Environmental Engineering Reference
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fact. It is only recently that this fact has been validated [70]. The research in this paper uses methods
of gas kinetic theory, developed for analyzing transfer processes in porous media. The approximat-
ing calculation equation for the dimensionless resisting force in this range of packing densities looks
as follows:
τ α
π
f
(
)
Kn
−
1
−
1
F
=
F
+
(17.18)
0
4
where τ
f
(α) = 1.27 − 3α. For a fan model ilter this value is equal to 1.43(1 − α) [66]. Deposition of
nondiffusing particles noticeably increases with the increase in the Knudsen number. When
R
<< 1
and α << 1 the capture coeficient is [4]
R
k
2
⎛
⎜
⎞
⎟
+
⎛
τ
Kn
R
⎞
⎟
η
=
1
(17.19)
⎜
R
1
when it follows that gas sliding in the vicinity of the iber surface effects signiicantly small particle
deposition irrespective of the iber diameter.
Diffusive deposition of point particles (
R
= 0) out of a thin boundary layer in the vicinity of a iber
(thickness δ = (2
k/Pe
)
1/3
<< 1) in a high-porous system of parallel cylinders with α << 1 was studied
in Ref. [25] at
Re
<< 1 and
Kn
<< 1. The relations obtained for the capture coeficient are as follows:
Kn
Pek
τ
(17.20)
η
= 3 2
.
D
1
for
Kn
> δ, and
1 3
/
2 9
1 0 55
+
.
Kn Pe k
Pe k
τ
(
/
)
1
η
=
.
(17.21)
D
/
(
2
)
1 3
1
for
Kn
< δ. If to take into account the particle inite size, as shown in Ref. [71], the numerically
calculated capture coeficients at
Kn
< 1 coincide with, and at
Kn
> 1 exceed the interception and
diffusion capture coeficients obtained analytically in the approximation
Kn
<< 1. These results are
conirmed in Ref. [72].
There has not been an experimental check of particle deposition in model ilters with known
parameters as function of
Kn
performed, although the calculated values of η
R
and η
D
are in good
qualitative conformity with the data obtained for real ilters (Figure 17.8).
As mentioned earlier, the deposition of particles of inite size is affected by the dispersion forces
(van der Waals forces) [73]. Particle deposition is explicitly studied in Refs [74-77], depending on
surface curvature of ibers and gas sliding. It is shown that the particle deposition on ibers due to
the van der Waals attraction can contribute about 15% to the overall capture coeficient (Figure
17.9). Paper [78] presents the calculated capture coeficient as a function of particles size and den-
sity, angle between the vectors of gravity force and low velocity before the ilter. It is established
that the radius of the most penetrating “heavy” particles for the down coming low appears to be
smaller than for the rising one.
17.4.4 P
articles
oF
tHe
M
ost
P
enetrating
s
ize
For
n
anoFibrous
F
ilters
As mentioned earlier, the most dificult task in the theory of iltration with high performance thin
iber ilters is to describe deposition under the worst conditions, that is, in the area of maximal
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