THE CURRENT EMITTED BY HIGHLY CONDUCTING TAYLOR CONES

When a liquid meniscus held at the exit of a metallic capillary tube i s charged to a high voltage V, the free surface often takes the form o f a cone whose apex emits a steady microjet, and thus injects a certai n 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 et diameter d(j) is much smaller than the diameter d(n) of the capillary tube. In the limit d(j)/d(n) --> 0, the structure of the jet (d(j) and I, in particular) becomes independent of electrostat ic parameters such as V or the electrode configuration, being governed mostly by the liquid properties and flow rate Q. Furthermore, the mea sured current is given approximately by I =f(epsilon) (gammaQK/epsilon )1/2 for a wide variety of liquids and conditions (epsilon, and gamma are, respectively, the dielectric constant of the liquid and the coeff icient of interfacial tension; f(epsilon) is shown in figure 11). The following explanation is proposed for this behaviour. Convection assoc iated with the liquid flow Q transports the net surface charge towards the cone tip. This upsets the electrostatic surface charge distributi on slightly at distances r from the apex large compared to a certain c harge relaxation length lambda, but substantially when r approximately lambda. When the fluid motion is modelled as a sink flow, lambda is o f the order of r = (Qepsilonepsilon0/k)1/3 (epsilon0 the electrical p ermittivity 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 I(s) approximately (gammaQK/epsil on)1/2, 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 'ets, we find the rough sca ling d(j) approximately 0.4r for the jet diameter, which shows that t he jet forms as soon as charge relaxation effects set in. In the limit epsilon much less than 1, an upper bound is found for the convected c urrent at the virtual cone apex, which accounts for only one-quarter o f the total measured spray current. The rest of the charge must accord ingly reach the head of the jet by conduction through the bulk.