AEROSOLS 23
air at atmospheric pressure and room temperature. There
exist distinct maxima in the coagulation coefficient in the
size range from 0.01 m m to 0.01 m m depending on particle
diameter. For a particle of 0.4 m m diameter at a number con-
centration of 10^8 particles/cm^3 , the half-life for Brownian
coagulation is about 14 s.Kelvin Effectp d / p in Figure 3 indicates the ratio of the vapor pressure over
a curved droplet surface to that over a flat surface of the same
liquid. The vapor pressure over a droplet surface increases with
a decrease in droplet diameter. This phenomenon is called the
Kelvin effect and is given by Eq. (3.8). If the saturation ratio
of water vapor S surrounding a single isolated water droplet
is larger than p d/ p , the droplet grows. If S < p d / p , that is,
the surrounding saturation ratio lies below the curve p d / p in
Figure 3, the water droplet evaporates. Thus the curve p d / p in
Figure 3 indicates the stability relationship between the drop-
let diameter and the surrounding vapor pressure.Phoretic PhenomenaPhoretic phenomena refer to particle motion that occurs
when there is a difference in the number of molecular colli-
sions onto the particle surface between different sides of the
particle. Thermophoresis, photophoresis and diffusiophore-
sis are representative phoretic phenomena.
When a temperature gradient is established in a gas, the
aerosol particles in that gas are driven from high to low tem-
perature regions. This effect is called thermophoresis. The
curve v th in Figure 3 is an example (NaCl particles in air) of
the thermophoretic velocity at a unit temperature gradient,
that is, 1 K/cm. If the temperature gradient is 10 K/cm, v th
becomes ten times higher than shown in the figure.
If a particle suspended in a gas is illuminated and non-
uniformly heated due to light absorption, the rebound of gas
molecules from the higher temperature regions of the par-
ticle give rise to a motion of the particle, which is called
photophoresis and is recognized as a special case of thermo-
phoresis. The particle motion due to photophoresis depends
on the particle size, shape, optical properties, intensity and
wavelength of the light, and accurate prediction of the phe-
nomenon is rather difficult.
Diffusiophoresis occurs in the presence of a gradient of
vapor molecules. The particle moves in the direction from
higher to lower vapor molecule concentration.OPTICAL PHENOMENAWhen a beam of light is directed at suspended particles, vari-
ous optical phenomena such as absorption and scattering of
the incident beam arise due to the difference in the refrac-
tive index between the particle and the medium. Optical
phenomena can be mainly characterized by a dimensionless
parameter defined as the ratio of the particle diameter D p to
the wavelength of the incident light l,a pD p / l. (24)Light ScatteringLight scattering is affected by the size, shape and refractive
index of the particles and by the wavelength, intensity, polar-
ization and scattering angle of the incident light. The theory
of light scattering for a uniform spherical particle is well
established (Van de Hulst, 1957). The intensity of the scat-
tered light in the direct u (angle between the directions of the
incident and scattered beams) consists of vertically polarized
and horizontally polarized components and is given asII
r 0 ii28 2212l
p() (25)where I 0 denotes the intensity of the incident beam, l the
wavelength and r the distance from the center of the particle,
i 1 and i 2 indicate the intensities of the vertical and horizontal
components, respectively, which are the functions of u, l,
D p and m.
The index of refraction m of a particle is given by the
inverse of the ratio of the propagation speed of light in a
vacuum k 0 to that in the actual medium k 1 as,m k 1 / k 0 (26)and can be written in a simple form as follows:m n 1 in 2. (27)The imaginary part n 2 gives rise to absorption of light, and
vanishes if the particle is nonconductive.
Light scattering phenomena are sometimes separated into
the following three cases: (1) Rayleigh scattering (molecu-
lar scattering), where the value of a is smaller than about 2,
(2) Mie scattering, where a is from 2 to 10, and (3) geo-
metrical optics (diffraction), where a is larger than about 10.
In the Rayleigh scattering range, the scattered intensity is
in proportion to the sixth power of particle size. In the Mie
scattering range, the scattered intensity increases with parti-
cle size at a rate that approaches the square of particle size as
the particle reaches the geometrical optics range. The ampli-
tude of the oscillation in scattered intensity is large in the
forward direction. The scattered intensity greatly depends on
the refractive index of the particles.
The curve denoted as pulse height in Figure 3 illustrates
a typical photomultiplier response of scattered light from a
particle. The intensity of scattered light is proportional to
the sixth power of the particle diameter when particle size is
smaller than the wavelength of the incident light (Rayleigh
scattering range). The curve demonstrates the steep decrease
in intensity of scattered light from a particle.Light ExtinctionWhen a parallel beam of light is passed through a suspen-
sion, the intensity of light is decreased because of the scat-
tering and absorption of light by particles. If a parallel lightC001_002_r03.indd 23C001_002_r03.indd 23 11/18/2005 10:09:12 AM11/18/2005 10:09:12 AM