Filtration and Sampling of Aerosols by Fibrous Filters - Aerosols: Measurement, Dosimetry, and Health Effects - page 447

The results of this research appeared to be in good conformity with recent theoretical research
[45-47], respectively.
Model ilters of parallel ibers were used to study deposition of nanoparticles [48]. No deposition
mechanisms except the diffusive one are to be considered while calculating nanoparticle deposi-
tion. No demands are laid down concerning nanoparticles nature because their diffusivity does not
depend on density. Apparently, this fact may be the reason for the phenomenon of particle diffusive
deposition to be the most studied.

17.4.2 D iffusive D eposition oF P articles in M odel F ilters
First works on point particle deposition in model ilters were performed by Fuchs and Stechkina
[49]. They obtained the diffusion capture coeficient from the solution of the equation for convective
diffusion:

(17.11)

− 1 3 / − 2 3 /

η D = 2 9 . k Pe

0

Later Stechkina [50] reined this equation:

(17.12)

− 1 3 / − 2 3 / − 1

η = 2 9 . k Pe + 0 624 . Pe

where

= 4π

(17.13)

k

F

Calculation results appeared to be in good conformity with experimental ones on deposition of
nanoparticles sized 1.5-7 nm in model hexagonal structure ilters [7]. Although calculation of diffu-
sive deposition is based on the theory of boundary layer applicable when Ре >> 1, good conformity
with experiment was obtained up to Ре ∼ 2 and η ∼ 1. Conformity with experiment for loose [7] and
dense [51] models permitted applying the relationship η ∼ Ре −2/3 to solving the inverse problem—
obtaining particle diffusion coeficient based on their penetration through iber systems with known
geometry and at known velocity [52-55].
Both theoretical and experimental results in papers [48,56-59] show the existence of geometrical
limitation for the capture coeficient in the system of parallel cylinders at low Peclet numbers. At
Ре << 1 the capture coeficient is described by the equation [59]:

− 1

⎛

∞

⎞

2 π Pe mPeh

a

⎛
⎜

⎞
⎟ + ∑

⎛
⎜

⎞
⎟

(17.14)

η = K 2 K

⎜ ⎟

0 0

Pe 4 2

⎝ ⎠

m = 1

where K 0 ( z ) is the modiied Bessel function. Calculation results as per Equations 17.11 and 17.14
aligned exactly with both the experiments for nanoparticles [48] at a/h << 1, Re << 1, Pe >> 1 and
Pe << 1 and direct numeric calculations [56] (Figure 17.6).
It lows out from the data in Figure 17.6 that the calculated curves for η( Ре ) for each a/h when
Ре → 0 transform into straight lines parallel the X -axis, the capture coeficient being constant,
η → h/a . It can be seen that the denser the grids are, the higher the Ре 's are when the curves reach
the plateau η = h/a . At a/h << 1 in the area of Ре < 1 there can be seen matching with the curve 5
calculated as per (17.14) for the limiting capture coeficient. Conformity with experiment at a/h << 1
can be seen for the wide range of the Pe numbers.