Environmental Engineering Reference
In-Depth Information
TABLE 17.1
Diffusion Coeficients of Aerosol Particles in 
Air, Pressure 1 atm Temperature 20°C
D  ( μ m)
0.01
0.1
0.5
1
D (cm 2 /s)
5.31E-04
6.84E-06
6.31E-07
2.76E-07
Source: Fuchs, N.A., The Mechanics of Aerosols , Pergamon
Press, Oxford, U.K., 1964.
Re = 2 aU /ν is the Reynolds number
ν is the gas kinematic viscosity
G = U G / U is the sedimentation parameter
U G is the particles setting velocity
F i is the dimensionless parameter, characterizing particle deposition due to external forces
Research of particle deposition in the area of the highest penetration (the worst particle deposition)
is the major task. It is necessary to take into account the particle's own size and electrostatic and
van der Waals forces. Joint action of all iltration mechanisms should be regarded in the area of the
highest penetration. For nonstationary iltration calculations of particle deposition turn out to be
even more complicated, the advance of the theory being signiicantly slowed down by the absence
of experimental works containing all the necessary quantitative data.
First, theoretical works on particle deposition on ilter ibers were based on the low ield in
the vicinity of a separate cylinder [1]. However, quantitative correspondence between theoretical
calculations and ilters experimental data was out of the question. First, because the low ield in the
vicinity of a separate iber is determined by Re , whereas the low ield in the ilter is independent
of the Reynolds number. Second, the measured values of F and η for different ilters vary several
times [25]. Because of a complicated microstructure of the ibrous iltering materials and hence
complicated low in them, it was necessary to use ibrous ilter models.
17.4 
MODELING FILTRATION PROCESSES
17.4.1  H ydrodynaMic  r esistance oF  P arallel  F iber  M odel  F ilters
A system of parallel cylinders perpendicular to the low direction was assumed as the simplest
model of a ibrous ilter [5-7]. As distinct from the Lamb low ield for a separate cylinder, the
low function for a system of cylinders in Stokes approximation does not depend on the Reynolds
number, but is deined by α, the packing density of the system. The low ield in such a system
was obtained with the help of the Kuwabara cell model [31]. The value of the resisting force for
the range of α 0.0043-0.27, experimentally obtained in Ref. [6], corresponded directly to the
equation
4
π
(17.8)
2
1
F
=
=
4
π
(
0
.
5 ln
α
0
.
75
+ −
α
0
.
25
α
)
k
0
The results of measurements for the low ield and resistance for a hexagonal model were theoretically
proved in Refs [31,32]. The simple view of the Kuwabara low function made this model popular.
It became the basis for estimating particle deposition on ibers. While studying deposition of larger
particles the iber rows were drawn apart to exclude the inluence of the diffusive trace behind the
 
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