Page 136 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

110 4 Properties of Aerosol Particles

4.5 Aerosol Particle Size Distribution

Although monodisperse particles are used in describing particles with a narrow size
distribution in nanoparticle manufacturing, threat agents and bioaerosols, most
engineers deal with polydisperse aerosol. Polydisperse aerosol is a group of par-
ticles with different sizes suspended in the air. In typical urban atmosphere, particle
3
8
7
concentration can reach as high as 10 –10 /cm ; their diameters can range from a
few nanometers to around 100 μm[22].
A great amount of literature shows that the size distribution of most polydisperse
aerosol particles is lognormal. To understand lognormal distribution, it is necessary
to revisit what we learned about normal distribution. Normal distribution is also
called Gaussian distribution. For a variate x with a mean of x and standard deviation
of σ, the normal probability fractional distribution function in the domain
−1\x\1 is described as
" 2 #
1 x x
fxðÞ ¼ p ffiffiffiffiffiffi exp p ffiffiffi ð4:48Þ
r 2p r 2

where fxðÞ 1: The corresponding cumulative distribution, which describes the
probability of the variable below certain value, is

1 u u
ð
;ðuÞ¼ fx\uÞ ¼ 1 þ erf p ffiffiffi ð4:49Þ
2 r u 2
where the error function is used to characterize the measurement errors. It is
described as

2 Z y 2
erf yðÞ ¼ p ffiffiffi exp z dz ð4:50Þ
p
0
An error function erf yðÞ is symmetric about its origin. For a quantity that is log-
normally distributed, its logarithm is governed by normal distribution by replacing
x with logx, x with logx and σ with logσ.
" #
2
1 logx logx
ð
f logxÞ ¼ p ffiffiffiffiffiffi exp p ffiffiffi ð4:51Þ
logr 2p 2lnr
For its specific applications to aerosol particles, the probability of the particle
number fraction can be described as

2
" #

1
logd p logd pg
f logd p ¼ p ffiffiffiffiffiffi exp p ffiffiffi ð4:52Þ
logr 2p 2lnr