diameter is equal to the geometric number mean diameter, D N. Thus Eq. (K) becomes d DsN exp[6(ln2 o-g)]. (L)

Table 9.3 gives the values of b to be used for converting the count geometric mean diameter to the other types of geometric or mean diameters, respectively.

While we have concentrated here on the geometric means weighted by number, mass, surface, or volume, respectively, other types of "average" diameters are also sometimes cited in the literature. One commonly used is the diameter of average mass, which is defined as the diameter such that the mass of this particle multiplied by the total number of particles gives the total mass. The geometric mean diameters discussed here can also be converted to these types of diameters using a form of the Hatch-Choate equations. The reader is referred to the discussion by Hinds (1982) for definition of these other types of diameters and their conversion to the geometric mean diameters discussed here.

Whitby and co-workers have indicated that the many atmospheric aerosol size distributions that they have measured under a variety of conditions and at many locations can be fit reasonably well assuming three additive log-normal distributions corresponding to the Aitken nuclei range, the accumulation range, and the coarse particle range, respectively, as described earlier. Each of these log-normal distributions has its own characteristic value of crg as well as, of course, average diameters. For example, Fig. 9.6 contains the number, surface, and volume distributions for a typical urban aerosol; these were calculated to be consistent with the sum of two, or in the case of the surface distribution, three, additive components. These components are shown by the dashed lines in Fig. 9.6. From these separate distributions, geometric mean diameters and ag could be found assuming smooth spheres. Table 9.4 summarizes the parameters derived by Whitby and

1 10 100 Particle diameter (|im)

FIGURE 9.14 Count and mass distributions for a hypothetical log-normal sample. The spread, crg, of the two curves is seen to be the same, but the mean diameters associated with each are different (adapted from Hinds, 1982).

TABLE 9.4 Summary of Parameters Dg and crg for the Three Additive Log-Normal Distributions Characterizing Data in Fig. 9.6"

Log-normal distribution

Type of distribution used Mode 1)' ((im) <rB

Log-normal distribution

Type of distribution used Mode 1)' ((im) <rB


Aitken nuclei


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