Filtration and Sampling of Aerosols by Fibrous Filters - Aerosols: Measurement, Dosimetry, and Health Effects - page 458

for particles with density ρ = 1 g/cm 3 for the Stokes low ield and for the low ield at Re ∼ 1. The
solid curves 1 and 3 are calculated with due consideration of air low inertia under normal condi-
tions, dotted curves—for the Stokes low ield. As is clear from this data, discrepancy between
block and dotted curves for high values of the interception parameter ( R = 0.2-0.4) in the range
of the Stokes number 0.7-10 is insigniicant. Absolutely different picture can be observed in the
case of smaller particles, that is, low interception parameters R . Discrepancy between block and
dotted curves takes place at lower Stokes numbers, in the area of St ∼ 1 the capture coeficients
difference is more than 10 times particularly for the case with R ∼ 0.1 at Re ≈ 1. Moreover, solid
curves intersect because for the identical St smaller particles have higher velocity ( Rе increases).
Thus, it can be seen that taking into account real low ield at Re ∼ 1 affects signiicantly the value
of η. In this case the capture coeficient depends, as mentioned earlier, not only on St and R but
also on the Reynolds number. The Reynolds number magnitude is different in every part of the
curve. In the end it should be noted that here and now empiric relations based on the performed
experiments have to be used to calculate the ibrous ilters eficiency in the inertia particles
capture area as yet .
17.9 REBOUND OF PARTICLES
The questions connected with nonstationary iltration are important for selecting duration and
velocity of sampling while aerosol monitoring. Sampling velocity is limited by the increase in par-
ticles rebound from ibers and, connected with it, decrease in inertia capture eficiency. Duration is
determined by dynamics of the deposit accumulation on ilter ibers.
A particle touching a iber is held on it due to the van der Waals forces. Their magnitudes depend
on the particle and iber composition, shape and surface as well as on a range of other factors. Force
values can vary several orders of magnitude even for a uniform system.
Aerosol particle energy, which it possesses after collision, may be suficient to overcome adhe-
sion energy. The latter can vary at collision (e.g., due to the particle distortion). Apparently, there
exists a certain velocity above which the collision of a particle with a iber becomes ineffective.
There is no quantitative theory that allows predicting a decrease in the capture coeficient of
aerosol particles due to rebound. We should note experimental works [107-109], which present stud-
ies on laws of behavior for polystyrene particles at their collision with lat surfaces. Paper [110] gives
a equation for probability of adhesion versus St , Re , and other parameters for spherical particles and
the case of van der Waals adhesion. The probability of adhesion decreases with the increase in the
particle size, velocity, and elastic properties and with reduction in the iber diameter. Calculations
were performed for a separate cylinder and they are in conformity with the experimental data for
quartz and parafin particles with diameters 3-20 μm up to velocity 1 m/s.
Correlation between adhesion and kinetic energy of the particle is found in Ref. [111]. The
calculation performed in the paper [111] with the help of the Kuwabara cell model showed the
existence of a strong dependence between the collision effectiveness and the Stokes number,
however, the data differ more than twice from the experiment. The similar results were obtained
in the work [112].
Experiments where the particles were observed to rebound from the surface of the FP ibers were
carried out in Ref. [104]. It was stated while testing material made of acetyl cellulose ibers with
diameters 5-7 μm that decrease of capturing eficiency of aerosol particles with diameter 0.8 μm
started at velocities higher than 5 m/s. Data on Figure 17.13 illustrate effect of rebound.
Experiments with copper dioxide and tungsten carbide aerosols showed the shift of velocity
corresponding to the maximal inertia capture coeficient to lower magnitudes with the particle size
increase. The results for latex particles rebound from polymer iber of FP material and from tung-
sten wires with the diameter 11 μm used to make fan-type models are described in Refs [113,114].