Encyclopedia of Environmental Science and Engineering, Volume I and II

24 AEROSOLS

beam of intensity I 0 is applied to the suspension, the intensity

I at a distance l into the medium is given by,

I  I 0 exp( gl ) (28)

where g is called the extinction coefficient,

g∫ 0 CnD Dext ()ppd

∞

(29)

n ( D p ) is the number distribution function of particles, and

C ext is the cross sectional area of each particle.

For a spherical particle, C ext can be calculated by the Mie

theory where the scattering angle is zero. The value of C ext

is also given by

C ext  C sca 
 C abs (30)

where C sca is the cross sectional area for light scattering and

C abs the cross sectional area for light absorption. The value of

C sca can be calculated by integrating the scattered intensity I

over the whole range of solid angles.

The total extinction coefficient g in the atmosphere can

be expressed as the sum of contributions for aerosol particle

scattering and absorption and gaseous molecular scattering and

absorption. Since the light extinction of visible rays by polluted

gases is negligible under the usual atmospheric conditions and

the refractive index of atmospheric conditions and the refrac-

tive index of atmospheric aerosol near the ground surface is

(1.33 ∼ 1.55)  (0.001 ∼ 0.05) i (Lodge et al., 1981), the extinc-

tion of the visible rays depends on aerosol particle scattering

rather than absorption. Accordingly, under uniform particle

concentrations, the extinction coefficient becomes a maximum

for particles having diameter 0.5 m m for visible light.

VISIBILITY

The visible distance that can be distinguished in the atmo-

sphere is considerably shortened by the light scattering and

light extinction due to the interaction of visible light with

the various suspended particles and gas molecules. To evalu-

ate the visibility quantitatively, the visual range, which is

defined as the maximum distance at which the object is just

distinguishable from the background, is usually introduced.

This visual range is related to the intensity of the contrast C

for an isolated object surrounded by a uniform and extensive

background. The brightness can be obtained by integrating

Eq. (28) over the distance from the object to the point of

observation. If the minimum contrast required to just dis-

tinguish an object from its background is denoted by C * , the

visual range L v for a black object can be given as

L v  (1/ g )ln( C * ) (31)

where g is the extinction coefficient. Introduction of the

value of 0.02 for C * gives the well known Koschmieder

equation,

L v  3.912/ g (32)

For aerosol consisting of 0.5 m m diameter particles ( m 

1.5) at a number concentration of 10^4 particles/cm^3 , the

extinction coefficient g is 6.5 10 ^5 cm and the daylight

visual range is about 6.0 10 4 cm (0.6 km). Since the

extinction coefficient depends on the wavelength of light,

refractive index, aerosol size and concentration, the visual

range greatly depends on the aerosol properties and atmo-

spheric conditions.

MEASUREMENT OF AEROSOLS

Methods of sizing aerosol particles are generally based upon

the dynamic and physical properties of particles suspended

in a gas (see Table 4).

Optical Methods

The light-scattering properties of an individual particle are a

function of its size, shape and refractive index. The intensity of

scattered light is a function of the scattering angle, the inten-

sity and wavelength of the incident light, in addition to the

above properties of an individual particle. An example of the

particle size-intensity response is illustrated in Figure 3. Many

different optical particle sizing devices have been developed

based on the Mie theory which describes the relation among

the above factors. The principle of one of the typical devices

is shown in Figure 7.

The particle size measured by this method is, in most

cases, an optical equivalent diameter which is referred to a

calibration particle such as one of polystyrene latex of known

size. Unless the particles being measured are spheres of

known refractive index, their real diameters cannot be evalu-

ated from the optical equivalent diameters measured. Several

light-scattering particle counters are commercially available.

Inertial Methods (Impactor)

The operating principle of an impactor is illustrated in

Figure 8. The particle trajectory which may or may not col-

lide with the impaction surface can be calculated from solv-

ing the equation of motion of a particle in the impactor flow

field. Marple’s results obtained for round jets are illustrated

in Figure 8 (Marple and Liu, 1974), where the collection

efficiency at the impaction surface is expressed in terms of

the Stokes number, Stk, defined as,

Stk

CDu

W

u

W

pc p



r

m

t

2

(^00)
18 ( ⁄⁄ 2 ) 2
(33)
where
t
r
m

ppcDC
2
18
(34)
C
DD
D
c
pp
p

1 2 514.

ll
l
0.80 exp 0.55
⎛
⎝⎜
⎞
⎠⎟
(35)
C001_002_r03.indd 24C001_002_r03.indd 24 11/18/2005 10:09:12 AM11/18/2005 10:09:12 AM