Size frequency curves

The distribution of particle sizes can be seen more readily by plotting a size frequency curve, such as that shown in Figure 1.6, in which the slope Ax/Ad) of the cumulative... 

The upper size limit of the larger sized population is 1000/x. This is based on review of the size/frequency data for close-in, early-time fallout collections. All reported size-frequency curves were dropping vertically between 800 and 1000/a. 

The size distributions of the particles in cloud samples from three coral surface bursts and one silicate surface burst were determined by optical and electron microscopy. These distributions were approximately lognormal below about 3/x, but followed an inverse power law between 3 and ca. 60 or 70p. The exponent was not determined unequivocally, but it has a value between 3 and 4.5. Above 70fi the size frequency curve drops off rather sharply as a result of particles having been lost from the cloud by sedimentation. The effect of sedimentation was investigated theoretically. Correction factors to the size distribution were calculated as a function of particle size, and theoretical cutoff sizes were determined. The correction to the size frequency curve is less than 5% below about 70but it rises rather rapidly above this size. The corrections allow the correlation of the experimentally determined size distributions of the samples with those of the clouds, assuming cloud homogeneity. 

Figure 2. Size frequency curves for three Koon samples...

Figure 3. Size frequency curves for a Bravo and a Zuni sample...

The curves have the following characteristics in common below a few microns they are approximately lognormal with medians between 0.5 and 1/x. Above a few microns the size frequency decreases as a p until a diameter a little smaller than the cutoff diameter is reached. For larger sizes the size frequency curves drop off rapidly. 

The size frequency curves for debris in cloud samples from surface and near-surface nuclear bursts generally has a lognormal shape below a few microns but obeys an r p law between a few microns and about 70 /x. The value of p is probably about 4 but is still subject to some conjecture. Removal of large particles prior to sampling as a result of sedimentation does not allow for any definitive conclusions about the shape of the size frequency curve in the cloud. 

Although the size frequency curves of samples obtained at different altitudes below and in a cloud differ in regard to their upper and lower bounds, the shapes are essentially the same. 

It is evident that the median and average particle-size are influenced by the shape of the size-frequency curve. Two widely differing types of distribution may have the same average size or the same median. In fact there is an infinite variety of size-frequency curves having a given mean or median. Thus, it js clear that parameters other than the median or average are necessary to define a size-distribution. ... 

One other parameter regarding size-distribution may be mentioned, namely the mode, or the value of d for which the size-frequency curve is a maximum. For example, in Figure 8, this value occurs for d = 17.5. If the distribution were symmetrical, that is, if the frequencies were evenly distributed about a line passing vertically through the mode (see Figure 9), the mode, mean, and median of the size-frequency distribution would be the same. If the distribution were moderately asymmetrical or skewed, then the relation between these averages would be given by the equation (see Yule, 1927)... 

Thus, the surface-area and volume of irregular particles are seen to be functions of the statistical parameters dg and [Pg.65]

From this distribution calculate the average diameter da9. Plot the size-frequency curve. 

Graphical Determination of Size-Frequency Curves—The usual sedimentation curves may be said to be historical in the sense that they picture the state of the suspension at any time t. However, by graphical means we may obtain the distribution function F(d) which gives the relation between the percentage weights of the suspended material and the corresponding diameters. Let be the particular sedimentation parameter observed. Note that... 

A photo-electric apparatus for delineating the size frequency curve of clays or dusts. J. Sci. Instruments, 13 229-233. 

If the size frequency curve dF/dx is to be used, the evaluation is carried out according to the modified equation 3.19 ... 

If a size frequency curve dF/dr is to be used instead of the cumulative curve, the evaluation is simpler since, according to equation 3.31... 

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