Environmental Engineering Reference
In-Depth Information
17.4.3 M
odel
F
ilters
oF
u
ltraFine
F
ibers
The iber diameter 2
a
for modern iltering materials made from polymer and glass ibers and for the
best specimens of membrane ilters is comparable to the mean free path of air molecules λ under
normal conditions (approximately 70 nm). Gas low through such ilters is seriously affected by the
so-called gas sliding along the surface of so thin ibers. Due to this phenomenon pressure drop on
the ilter decreases with decreasing
а
(increase in the Knudsen number,
Kn
= λ/
a
), the low veloc-
ity being constant. Eficiency of aerosol particle deposition increases. It is usually assumed, while
describing gas low in the vicinity of thin ibers, that tangential low velocity
U
on the iber surface
is not zero. At α <<1 and
Kn
<< 1 allowing gas sliding gives the equation for low function in the
linear approximation according to the Knudsen number (Figure 17.7) [25]:
⎡
⎢
⎤
⎥
1
2
1
⎛
⎜
1
⎞
⎟
Ψ =
− +
r
2
r
ln
r
+
2
τ
Kn r
−
sin
θ
k
r
r
where
k
1
=
k
+
τ
Kn
(17.17)
0
Dimensionless drag force, applied to the iber unit length, can be presented as
F
= 4π/
k
1
. Numerous
experiments showed that the linear relationship between 1/
F
and
Kn
is still in force at
Kn
> 1 for
iltering materials with both identical and polydisperse ibers (polydispersity degree being not high)
[66]. The linear relationship between 1/
F
and
Kn
up to the values
Kn
= 3 was obtained in experi-
ments with model ilters (grids with wire diameter 8.9 μm). The slope ratios of this relationship let
determine the value τ ≈ 1.15 [67], which is in conformity with the theoretical value τ = 1.147 [68].
The linear relationship between 1/
F
and
Kn
for dilute gas low is in force even at high temperature
up to 500°C [69]. It should be noted that the linear relationship between 1/
F
and
Kn
for dilute gas
low through loose porous medium at
Re
<< 1 and
Kn
∼ 1 was considered so far as an experimental
FIGURE 17.7
Photograph of a layer of luoropolymer ibers with mean diameter 90 nm obtained by electro-
spinning. (From Kirsh, V.A. et al.,
Colloid J
., 70(5), 547, 2008.)
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