Page 146 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 3 CHARACTERISTICS AND BEHAVIOR OF NANOPARTICLES AND ITS DISPERSION SYSTEMS

Direction of temperature or concentration gradient

Collision of molecules Collision of molecules
with small velocity or mass Particle with large velocity or mass
(small momentum) (large momentum)

Direction of particle motion
Figure3.2.1
Mechanisms of phoretic motion of particles in gas phase.

particle deposition onto cooled surfaces, its impor- Fig. 3.2.2 shows the dependence on particle size d p
tance has been pronounced in the fields involving par- of the thermophoretic velocity v derived from equa-
T
ticle collectors equipped with cooled plates, scaling tion (3.2.22). For particles in air under normal condi-
phenomena in heat exchangers, electrical and optical tions and smaller than about 0.5 m in diameter, v is
T
material manufacturing process by particle deposition, almost independent of d and is expressed by equation
p
particulate contamination control and so on. (3.2.21). However, for larger particles, a temperature
When particle size (d ) is much smaller than the distribution can be formed inside the particle, and v T
p
mean free path of gas molecules ( ), in which case the exhibits a dependence on the d and thermal conduc-
p
particle–gas system is called the free molecular tivity of the particles. Furthermore, as shown in the fig-
regime (Knudsen number: Kn 2 /d 1), and heat ure, the v of particles less than 0.1 m in diameter is
T
p
transfer is governed by conduction and convection higher than the gravitational settling velocity in the
and not by radiation, the particle velocity vector by presence of the temperature gradient dT/dx 100 K/m.
thermophoresis, v , is given as [1, 2] The phenomenon by which particles irradiated by
T
light move in the direction of the light source is called
T photophoresis. Light absorption by a particle leads to
v 055 , (3.2.21)
.
T
T the formation of a temperature distribution in the par-
ticle. Photophoresis is induced by a temperature gra-
where v and T are the kinetic viscosity and tempera- dient of the gas surrounding the particle having such
ture of the gas, respectively. Equation (3.2.21) indi- a temperature distribution. Thus, one can consider
cates that particles move from a high-temperature photophoresis as a special case of thermophoresis.
region to a low-temperature region and that ther- Equations similar to equation (3.2.22) have been pro-
mophoretic velocity depends on temperature gradient, posed for photophoretic velocity. However, the
not on particle size. expression of photophoretic velocity is very compli-
On the other hand, for a wide range of conditions cated and depends on the refractive index of particles
including the continuum regime characterized by and the wavelength of light as well as Knudsen num-
Kn 1, the next equation was proposed considering ber because the increase in particle temperature is
the temperature gradient inside a single particle and a influenced by the light absorption property of parti-
non-zero gas velocity on the particle surface [3, 4]. cles [5]. Moreover, it is also difficult to determine the
association between the temperature distributions
234(
218Kn )C T inside and the surroundings of the particle.
.
.
v C
T (3.2.22) Generally, photophoretic velocity reaches its maxi-
1 ( 3 42Kn )( 1 2
4 36Kn ) T
.
.
mum if the particle diameter and light wavelength are
comparable. For particles with a high light
Here,
is the ratio of thermal conductivity of the gas absorbance, particles move in the direction away from
to that of the particle, and C the Cunningham’s cor- the light source because the temperature of the parti-
C
rection factor. cle surface on the irradiated side is higher than that on
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