Stability of an electrified liquid jet approaching to critical point

Zixuan Fang,Ping Wang

doi:10.1177/1687814020936377

Abstract

This article reports the linear stability analysis of a thermodynamic-transcritical jet sprayed to a radial electrical field. An asymptotic approach was used to obtain the stability solution of a supercritical jet subjected to electrical field. In order to obtain the solutions for the electrified supercritical jet, the surface tension was decreased and consequently led the increase in Weber number in the linear governing equation of subcritical charged jet. To investigate the role of surface tension and electric stress playing in the destabilizing process when approaching the critical point, the energy budget is performed by tracing the energy sources. It was found that, when the Weber number is increased to a sufficiently large value, the solution will become an asymptotic value, which can be considered as a solution under the supercritical conditions. The electric stress can increase both the maximum growth rate and the dominant wave number of electrified supercritical jet, that is, higher electrical field intensity would enhance the instability of the electrified supercritical jet and decrease the wavelength of the disturbances.

Highlights

This phenomenon is called electrospray and exhibits a few modes that depend on the ratio of electrostatic to surface tension forces, which have different applications in many fields ranging from aerospace microthrust to electrospray ionization mass spectrometry (ESI-MS) technologies
With the critical point gradually being approached, the value of the surface tension decreases; at the critical point, surface tension completely disappears, which indicates that the Weber number tends to infinity at the critical point
The surface tension was decreased conceptually to approach supercritical conditions, while mathematically the Weber number increased in our governing equations of an electrified subcritical liquid jet

Summary

Introduction

When the fluid jet is subjected to an electrostatic electric field, spray may occur on the surface of the fluid due to an imbalance between the electrostatic stress and the surface tension.[1,2,3] This phenomenon is called electrospray and exhibits a few modes that depend on the ratio of electrostatic to surface tension forces, which have different applications in many fields ranging from aerospace microthrust to electrospray ionization mass spectrometry (ESI-MS) technologies. For ESI-MS technique, the breakup of the jet is favorable, so we need to enhance the instability. For electrospinning technique, the electric field and surface tension forces do not break down the slender jet to produce a fine fiber, the instability of jet should be damped. There have been many fundamental studies on the electrified jets’ instability. Hartman et al.[5] proposed an analytical physical model and revealed the relationship between the jet breakup and axisymmetric or varicose instabilities. Turnbull[6,7] studied conductive and dielectric jets’ temporal stability in both radial and axial electric fields. Li et al.[8] considered the viscous of liquid jet and established a new model under a radial electric field.

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Results

Conclusion