Theory of Operation
B–7
Table B-3
Coefficients for Equation B-4
a
i
(N)
N=-2
N=-1
N=0
N=1
N=2
a
o
-26.3328
-2.3197 -0.0003 -2.3484 -44.4756
a
1
35.9044
0.6175 -0.1014 0.6044 79.3772
a
2
-21.4608
0.6201 0.3073 0.4800 -62.8900
a
3
7.0867 -0.1105 0.3372 0.0013 26.4492
a
4
-1.3088 -0.1260 0.1023 -0.1553 -5.7480
a
5
0.1051 0.0297 -0.0105 0.0320 0.5049
For the fraction of particles carrying three or more charges, use
Equation B-5 which is based on an derivation by Gunn from 1956.
2
0
2
2
0
0
2
2
2
ln
2
exp
4
)
(
e
kT
D
Z
Z
e
kT
D
N
kT
D
e
N
f
p
i
i
p
p
πε
πε
ε
π
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−
=
−
+
Equation
B-5
where:
e
= elementary charge
= 1.60217733E-19 coulomb
ε
0
= dielectric constant
= 8.854187817E-12 farad/m (for air)
D
p
= particle diameter [m]
k
= Boltzmann’s constant
= 1.380658E-23 joule/K (for air)
T
= Temperature [K]
N
= number of elementary charge units
Z
i+
/Z
i-
= ion mobility ratio
= 0.875 (Wiedensohler)
A i r a n d C O
2
F l o w C o n t r o l
This section describes the flow of air and CO
2
through the
Electrospray. A flow schematic is shown in Figure B-3.
