Electrohydrodynamically (EHD) driven capillary jets are analysed
in this
work in
the parametrical limit of negligible charge relaxation effects, i.e. when
the electric
relaxation time of the liquid is small compared to the hydrodynamic times.
This
regime can be found in the electrospraying of liquids when Taylor's
charged
capillary
jets are formed in a steady regime. A quasi-one-dimensional EHD model comprising
temporal balance equations of mass, momentum, charge, the capillary balance
across
the surface, and the inner and outer electric fields equations is presented.
The steady
forms of the temporal equations take into account surface charge convection
as well
as Ohmic bulk conduction, inner and outer electric field equations, momentum
and
pressure balances. Other existing models are also compared. The propagation
speed
of surface disturbances is obtained using classical techniques. It is shown
here that,
in contrast with previous models, surface charge convection provokes a
difference
between the upstream and the downstream wave speed values, the upstream
wave
speed, to some extent, being delayed. Subcritical, supercritical and convectively
unstable regions are then identified. The supercritical nature of the microjets
emitted
from Taylor's cones is highlighted, and the point where the jet switches
from a stable
to a convectively unstable regime (i.e. where the propagation speed of
perturbations
become zero) is identified. The electric current carried by those jets
is
an eigenvalue
of the problem, almost independent of the boundary conditions downstream,
in an
analogous way to the gas flow in convergent–divergent nozzles exiting
into
very low
pressure. The EHD model is applied to an experiment and the relevant physical
quantities of the phenomenon are obtained. The EHD hypotheses of the model
are
then checked and confirmed within the limits of the one-dimensional assumptions.
On the energy estimates of semi-discrete wave equations with time dependent propagation speed
