Biomedical Engineering Reference
In-Depth Information
process interactively. He found that it was diffi cult to establish a cone-jet electrospraying pattern
using undistilled water as the electrosprayed precursor but was successful with alcohol, lubricat-
ing oil, and distilled water. This is attributed to the low electrical conductivity of alcohol and
distilled water.
In between Zeleny's pioneering studies on electrospraying early last century and the research
work carried out in 1952 by Vonnegut and Neubauer, who reported the generation of monodispersed
aerosol droplets produced by electrospraying, very little knowledge was developed in the fi eld of
electrospraying [19]. In 1964, Taylor gave the fi rst explanation and theoretical description of the
conical shape of the droplet at the capillary exit by investigating the hydrostatic balance between
electrical and surface tension forces [20]. The cone jet is also referred to as a Taylor cone in honor
of his contribution to the understanding of electrospraying. In 1982, Joffre et al. developed a math-
ematical model for calculating the conical shape of a stable droplet at the tip of a capillary under
electrospraying, which demonstrated consistency between the experimental data and the modeled
results [21]. The equations are based on the balance of the inner pressure of the droplet and the elec-
trical potential distribution between the capillary and a counter-electrode plate. Since then, there
have been a number of experiments on the stability limits of the cone-jet mode and on the infl uences
of the liquid properties and the processing parameters. Experiments have also covered the electro-
static conditions of current and the droplet size emitted from an electrifi ed conical point [22-24]. In
1979, Mutoh et al. estimated the upper conductivity limit for a cone jet to be 10
−
5
S/m [25]. Smith,
however, investigated the stability of the cone shape based on the onset potential, capillary radius,
and liquid conductivity and viscosity and established the upper conductivity limit of a cone jet at
10
−
1
S/m [26]. In 1999, Hartman et al. developed a model to calculate the shape of a cone jet [27].
This model is also capable of calculating surface charge density and the values of the electric fi eld
both inside and outside the cone jet.
The electric current of the electrospraying system can be calculated from the developed model.
In particular, Tang et al. experimentally defi ned the stability of the cone jet in the voltage-liquid
fl ow rate (
V
Q
) plane in 1994 [28]. For a given liquid, the voltage and the liquid fl ow rate are the
two primary independent variables. In 1994, Fernandez et al. studied the electric current and the
cone-jet droplet size based on the liquid properties, the fl ow rate of the solution, the electric poten-
tials, and the confi guration of the system [29]. They established the following equation to describe
the relationship coupling the electric current
I
of the electrospraying with the fl ow rate of solution
Q
and the physical properties of the solution:
-
fl
(
ε
)(
γQK
/
ε
)
1/2
I
=
(11.2)
where
K
is the electrical conductivity of the solution,
ε
the relative permittivity of the solution,
γ
the
surface tension of the solution, and the function
fl
(
ε
) is experimentally determined.
In 1997, Gañán et al. carried out an experimental measurement of the current and the size of the
primary droplets by electrospraying a variety of liquids with different electrical conductivities, sur-
face tension, permittivities, densities, and viscosities [30]. They derived scaling laws for the spray
currents as well as the charges and sizes of the droplets based on a theoretical model of charge trans-
port. Their results show that the current and size of the droplets generated through electrospraying
solutions with higher viscosity and conductivity exhibit different behavior from those liquids with
lower viscosity and conductivity. These experimental results fi t theoretical predictions very well.
The separation between both behaviors is governed by the dimensionless parameters determined by
the liquid viscosity, conductivity, and surface tension of the solution:
γ
3
ε
2
1/3
[
]
______
D
=
µK
2
Q
(11.3)
where
γ
is the liquid surface tension,
ε
0
the permittivity of the vacuum,
µ
the liquid viscosity,
K
the
liquid electrical conductivity, and
Q
the liquid fl ow rate. Gañán found a square root dependence of
