Filtration and Sampling of Aerosols by Fibrous Filters - Aerosols: Measurement, Dosimetry, and Health Effects - page 452

1

0.02 0.04 0.06 0.08 0.1

r

FIGURE 17.10 Function of the capture coeficients ratio in the area of maximal particles penetration. Curves,
theory; dots, experiment. (From Tamaru, S. et al., Development and application of ultra-high performance
luorocarbon polymer air ilter, Proceedings of 13th International Symposium on Contamination Control ,
September 16-20, 1996, The Hague, The Netherlands, ICCCS, Stouthart Communicatie, Waddinxveen, The
Netherlands, pp. 236-242, 1996.)

for practical calculations of analytical iltration to determine particle size with the help of simple
analytical equations according to the fraction of particles deposited on or penetrated through the il-
ter with known parameters and at known velocity. Experimental data available on particles penetra-
tion through high performance ilters consisting of ultraine ibers for which the Knudsen number
under normal pressure can achieve the value of the order of unity usually correspond to big capture
coeficients and small or medium Pe numbers.
The authors of the paper [26] used monodisperse latex aerosols as test ones; they found out that
the most penetrating particle radius r

p *

⊕ ⊕0 04 μm at the velocity 1.5 cm/s. Figure 17.10 shows
curves for relationship between the capture coeficients ratio η/η * (η * is the capture coeficient cor-
responding to the minimum on the curve η( r ), that is η

a .

= r p ) and the particle radius r p . Filtering
material iber dimensions plotted on the grid were obtained from microphotograph. Hence, the real
low velocity could be higher than 1.5 cm/s.
In Figure 17.10, the block curve was calculated for U = 1.5 cm/s, the point curve—for doubled
velocity. It can be seen from data in Figure 17.10 that the type of the relationship and the area of the
curves' minimum corresponding to r p * , agree with experiment, a better agreement being seen for
higher velocity. Thus, it is possible to evaluate on the basis of the advanced theory the location of
r p * and the type of the curve describing relationship between particles penetration and their radii for
ultra ine iber ilters even for high performance ilters with η ∼ 1.
Relatively simple models of parallel cylinders with the known low ield appeared to be useful
while studying various problems of the iltration theory, such as modeling of solid particles deposit
growth [79], growth of droplets on ibers [47], effect of external electric ield on particles capturing
eficiency [80], deposition of particles on porous ibers [81] and on ibers, covered porous shell [82],
inertial deposition of particles [83], etc.

* η ( * )

17.4.5 F an -t yPe M odeling F ilter
The ilter model with parallel ibers let us solve many problems in the theory of iltration. However,
the low ield in real ilters is 3D and is extremely hard to be determined. The closest in its qualities
and structure to the real ilters idea is a fan model ilter , where layers of parallel ibers are turned
relative each other through an arbitrary angle φ. The resisting force F f of the fan-type model equals
F of a stagger model whose packing density is 1.6 times lower [6]. This problem was not paid due
cognizance for a long time despite the importance of determining hydrodynamic drag force for