Theory of Operation B–13
The range of particle diameters removed from the Electrostatic
Classifier not only depends on particle electrical mobility. Knutson
[1975] determined the relationship between the particle electrical
mobility and the Classifier parameters. The relationship is given in
equation B-5.
=
1
2
ln
2
*
r
r
VL
sh
q
p
Z
π
Equation B-5
and the mobility bandwidth,
Z
p
, is:
Equation B-6
where:
Z
p
*
= set mobility (if q
a
= q
sh
then Z
p
= Z
p
*
)
q
a
= aerosol flow rate through the Classifier (q
s
+ q
p
;
monodisperse flow rate and the polydisperse flow rate)
q
sh
= sheath air flow rate (equal to excess air flow rate)
r
2
= outer radius of annular space
= 1.961 cm (for Long DMA)
= 1.905 cm (for Nano DMA)
r
1
= inner radius of annular space
= 0.937 cm (for Long DMA)
= 0.937 cm (for Nano DMA)
= average voltage on the inner collector rod (volts)
L = length between exit slit and polydisperse aerosol inlet
= 44.369 cm (for Long DMA
†
)
= 4.987 cm (for Nano DMA)
b = gap spacing between plates
Equations B-4 and B-5 can be combined to give an equation that
relates the particle diameter to collector rod voltage, number of
charges on the particle, Classifier flow rate, and geometry for the
Long DMA or Nano DMA:
Equation B-7
†
The length measurement is based on the geometrical value of the distance between the vertical midpoint of the
inlet slit and the midpoint of the exit slit. Traditionally, a value of 44.44 cm has been used. Kinney, et. al. [1991]
suggests using a value of 43.6 cm as an “effective length” to account for entrance and exit effects. TSI firmware
and software uses the value of 44.369 since this is a physically verifiable number.
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