electrons in cyclohexane and their conversion into negative ions is included in the analysis. Detailed steady-state characteristics of EHD plumes under weak injection and space-charge limited injection are studied. It is found that the plume characteristics far from both electrodes and under weak injection can be accurately described with an asymptotic simplified solution proposed by Vazquez et al. [“Dynamics of electrohydrodynamic laminar plumes: Scaling analysis and integral model,” Phys. Fluids 12, 2809 (2000)] when the correct longitudinal electric field distribution and liquid velocity radial profile are used as input. However, this asymptotic solution deviates from the self-consistently calculated plume parameters under space-charge limited injection since it neglects the radial variations of the electric field produced by a high-density charged core. In addition, no significant differences in the model estimates of the plume are found when the simulations are obtained either with the finite element method or with a diffusion-free particle method. It is shown that the model also enables the calculation of the current-voltage characteristic of EHD laminar plumes produced by electron field emission, with good agreement with measured values reported in the literature.