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).
property used for the distribution. This can be seen in Fig. 9.14, which shows a count and mass distribution for a hypothetical log-normal sample; the spread, a, is seen to be the same for each distribution, but the geometric mean diameters, Dsn and Dg u, are quite different.
In practice, when one measures the size distributions of aerosols using techniques discussed in Chapter 11, one normally measures one parameter, for example, number or mass, as a function of size. For example, impactor data usually give the mass of particles by size interval. From such data, one can obtain the geometric mass mean diameter (which applies only to the mass distribution), and crg, which, as discussed, is the same for all types of log-normal distributions for this one sample. Given the geometric mass mean diameter (DgM) in this case and a, an important question is whether the other types of mean diameters (i.e., number, surface, and volume) can be determined from these data or if separate experimental measurements are required. The answer is that these other types of mean diameters can indeed be calculated for smooth spheres whose density is independent of diameter. The conversions are carried out using equations developed for fine-particle technology in 1929 by Hatch and Choate.
These Hatch-Choate equations are of the form d (Number median diameter) exp[6(ln2 o-g)], (K)
where d is the average diameter to be determined using a known value of the number median diameter, o"g is the geometric standard deviation, and b is a constant whose value is determined by the type of average diameter, d, which is to be calculated. Recall that for a log-normal distribution, the number median
Type of mean
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