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414 13 Nanoaerosol
2
E ad ¼ Dcpa
Then the critical speed and impact speed are calculated using
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
12E ad 48kT
v cr ¼ 3 2 ; v im ¼ 2 3
pq d e p q d
p p
p p
Then the adhesion efficiency is determined by
2 v cr 2z 2
z ¼ p ffiffiffi ; g ¼ erf zðÞ p exp z
ad
ffiffiffi
p v im p
In calculation using spread sheet, the error function is approximated with
1
erf zðÞ 1
2 3 4 4
ð1 þ a 1 z þ a 2 z þ a 3 z þ a 4 z Þ
where a 1 = 0.278393, a 2 = 0.230389, a 3 = 0.000972, and a 4 = 0.078108.
The results are shown in Fig. 13.7 in terms of penetration efficiency.
100%
Conventional Filtration
90% Efficiency
Thermal rebound: DMT
80%
Penetration efficiency 60%
70%
50%
40%
30%
20%
10%
0%
1 10 100
Particle Diameter (nm)
Fig. 13.7 Calculated penetration efficiency using DMT model
