Size-frequency distribution

Thru a combination of sedimentation and transmission measurements, a particle size distribution can be found. Tranquil settling of a dispersion of non-uniform particles will result in a separation of particles according to size so that transmission measurements at known distances below the surface at selected time intervals, will, with Stokes law, give the concn of particles of known diameter. Thus, a size frequency distribution can be obtained... 

Fig. 2 Normal, or Gaussian, size-frequency distribution curve. Percentage of particles lying within 1 and 2 standard deviations about the arithmetic mean diameter are indicated.

Fig. 3 (a) A skewed size-frequency distribution typical of pharmaceutical powders, (b)... 

The characteristics of an individual emulsion are primarily dependent on two factors, the size-frequency distribution of the crystals and the... 

Figure 8. Size-frequency Distribution for Examples in, Text.

The equation of the normal-probability curve, as applied to size-frequency distributions, is... 

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)... 

Other Size-Frequency Distributions—Since it is conceivable that there is a smallest particle below which no other particles are found, and also a largest particle above which no larger particles are found, the size-distribution curve is limited at two extremes. It is probable that a most general type of particle-distribution occurring in nature is a... 

Figure 11. General Type of Size-frequency Distribution.

Using the data given in Problem 1 of the previous chapter plot the corresponding size-frequency distributions. 

The values of ag and 0/ are the same, that is, the geometric standard deviations by count and weight are equal. This is easily proved by substitution of Eq (5-8) and the value of n given by the size-frequency distribution by count in Eq (5-2). Hence,... 

Hatch extended his method of analysis to size-distribution curves ranging from coarse-screen analysis through fine particles measured microscopically. While excellent results were obtained by using this technique on laboratory samples, the method cannot be generalized to cover all types of distributions encountered in practice. As already explained in Chapter 3, size-frequency distributions may assume a variety of shapes. The Hatch development applies only to distributions which follow the normal or log-probability law. When size-distributions are hyperbolic in the lower extremes and follow normal log-probability laws in the upper extremes, the Hatch analysis must necessarily fail. Nevertheless, the relationships developed by Hatch have a far-reaching practical importance... 

Weber and Moran Method of Calibration—Another method of calibrating sieves consists in measuring random openings in the sieve and obtaining size-frequency distributions as qutlined in Chapter 3. The openings are measured by filar micrometer or by projection methods. Two screens are then identical if the mean size of the openings and the standard deviations are the same. Weber and Moran (1938) use the coefficient of variation... 

Calculate the calibration size (weight basis) for a sand (p = 2.64) passing a 200-mesh and retained on a 325-mesh Tyler sieve, given the following size-frequency distribution ... 

Size-Distribution—The size-frequency distribution of atmospheric dust is shown in Figure 115. 

Figure 115. Size-frequency Distribution of Atmospheric and Industrial Dusts.

Particle-Size Distribution—The size-frequency distribution of ground materials differs from the usual type of frequency-distribution in chance sampling. As a general rule the number of particles increases with decreasing particle-diameter. Martin (1923) has shown that frequency-distribution follows the law of compound interest, namely... 

Size-frequency distribution of sediments and the normal phi curve. J. Sediment. Petrol., 8 84-90. 

I have refrained from using the term mechanical analysis except once or twice in the first part of the text. The use of this term to describe a size-frequency distribution of particles is unfortunate and should be discouraged because its meaning is too limited. 

T] = 0.00125 Pa s. Alternatively, for comparison purposes, a size frequency distribution may be plotted or tabulated against free-falling diameter. 

Rubin A. E. (1989) Size-frequency distributions of chondrules in CO3 chondrites. Meteoritics 24, 179-189. 

Hiesinger H., Head J. W., Ill, Wolf U., Jaumann R., and Neukum G. (2002) Lunar mare basalt flow units thicknesses determined from crater size-frequency distributions. Geophys. Res. Lett. 29, 8891—8894. 

Figure 9.10 gives an example of a size frequency distribution of considerable width. It would be a reasonable example for a homogenized emulsion, assuming the d scale to be in 10 7m. It is seen that the number frequency can give a quite misleading picture more than half of the volume of the particles is not even shown in the number distribution. We will use this figure to illustrate some characteristic numbers. 

Krumbein, W.C., 1934. Size frequency distribution of sediments. Journal of Sediment Petrology, 4 65-77. 

Compared to the extensive data describing the ocean particulate (10, 11), size distribution data on particulates in fresh water systems and wastewaters are relatively scarce. Particle size distribution data for several low ionic strength solutions are shown in Figure 1 with the water source, particulate counting method, and references as noted. The size frequency distribution of the four heterogeneous suspensions shown can be modeled by a two-parameter power-law distribution function (2) given by the expression... 

Figure 1. Examples of particulate size frequency distributions in natural waters and wastewaters. (A) Effluent, sedimentation basin, pilot-activated sludge plant, light microscope (26) (%) Lake Zurich, 40 m, 612176, Zeiss Videomat (19 (D) Deer Creek Reservoir, Utah, 20 m, 3/76, HI AC-12 Channel Counter (16) (O) digested primary and secondary sludge. Coulter Counter (S).

Figure 6. Effect of increasing mixing intensity on size frequency distributions (15 mgjL alum as coagulant). Particle counting with HI AC six-channel counter and 2.5-150-fim sensor. (A) Influent sample (/3 = 3.6) (B) G = 175 sec- (p = 3.6) (C) G = 70 sec = 2.5) (D) 30 sec ...

Figure 7. Comparison of size frequency distributions effect of flocculation preceding granular-media filtration. (0) Filter influent, with flocculation (O) filter influent without flocculation ( , filter effluents.

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