Geometrical mean diameters

Another frequentiy used average is the geometric mean, which is particularly usehil for log-normal or wider (spanning over a decade) distributions. The geometric mean diameter, d is calculated usiag the logarithm values of the measured diameters ... 

The classification as a carcinogen need not apply to fibres with a length weighted geometric mean diameter less two standard errors greater than 6 pm Sodium dichromate Sodium dichromate dihydrate... 

Mean diameter The geometric mean diameter of the size range. 

Irani and Callis (Ref 14) used two parameters of the distribution of ground monocalcium phosphate (which follows the commonly used log normal distribution law) namely, Mg and Og, the geometric mean diameter and the geometric standard deviation, to evaluate the precision and accuracy of electro-formed sieves vs sedimentation as a reference procedure ... 

Geometric mean diameter and 4.7% 4.6% standard deviation between electro-formed sieves sedimentation... 

The foregoing close agreement of the geometric mean diameter and geometric standard deviation results indicates that accuracy evaluations were made on an absolute scale, and did not refer to some arbitrary scale... 

Another diameter of interest is the geometric mean diameter, dg. This is particularly useful if one wishes to compare the microscopic diameter with the one estimated by sieving, dg(see Fig. 3b). For microscopy data, dg can be obtained using the relationship... 

The geometric mean diameter can then be found from the antilogarithm of log... 

Fig. 11 Sieving data presented as a cumulative percentage undersize plot. The data were used to determine the geometric mean diameter of ethylcellulose microcapsules. (Adapted from Ref. 19.)...

An advantage of applying the log-normal distribution to atmospheric aerosols is that the value of the geometric standard deviation, crg, is the same for a given sample for all types of distributions—count, mass, surface, and volume. It is only the value of the geometric mean diameter that changes, depending on the... 

TABLE 9.3 Values of the Constant b in the Hatch - Choate Equations for Converting the Count Geometric Mean Diameter to Mass, Surface, or Volume Diameters... 

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. 

A word of caution is also in order with respect to assigning a particular particle to the fine or coarse particle modes. Since the size distributions can generally be described as log-normal, they do not have sharp cutoffs. A few particles at the top end of the fine mode distribution will have diameters larger than 2.5 [jlm and a few at the bottom end of the coarse mode will have diameters smaller than this. For example, as Lodge (1985) points out, for a coarse particle distribution with a geometric mean diameter of 15 fim and a geometric standard deviation of 3, about 5% of the particles will have diameters below the 2.5-gm fine particle cutoff. This may be responsible for observations that while Si and Ca dominate the coarse particle mode, they are also often found at significant levels in fine particles (e.g., see Katrinak et al., 1995). 

The data were obtained from the samples summarized in Table L The fallout samples were separated into particle-size classes by standard sieves for particles larger than 44p and by the Roller analyzer for particles smaller than 44fi. In the sequel the size classes are characterized by their geometric mean diameters. The larger size classes of the Tewa sample were separated mechanically under the microscope into spherical and irregular fractions. Very few spheres could be found below the 177-/x class. The ratio of active to inactive particles was measured auto-... 

Table 5—Method of Determining the Geometric Mean Diameter of 245 Particles Measured by Means of an Optical Micrometer...

The terms dg and ag are called geometric mean diameter and geometric standard deviation, respectively. 

Example 2.9 Given a lognormally distributed aerosol with a geometric mean diameter of 1.5 pm and a og of 2.3, what are the surface-area median diameter and the mass median diameter of this aerosol ... 

Geometric mean diameter - ds, (Jim Geometric standard deviation aK ... 

Example 2.6 Compute the geometric mean diameter dg and geometric standard deviation ag for the data given in Example 2.1. 

Example 8.6 An aerosol made up of unit-density spheres is lognormally distributed with a geometric mean diameter of 2.0 pm and a geometric standard deviation of 2.2. Calculate the respirable fraction of this aerosol as sampled by a sampler which follows the BMRC curve and a sampler which follows the ACGIH curve. 

For the case of a lognormal aerosol having a geometric mean diameter of dg and geometric standard deviation of ag,... 

In Prob. 5, what would be the implied geometric mean diameter if the geometric standard deviation were assumed to be 2.0 ... 

Substituting this relationship into equations (2.86) to (2.89) yields the equivalent relationships relating surface average sizes with the surface geometric mean diameter. 

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