Environmental Engineering Reference
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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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