Encyclopedia of Environmental Science and Engineering, Volume I and II

16 AEROSOLS

When particles, at total number concentration N, are

measured based on a certain characteristic diameter as shown

in Table 1 and the number of particles, d n, having diameters

between D p and D p 
 d D p are counted, the normalized par-

ticle size distribution f ( D p ) is defined as follows:

fD

N

n

p Dp

()

1d

d

, (1)

where

∫ 0 fD D()ppd ^1

∞

.^

The discrete analog which gives a size distribution histo-

gram is

fD

N

n

p Dp

()

1 



(2)

where  n is the particle number concentration between D p 

 D p /2 and D p 
  D p /2.

The cumulative number concentration of particles up to

any diameter D p is given as

FDppf D D f D D

D

ppD p

p

p

()∫∫() ()

′

0

dd′′ 1 ∞ ′

d

d

F

D

fD

p

 ()p. (3)

The size distribution and the cumulative distribution

as defined above are based on the number concentration of

particles. If total mass M and fractional mass d m are used

instead of N and d n, respectively, the size distributions can

then be defined on a mass basis.

Many particle size distributions are well described by

the normal or the log-normal distributions. The normal, or

Gaussian, distribution function is defined as,

fD

DD

p

p p

()

()

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟



1 

2 2

2

2

ps s

exp (4)

0.1 0.5 1 5 10 50

99.9

99

90

70

50

30

10

1

0.1

Dp ( m)

F = 84.13%

Dg Dg

NMD MMD

Dmode

Dh

D 1

Dv

D 2

D 3

D 4

number basismass basis

100-F (%)

σg

x 2.0

D 8

μ

FIGURE 1 Log-normal size distribution for particles with geo-

metric mean diameter of 1 μ m and geometric standard deviation

of 2.0. The different average particle diameters for this distribution

are defined in Table 2.

TABLE 1 (continued)

Measures of particle size

Definition of characteristic diameters

Physical meaning and corresponding

measuring method

thickness: t

volume: v

aerodynamic diam. diameter of the sphere having unit specific

gravity and having the same gravitational

setting velocity as that of a particle, Dae 

[18 mut/gCc]1/2, obtained by the same

methods as the above.

surface

area: s

electrical mobility equivalent

diam.

diameter of the sphere having the same

electrical mobility as that of a particle, De

= npeCc/3pmBe, obtained by electrical

mobility analyzer.

equivalent diffusion diam. diameter of the sphere having the same

penetration as that of a particle obtained

by diffusion battery.

equivalent light scattering

diam.

diameter of the sphere having the same

intensity of light scattering as that of a

standard particle such as a PSL particle,

obtained by light scattering method.

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