Injection of charge into a dielectric liquid, and a Coulomb force that sets
the liquid into motion, may be obtained by applying a dc voltage to a blad
e-shaped, metallic electrode immersed in the liquid. An analysis of this mo
tion and its influence on the transport of electric charge is carried out f
or a simple charge injection law. It is shown that the liquid motion, the e
lectric field, and the charge distribution in a region around the electrode
tip of size of the order of the electrode curvature radius determine the i
njected current as a function of the far electric potential seen by this re
gion. The current increases exponentially with the potential when the contr
ibution of the space charge to the electric field is negligible and algebra
ically when it is dominant, and presents a range of multiplicity in between
. When the inertia of the liquid matters, the region around the electrode t
ip is also the origin of an electrohydrodynamic plume. An oscillatory curre
nt regime is found in which the space charge in the interelectrode space re
arranges into many discrete lumps that, under constant voltage bias and sma
ll current, induce oscillations of the electric field at the injecting elec
trode and thus fire new lumps. An order of magnitude analysis and numerical
computations for this regime give results in line with known experimental
data. In conjunction with the hydrodynamic instability of the plume, this p
ulse firing mechanism is seen to lead to more complex, nonperiodic oscillat
ions. (C) 2000 American Institute of Physics. [S1070-6631(00)50611-4].