Biomedical Engineering Reference
In-Depth Information
Electrode configuration
Assumed cone shape
Liquid velocity cone surface
Current balance inside the cone
Numerical calculation electric field
No
Converged?
Yes
No
Third time converged?
Yes
Cone shape calculation
No
Cone shape converged?
Yes
FIGURE 11.6 Flowchart of calculation for liquid cone-jet shape. (Reprinted from Hartman, R.P.A. et al.,
J. Aerosol Sci. , 30, 823, 1999. © Elsevier Science. With permission.)
where p, z, r s , u z , C p , σ are the pressure, the axial coordinate for the cylindrical coordinate system,
the radial distance of the liquid-air interface from the axis, the liquid velocity in the axial direc-
tion, a correction factor for the radial velocity profi le inside the liquid, and surface charge. E t is the
electric fi eld tangential to the liquid-air surface, and E n,i and E n,o are the electric fi elds normal inside
and outside the liquid cone.
Electric fi eld strengths, surface charge, and radial velocity profi le inside the liquid cone must
be known to solve the equations. The electric fi elds inside and outside the liquid can be numerically
calculated using Gauss' law through Equations 11.17 through 11.19. Surface charge can be known
from the liquid velocity and the current balance at the liquid-air interface. The one-dimensional
Navier-Stokes equation is then used to calculate the new cone shape, which will be used as input
for the new electric fi eld and surface charge calculations. These calculations are repeated until the
input and the output cone shapes have converged. Figure 11.6 shows a schematic representation of
the cone-shape calculation method.
∂( r s u z , s σ )
(
(
d r s
2
1/2
)
)
________
___
z
=
Kr s E n,i
1
+
d z
(11.17)
(
1
__
)
2 ρu z 2
(
r u z
)
r
μ 1
__
__
___
________
r
r
=
z
(11.18)
 
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