Particle distribution curve

Figure 46. Particle distribution curves for the carbon blacks of Figure 45...

Fig. 5.17. Exact results (full curves) and Smoluchowski theory (dashed curves) for the A + A —> 0 reaction in one-dimension for (a) random particle distribution (curves 1), equidistant particle distribution (curves 2) and clustered distribution (b) [89],...

Fig. 1.13 Gaussian particle size distributions. Curve I represents a more uniform size distribution than does Curve II.

The distribution curves may be regarded as histograms in which the class intervals (see p. 26) are indefinitely narrow and in which the size distribution follows the normal or log-normal law exactly. The distribution curves constructed from experimental data will deviate more or less widely from the ideal form, partly because the number of particles in the sample is necessarily severely limited, and partly because the postulated distribution... 

Now the relationship between v and A is given by the size distribution curve the value of A merely represents the lengths of the particles measured in terms of a particular, arbitrary, unit. Thus, if the size distribution curve remains of exactly the same shape during the grinding process, the values of... 

Particle Size Distribution. For many P/M processes, the average particle size is not necessarily a decisive factor, whereas the distribution of the particles of various sizes ia the powder mass is. The distribution curve can be irregular, show a rather regular distribution with one maximum, have more than one maximum, or be perfecdy uniform. 

Experimental exponents for cake thickness vary from 0.5 to as much as 3.0. The theoretical value of //2 may be approached only by incompressible cakes of a narrow range of sizes. The proper and characteristic value for the mean particle size, d, is difficult to ascertain. In practice, the most finely divided particles, eg, 10—15 wt % of soHds, almost whoUy determine the Hquid content of a cake, regardless of the rest of the size distribution. It seems reasonable to use a d closely related to Hquid content, eg, the 10% point on a cumulative weight-distribution curve. 

FIG. 20-1 Particle -size distribution curve plotted on linear axes,... 

Size Distribution Curves for Three Methods of Particle Size Analysis — Tungsten M-10... 

As mentioned, the data obtained by this method are expressed as cumulative size distribution curves. Since the computations assume Stokes law for spherical particles, the plotted curves give the distribution of spherical particles which would behave like the actual sample with respect to this experiment. For this reason, the sizes on the distribution curves should be labelled Stokes Equivalent Diameter . Because of the underlying assumptions and the above interpretation of the results, it is clear that the repeatability of this method has more meaning than accuracy of comparison with results of other methods... 

DIVER METHOD- This is a modification of the hydrometer method. Variation in effective density i and hence concn, is measured by totally immersed divers. These are small glass vessels of approximately streamline shape, ballasted to be in stable equilibrium, with the axis vertical, and to have a known density slightly greater than that of the sedimentation liq. As the particles settle, the diver moves downwards in hydrodynamic equilibrium at the appropriate density level. The diver indicates the position of a weight concn equal to the density difference between the diver and the sedimentation liq. Several divers of various densities are required, since each gives only one point on the size distribution curve... 

As it turns out, one vendor s material contains almost no particles (0.5%) in the 261-564 /xm class (bin 15) this means that the %-weight results accurately represent the situation. The other vendor s material, however, contains a sizable fraction (typically 5%, maximally 9%) in this largest size class this implies that 1-5% invisible material is in the size class >564 /xm. Evidently then, the size distribution curve for this second material is accurate only on... 

Figure 2 shows the particle size distribution of the three catalysts. The distribution curves show that 10%Pd/CPS4 has the narrowest distribution. The particle size distribution and filtration rates of the three catalysts are summarized... 

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.

Sum Distribution. A cumulative presentation of equivalent diameters, which converts the density distribution curve to a plot that represents percentages of particles which are smaller than a given equivalent diameter D. 

Figure 2-40 shows the state density distribution curves of hydrated redox particles in two cases in which (a) Nked = JVox and (b) AThed < iVox-... 

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