Abstract :
Electrosprays and the liquid–metal ion source (LMIS) have a clear similarity, in that both are electrohydrodynamically (EHD) driven devices operating in the cone-jet mode. There are also clear differences, not least the difference in the desired emission product. This paper begins by reviewing some of the main facts about liquid–metal ion sources. These include the nature of the emission mechanism, the size of the field at the end of the liquid emitter, the size of the end of the emitter, the fact that the emitter has an electrically well-defined surface, the absence of any significant voltage drop along the emitter, the existence of a high space charge above the end of the emitter, and the important role of the space charge in controlling the emission current, and the length of the liquid emitter cusp. Detailed discussion of LMIS behaviour may be found in Forbes (1997) Vacuum 48, 85.
On the EHD side we may note the following about the LMIS: the existence of onset phenomena is well explained by Taylor’s arguments about the total “Maxwell” force on the emitter; the basic cone-jet shape is explained partially by Taylor’s arguments, partially by other EHD effects; the LMIS appears to be a device driven by negative pressure at its apex, with the formation of the liquid cusp being the electrical equivalent of a vena contracta.
Our best understanding of LMIS behaviour is that the liquid–metal ion emitters operate mainly in an approximately steady-state-flow mode, but go unstable and emit microdroplets and/or nanodroplets between periods of approximately steady-state flow. Some possible reasons for the stability of the liquid–metal ion source, at least over short periods of time, will be put forward.
Obviously, an important difference between a LMIS and an EHD sprayer is the difference in electrical conductivity. This appears to mean that for a LMIS there is no significant voltage drop along the liquid jet, but that for an EHD sprayer the voltage drop may be significant. Numerical arguments will be presented to suggest that, because of this difference in the voltage drop, the driving force for a LMIS is the Maxwell stress on the jet apex, but that for an EHD sprayer the driving force is the tangential electrical force on the quasi-cylindrical sides of the liquid jet.
Another important difference appears to be in the size of the apex of the liquid cusp and the resultant difference in the size of the electric field there. It is the high field at the apex of the LMIS there that allows ion emission to be a significant method of removing material. It is an important question to decide why such small apex sizes and high fields cannot be achieved with EHD sprayers.
A curious difference between the theories of the LMIS and the EHD sprayer is the difference in importance given to the parameter “flow rate”: this is an important parameter for the sprayer, but does not normally appear in standard LMIS theory. However, discussions of the LMIS make use of the concepts of a “viscous-drag-free source” (for which the cone base pressure is zero), and “viscous-drag-limited” sources (for which the cone base pressure is non-zero).
Liquid–metal ion source operation has been modelled, both analytically and numerically. Progress in modelling the steady-state-flow mode has been substantial and successful. Attempts to model time-dependent EHD behaviour have run into fundamental computational difficulties.
