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When a liquid meniscus held at the exit of a metallic capillary tube is charged to a high voltage V, the free surface often takes the form of a cone whose apex emits a steady microjet, and thus injects a certain charge I and liquid volume Q per unit time into the surrounding gas. This work deals with liquids with relatively large conductivities K, for which the jet diameter dj is much smaller than the diameter dn of the capillary tube. In the limit dj/dn → 0, the structure of the jet (dj and I, in particular) becomes independent of electrostatic parameters such as V or the electrode configuration, being governed mostly by the liquid properties and flow rate Q. Furthermore, the measured current is given approximately by I = f(ε) (γQK/ε)½ for a wide variety of liquids and conditions (ε, and γ are, respectively, the dielectric constant of the liquid and the coefficient of interfacial tension; f(ε) is shown in figure 11). The following explanation is proposed for this behaviour. Convection associated with the liquid flow Q transports the net surface charge towards the cone tip. This upsets the electrostatic surface charge distribution slightly at distances r from the apex large compared to a certain charge relaxation length λ, but substantially when r ∼ λ. When the fluid motion is modelled as a sink flow, λ is of the order of r* = (Qεε0/K)$\frac13$ (ε0 is the electrical permittivity of vacuum). If, in addition, the surface charge density is described through Taylor's theory, the corresponding surface current convected towards the apex scales as Is ∼ (γQK/ε)½, as observed for the spray current. The sink flow hypothesis is shown to be realistic for sufficiently small jet Reynolds numbers. In a few photographs of ethylene glycol cone jets, we find the rough scaling dj ∼ 0.4r* for the jet diameter, which shows that the jet forms as soon as charge relaxation effects set in. In the limit ε [Gt ] 1, an upper bound is found for the convected current at the virtual cone apex, which accounts for only one-quarter of the total measured spray current. The rest of the charge must accordingly reach the head of the jet by conduction through the bulk.

The formation of cone-jets in charged liquids with electrical conductivities larger than 10−4 S/m is reviewed for steady supported menisci and transient Coulomb fissions in charged drops. Taylor's hydrostatic model does not apply strictly, but it forms the basis for subsequent developments. The jet structure is critically dependent on the model used for charge transport, which has been based mostly on a constant conductivity assumption. Saville's (1997) more general model predicts the formation of rarefaction fronts with wide space charge–dominated regions near the liquid surface, which apparently do arise in polar liquids near the minimum flow rate. Known approximate scaling laws for the jet break down at electrical conductivities of about 1 S/m due to ion evaporation from the meniscus. In molten salts and liquid metals a regime of purely ionic emissions exists without drop or jet formation.

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The phenomenon of ion evaporation from charged liquid surfaces is at the basis of electrospray ionization, a source of a stunning variety of gas phase ions. It is studied here by producing a monodisperse cloud of charged droplets and measuring the charge q and diameter dr of the residue particles left after complete evaporation of the solvent. When the droplets contain small monovalent dissolved ions, the electric field E on the surface of their solid residues is found to be independent of dr. One can thus argue that the source of small ions in electrospray ionization is field-emission, and not other proposed mechanisms such as Dole’s charged residue model. A consequence of the observed independence of E on dr is that the rate of ion ejection is simply related to the rate of solvent evaporation, estimated here as that for a clean surface of pure solvent. The reduction G(E) brought about by the electric field E in the activation energy for ion evaporation has thus been inferred as a function of the measured field E in the range 1.5<E(V/nm)<3.25. It agrees surprisingly well with the so-called Schottky hump from the image potential model (IPM), GIPM=(e3E/4πε0)1/2. This remarkably simple result is paradoxical in view of two major objections raised earlier against the use of the IPM for ion evaporation from liquids. However, the correct mechanism (first introduced by Iribarne and Thomson) leading to an attractive interaction between the liquid surface and the escaping ion is not the creation of an image charge, but the polarization of the dielectric liquid by the ion. In the limit of a large dielectric constant ε≫1, the image force and the polarization force coincide numerically, though the later sets in much faster and is apparently free from the paradox raised by Röllgen. Also, the dielectric nature of the liquid and its strong screening of the net charges near its surface resolves another paradox raised by Fenn regarding the discrete distribution of charges. This screening also introduces a correction in the model proposed by Iribarne and Thomson for G(E), making its predictions virtually indistinguishable from those of GIPM(E). In conclusion, small ions observed in electrospray ionization are produced by field-emission. Measured ionization rates are well represented by results from a ‘‘polarization potential model’’ which appears to be physically sound. These predictions coincide with those from the IPM in the limit ε≫1, the only case studied so far.