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FIGURE 9.2 Plot of number of particles (AO against D (D aerodynamic diameter) determined using a four-stage impactor with the cutoff points given in Table 9.1. It has been assumed that the particles are spherical with density 2.6 g cm Data from Wesolowski et al. (1980).

characterized by the 50% cutoff point for each stage, where the 50% cutoff point is defined as the diameter of spheres of unit density, 50% of which are collected by that stage of the impactor. For example, a typical set of 50% cutoff points is 8.0 (stage f), 4.0 (stage 2), 1.5 (stage 3), and 0.5 /¿m (stage 4), respectively, with particles smaller than 0.5 /¿m being collected on an afterfilter. One might then use the approximation that each stage captures particles ranging from a diameter corresponding to midway between its cut point and that of the next higher and lower stages. With these assumptions, the ranges of particle diameters captured by each stage for a typical impactor are given in Table 9.1; also given are the diameter intervals AD as well as A log D for each stage. It is seen that neither the intervals in terms of diameter nor those in terms of the logarithm of the diameter are equal. As a result, a plot of AN against D or log D will look something like those shown in Figs. 9.2 and 9.3.

These give a somewhat distorted picture of the size distribution, however, because the height of any bar, that is, the number of particles, depends on the width of the interval taken, that is, AD or A log D. To give a more physically descriptive picture of the size distribution, a modified plot of the number of particles normalized for the width of the diameter interval is used; that is, the number of particles per unit size interval is plotted on the vertical axis. With log D as the horizontal axis then, a normalized plot is one of AN A log D against log D, where AN is the number of particles in that interval of A log D; Fig. 9.4 is an example of this type of plot using the data in Figs. 9.2 and 9.3. The area under each rectangle then gives the number of particles in that size range.

Rather than showing histograms, one usually draws a smooth curve through the data. Figure 9.5, for example, shows one such curve of AN A log D against log D for a typical urban model aerosol; to emphasize the wide range of numbers involved, a logarithmic scale has also been used for the vertical axis (Whitby and Sverdrup, 1980).

However, it is not only the number of particles in each size interval that is of interest but also how other properties such as mass, volume, and surface area are distributed among the various size ranges. For example, the U.S. Environmental Protection Agency's air quality

log D

FIGURE 9.3 Plot of number of particles (AO against log D (D aerodynamic diameter). Data same as those in Fig. 9.2.

log D

FIGURE 9.3 Plot of number of particles (AO against log D (D aerodynamic diameter). Data same as those in Fig. 9.2.

TABLE 9.1 Typical 50% Cutoff Points and Approximate Range of Particle Diameters Captured by

Each Stage in a Four-Stage Impactor"

Approximate range of particle diameters

50% cutoff captured by that stage A D A log D

4 0.5 1.0-0.3' 0.7 0.52 Afterfilter 0.5 0.3-0.001' 0.3 2.48

" From Wesolowski et al. (1980).

h Assuming a cutoff of 20 /xm for the sampling probe.

' Assuming the afterfilter collects all particles >0.001-/xm diameter.

standards for particles are expressed in terms of mass of particulate matter, with diameters 10 yu,m per unit volume of air, PMI(), and those with diameters 2.5 /jum, PM25 (see Chapter 2.D). It is thus important to know the mass distribution of atmospheric particulate matter. Similarly, surface and volume distributions are important when considering reactions of gases at the surface of particles or reactions occurring within the particles themselves, for example, the oxidation of S02 to sulfate.

Because of this need to know how the mass, surface, and volume are distributed among the various particle sizes, distribution functions for these parameters (i.e., mass, surface, and volume) are also commonly used for atmospheric aerosols in a manner analogous to the number distribution. That is, Am A log D, AS A log D, or AV A log D is plotted against D on a logarithmic scale, where Am, AS, and AV are the mass, surface area, and volume, respectively, found in a given size interval; again the area under these curves gives the total mass, surface, or volume in the interval considered. Figure 9.6 shows the surface and volume distributions for the number distribution shown in Fig. 9.5; also shown is the same number distribution for comparison, where the vertical axis is now linear (rather than logarithmic as in Fig. 9.5).

When the particle data are plotted as mass, surface, or volume distributions, an important characteristic of typical urban aerosols emerges clearly. As seen in the number distribution of Fig. 9.6a, there is a large peak at ~0.02 ¡¿m and a slight "knee" in the curve around 0.1 /iim.

The volume distribution for the same aerosol (Fig. 9.6c) shows two strong peaks, one in the O.f- to 1.0-yu,m range and the second in the f- to fO-^m region, with a minimum in the 1- to 2-/j,m region. The surface distribution (Fig. 9.6b) shows a major peak in the vicinity of O.f /¿m, with smaller peaks in the region between 0.01 and 0.1 /am and between f and fO ¡xm.

The "knee" observed in the number distribution

log D

FIGURE 9.4 "Normalized" plot of AN A log D versus log D for data shown in Figs. 9.2 and 9.3.

log D

FIGURE 9.4 "Normalized" plot of AN A log D versus log D for data shown in Figs. 9.2 and 9.3.

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