Filtration and Sampling of Aerosols by Fibrous Filters - Aerosols: Measurement, Dosimetry, and Health Effects - page 445

ibers; in this case rows reciprocal action disappeared. Hydrodynamic resistance of rows did not
depend on the Reynolds number, but was deined by the value a/h , which is the ratio of the iber
diameter and the distance between ibers in the row.
Analytical solutions for F both for dense and rareied rows were obtained earlier. Keller was
the irst to determine the iber drag force at a/h → 1 using the approximation of the hydrodynamic
lubrication theory [33]:

9
2 2

π 1

(17.9)

F =

5 2 /

( 1 − a h / )

The Miyagi equation appeared to be applicable to the rareied row [34]:

− 1

⎛
⎜

2
3

1
9

8
135

53
1350

⎞
⎟

2 4 6 8

F = 8 π 1 2 − ln 2 t + t − t + t − t + (17.10)

where t = π a /2 h . Figure 17.3 shows comparison of the iber drag force F ( a/h ) (point 1) [35] and the
curves based on Equations 17.9 and 17.10.
The separate row model was used to investigate the effect of the iber cross-sectional shape on
low resistance and particle deposition. Papers [36,37] show that band-type ibers with dumbbell-
shaped cross section obtained by electrospinning (Figure 17.4) can be approximated as elliptical
cross-sectional ones or as a couple of doubled ibers. As calculations showed the dumbbell jumper
dimension does not affect the iber drag force.
Figure 17.5 shows the comparison of the drag force for different ibers having the same middle
cross section with the drag force of the ibers couple. It should be noted that calculation data for the
range of elliptic ibers aligned with the analytical solution in another Kuwabara paper [38].
The effect of nonuniformity in ibers arrangement and their polydispersity on the low resistance
at Re << 1 and on particle deposition was investigated on a separate row of parallel ibers [25].

10 4

3

10 3

F

10 2

4

10

-1
-2

1

0 0.2 0.4 0.6 0.8 1

ah -1

FIGURE 17.3 Dimensionless iber drag force versus lattice spacing: 1, numerical modeling (From Kirsh,
V.A., Colloid J ., 68(3), 261, 2006.); 2, experiment (From Kirsch, A.A. and Fuchs, N.A., Ann. Occup. Hyg ., 10,
23, 1967.); 3, Equation 17.9; 4, Equation 17.10.