Influence of Filter Inhomogeneity on Air Filtration of Nanoparticles

Thermal rebound of nanoparticles on the surface of fibers is of big concern in collecting nanoparticles. Another factor influencing the collection of nanoparticles is the inhomogeneity of fiber packing. The present work studied the influence of filter inhomogeneity on the collection efficiency of nanoparticles by using wire screens as uniform structure in comparison to real filters. As a result, the single fiber collection efficiencies of nanoparticles through wire screens are in good agreement with those predicted by Kirsch and Fuchs (ηD = 2.7Pe), but the dependence of real filters on Pe is somewhat smaller than –2/3 and in agreement with (ηD = 0.84Pe, Wang et al., 2007). The dependence of single fiber collection efficiency on Pe for the real filters is well explained by considering non-uniformly packed filter consisting of two regions of densely packed and loosely packed fibers.


INTRODUCTION
Nanoparticles are of great interest as a new functional material but at the same time the adverse health effect is also of great concern because of their high reactivity and large surface area.As far as the collection of airborne nanoparticles with fibrous air filters concerns, it seems that air filters are very effective since the motion of nanopaticles are governed by Brownian diffusion and the diffusivity is almost the same as gas molecules.Therefore, the collection efficiency seems to be readily predicted by the conventional diffusion collection theory (Kirsch and Fuchs, 1968).However, Wang and Kasper (1991) pointed out that as the size of particle decreases, thermal rebound may reduce the collection efficiency.Since the publication of this paper, many researches tried to measure the reduction in collection efficiency by thermal rebound on fiber surfaces (Otani et al., 1995;Ichitsubo et al., 1996;Alonso et al., 1997;Heim et al., 2005;Kim et al., 2007) However, because of difficulty in generating monodisperse single-digit nanoparticles and their detection, we do not have rigid reliable data for the reduction in collection efficiency.Judging from the data reported so far, it is said that the thermal rebound does not occur or does not play any significant role for the collection of particles as small as 2 nm.Other than the thermal rebound, Wang et al. (2007) claimed that the exponent of Peclet number, Pe, in single fiber collection efficiency is not -2/3 but somewhat smaller than -2/3.Podgorski (2009) and Guillaume et al. (2009) also observed smaller dependence on Pe, and claimed that the fiber size distribution and pinholes are the cause of smaller dependence on Pe.
In the present paper, we hypothesized that the inhomogeneity in fiber packing would be the cause of smaller dependence on Pe and constructed a model to predict the collection efficiency based on the hypothesis and prove the hypothesis by comparing the model-based predictions with the experimental data.

Experimental Apparatus
Fig. 1 shows the experimental setup for measuring the particle penetration.The test particles are NaCl particles, which are generated by evaporation/condensation type aerosol generator.The test particles are charged in charge equilibrium state as they pass through an 241 Am bipolar charger and classified into 10 nm to 50 nm by nano-DMA (Laboratory made).The DMA-classified particles are again passed through an 241 Am neutralizer and then charged particles are removed with a parallel-plate condenser to obtain neutral monodisperse nanoparticles.
The filtration velocities are varied from 0.03 to 0.5 m/s by diluting the aerosol with dry clean air upstream of the filter.When the flow is switched from the blank filter holder to the test filter holder, the flow rate is decreased because of the resistance of mounted filter.However, mass flow controller (MFC) connected downstream of the holders automatically adjusts the flow rate to the prescribed flow rate.In the measurement of collection efficiency of nanoparticles, the particle loss due to diffusional deposition in conduits is of big concern.In the present work, two identical filter holders are used and they are connected in parallel so as to give the same particles loss in the conduits.Letting the outlet concentration of filter holder without a filter C blank and that with a filter C filter , the penetration is given by Eq. (1).(1) Although the above equation cancels out the loss of particles in the conduits, the experimentally evaluated loss of 10-nm particles in the conduit is as large as 10%.Therefore, with the present experimental setup, the correction for particle deposition loss is as much as 10%.

Test Filters
Wire screens as a uniformly packed filter and medium performance glass fiber filter and PP filter as a real filter were used.The major properties of these test filters are given in Table 1.

Nanoparticle Penetrations thorough Test Filters
Fig. 3 shows the particle penetration through the wire screens (a) and the fibrous filters (b), at filtration velocity of 0.05 m/s.The solid lines are the theoretical penetrations predicted by Kirsch and Fuchs (1968).As shown in these figures, the penetration becomes smaller with decreasing the particle size, suggesting that the Brownian diffusion is the dominant collection mechanism.For PP filter with high particle penetration, the experimental penetrations are in good agreement with the predicted ones, except the data for d p = 10 nm.For medium performance filter, the experimental penetration is higher than the theory for all particle sizes tested in the study.The particle penetration, P, is converted to the single fiber collection efficiency, η, by the following log-penetrating equation: where α is the packing density of filter, L is the filter thickness, d f is the fiber diameter.The packing density of wire screen shown in Table 1 was determined from the  geometry of wire screen because it has regular fiber arrangement.On the other hand, for fibrous filters, since they are very fluffy and difficult to measure the filter thickness, we employed the effective packing density, α', which is determined from the pressure drop of filter by applying Davies equation.Davies equation is given by the following equation (Davies, 1952): where μ is the air viscosity and u is the filtration velocity.where Pe is the Peclet number defined by: where D is the diffusivity of particles.Figs.4(a) and (b) for wire screens shows that the single fiber collection efficiency of wire screen is in good agreement with Eq. ( 4) over the whole range of Pe studied in the present work.On the other hand, in Figs.4(c) and (d) for fibrous filters, the single fiber collection efficiency is in agreement with Eq. ( 5).Therefore, we may say that the deviation from Eq. ( 4) comes from non-uniformity in fiber packing because Eq. (4) gives good prediction for wire screen with regular fiber arrangement.Wang et al. (2007) also claimed that the deviation of experimental data from Eq. ( 4) comes from the inhomogeneity of fiber packing but they did not discuss this matter in detail.Therefore, our next effort is to construct a filter model which explains the deviation of experimental data from Eq. ( 4) by accounting for the inhomogeneity in fiber packing.

