Biomedical Engineering Reference
In-Depth Information
The dimensionless electrical voltage
V
[
ε
0
/(
γd
0
)
1/2
] is related to the Taylor's number
V
[
ε
0
/(
γd
n
)
1/2
].
Experimental results have shown that the current of droplets increased with an increase of applied
voltage, while the droplet size decreased [30]. For a given fl ow rate, the range of the applied poten-
tial
V
is relatively narrow for cone-jet mode electrospraying. Lower and higher applied voltages
will result in single-jet and multijet spraying modes, respectively. The effect of applied voltage on
the cone-jet spraying characteristics is therefore very small, and the impact of Talyor's number can
consequently be ignored in these equations.
Based on the principle of mass conservation, the particle size has a direct relationship with the
droplet size generated through electrospraying, and thus the relationship among the fi nal solid spher-
ical particle size
d
p
, the initial droplet size
d
, and the weight concentration of solid materials in the
solution
w
is given by Equation 11.13 [42]. It can be concluded that the particle size decreases with a
decrease of solution concentration. The droplet diameter can be obtained through Equation 11.13:
(
ρ
s
w
1/3
_______________
)
d
p
=
w
)
d
3
(11.13)
ρ
s
w
+
ρ
p
(1
−
where
ρ
s
and
ρ
p
are the densities of the solvent and the solid materials, respectively.
11.2. 5 T
HEORY
D
ESCRIPTION
AND
M
ODELING
11.2.5.1
Physical Model of Liquid Cone Jet
It is known that a liquid droplet is atomized under a strong electrical fi eld, which induces a free
charge and electric stress on the liquid surface. Hartman et al. [27,43] proposed the following physi-
cal-numerical model to investigate the infl uence of the processing parameters and the liquid proper-
ties on the cone shape and the size and charge of the electrosprayed droplets. The forces that are taken
into account in the model are shown in Figure 11.5. The shape of the liquid cone can be calculated by
solving the Navier-Stokes equation in one dimension, assuming an antisymmetric and steady-state
situation. In Equation 11.14, the change in potential energy (pressure
p
liq
, gravitation
p
g
) and kinetic
energy
p
Ekin
(velocity pressure) is balanced with the energy input from the tangential electric stress
τ
Et
, the change in polarization stress
σ
ε
,
and the energy dissipation due to the viscous stresses in the
liquid
σ
µ
,
τ
µ
.
The tangential and normal electric stresses, surface tension, and pressure in the liquid
cone mainly determine the shape of the liquid cone:
∂(
p
Ekin
+
p
liq
−
σ
µ
−
σ
ε
−
p
g
)
2
_______________________
__
∂z
=
r
s
(
τ
µ
+
τ
Er
)
(11.14)
where
p
liq
=
Δ
p
s
.
The Equation 11.14 can be fully expressed in the substituted forms as follows:
p
out
+
Δ
p
n,µ
+
Δ
p
En
+
(
2
µ
∂
__
3
µ
∂
__
(
u
z
u
z
)
∂
z
d
r
s
)
2
C
p
ρ
__
1
1
__
__
___
___
___
∂
u
z
2
+
p
−
∂
z
−
2
ε
0
(
ε
r
−
1)(
E
n,t
2
+
E
t
2
)
-
ρgz
d
z
________________________________________________
2
__
_________
1
∂
z
=
r
+
E
t
σ
(11.15)
(
d
r
s
2
)
___
+
d
z
(
γ
d
2
r
s
d
r
s
2
)
____
___
µ
∂
__
d
z
2
2
d
z
−
1
u
z
γ
__________
____
_______
_
_____
____________
p
=
∂
z
+
−
(
(
(
d
r
s
(
(
2
d
r
s
2
1/2
d
r
s
2
3/2
)
)
)
)
)
___
___
___
d
z
+
1
r
s
1
+
d
z
1
+
d
z
(11.16)
1
__
−
2
ε
0
(
E
n,o
2
−
2
ε
r
E
n,i
2
+
E
n,i
2
)