Model of Non-uniformly Packed Filter
Filter model proposed in the present work is illustrated in Fig. 5.In a real filter, densely and loosely packed fibers are distributed locally over the whole surface of filter but, here, for the sake of simplicity, we consider a filter, which consists of two parts, one of which is densely packed at the packing density of α 1 with the fraction of filter area of α and the other is loosely packed at α 2 with fractional area of 1 -α, i.e., packing density-segregated filter.The average packing density of segregated filter, α model , is given by: The penetration of particles through the segregated filter model, P model , is given by where C in is the inlet particle concentration, and Q is the volumetric flow rate.The subscripts 0, 1 and 2 denote, respectively, the total, the densely packed part and the loosely packed part of filter.r is the fraction of volumetric flow rate through densely packed filter over that total flow rate.By employing the superficial filtration velocity through filter, u, the fraction r is given by the following equation: where A is the filter surface area.In order to calculate the penetration P model , we must know P 1 , P 2 and r.
When an air flow is split into two flows and then the two flows merge, the volumetric flow rate is divided in such a way that the pressure drops of air flows after splitting are equal to each other: Yamada et al., Aerosol and Air Quality Research, 11: 155-160, 2011 159 where ΔP is the pressure drop.By introducing the drag coefficient of fiber to Eq. ( 10) where F is the drag coefficient of fiber, and l is the total length of fiber per unit filter area.We obtain the ratio of filtration velocities as Substituting Eq. ( 12) into Eq.( 9), we have Consequently, if α  , α 2 and a are known, we can determine the fraction of volumetric flow rate through densely packed part.
Once α  , α 2 and a are known, we can also calculate the filtration velocities through the segregated filter by using Eq. ( 12) together with the continuity equation (Q 0 = Q 1 + Q 2 ).Then we may obtain P 1 and P 2 through Eq. ( 2) and Eq. ( 4), and the penetration of segregated filter by Eq. ( 8).
What follows from the above derivation is that we have to know three parameters, α 1 , α 2 and α in order to calculate the penetration of segregated filter.In determining these parameters, the objective function of Eq. ( 14), which is the square of difference between experimental penetration, P exp , and the predicted one, P model , is minimized 2 model exp ) ln (ln under the following constraints, (i) the pressure drop of segregated filter is equal to the experimental one, (ii) the average packing density given by Eq. ( 7) is equal to the measured packing density.Fig. 6 compares the experimental penetrations with those predicted by the present model.The three parameters determined to fit the experimental data are given in Table 2.As seen in Fig. 6, one set of three parameters well describe the dependence of experimental penetrations on both particle diameter and filtration velocity for these filters.The single fiber collection efficiencies calculated by Eq.
(2) from the predicted penetrations are plotted in Figs.4(c) and (d) by solid lines.The solid lines are in good agreement with the experimental single fiber efficiency and the slope of single fiber collection efficiency against Pe is in agreement with that by Wang et al.Consequently, the present segregated filter model can explain the weaker dependence of single fiber efficiency on Pe.
In Table 2, we can see that the densely packed part occupies 69% of whole filter surface area for the medium performance filter, 76% for PP filter A and the packing density of densely packed part is about 3 times of loosely packed part, which is quite non-uniform.In order to improve the collection efficiency for nanoparticles, filters should be made with higher uniformity in fiber packing.

CONCLUSION
The single fiber collection efficiency through wire screens was in good agreement with the classical diffusion theory, but those of fibrous filters showed smaller dependence on Pe.This result confirms that the filter inhomogeneity leads to the smaller dependence on Peclet number.By constructing a segregated filter model which consists of densely and loosely packed parts of fibers, the dependence of single fiber collection efficiency on Pe was successfully explained.

Fig. 4
shows the single fiber collection efficiency for wire screens ((a) and (b)) and for fibrous filters ((c) and (d)).In these figures, dotted broken lines are predicted by the following equation(Kirsch and Fuchs, 1968while broken lines are the empirical equation proposed byWang et al. (2007):

Fig. 4 .
Fig. 4. Single fiber collection efficiency through wire screen of 72 mesh (a), wire screen of 150 mesh (b), medium performance filter (c) and PP filter (d).

Fig. 6 .
Fig. 6.Comparison of penetrations through medium performance filter (a) and PP filter (b) with those predicted by the present model.