Cumulative size distribution

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... 

Fig. 35. (a) Size distributions [c (x, q)] obtained for erosion-controlled fragmentation for increasing fragmentation time (q). (b) Comparison of theoretically predicted cumulative size distribution for erosion-controlled fragmentation to experimental data (Hansen and Ot-tino, 1996a). 

FIGURE 8.4 Cumulative size distribution of gelatin (lime-cured type B, bloom number 225) microparticles prepared at high pH obtained using a Coulter Counter and plotted as a log-probit function. (From Lou, Y. and Groves, M.J. (1995). J. Pharm. Pharmacol., 47, 97-102. With permission.)... 

Figure 12.1. Normalized cumulative size distribution curves of comminuted products, (a) From various kinds of crushing equipment, (b) From rod and ball mills, (c) RRS plots of two curves Taggart, 1951).

Crushing is applied to large lumps of feed stock and grinding to smaller lumps, often the products of crushing, but the size distinction is not overly sharp. The process of size reduction results in a range of product sizes whose proper description is with the complete cumulative size distribution, but for convenience a characteristic diameter corresponding to 80% pass in the cumulative distribution curve is commonly quoted. 

Figure 16.9. Cumulative size distribution in continuous stirred tanks, (a) one tank (b) two tanks in series, nucleation in both (c) two tanks in series, nucleation in only the first.

Since the cumulative size distribution is often S-shaped, various types... 

The particle size distributions of each of these two sanq)les was determined by sieve analysis using five sieves. The cumulative size distribution is plotted on log probability paper in Figure 2.12. Compare the two ceramic powders, 1 and 2. 

FIGURE 4.8 Cumulative size distribution of grovind material after various dimensionless times in a continuous open-circuit ball mill, size selectivity Sbc) = kxfi, /3 = 0. Taken from AIME [22] and Randolph and Larson [23],... 

Figure 4.2 Cumulative size distribution for wet sieved standard strong cation resin (Hform)...

One way of determining the average particle size is to plot the cumulative size distribution in manner such that the distribution is linearized, and from this plot the mean and standard deviation can be graphically determined. For example, if we had a random variable x which was distributed ... 

Total mass throughput of a mill g/s Ib/s AYj, Cumulative size-distribution intervals cm in... 

Usually, the width of the distribution is expressed by dp,xt/dpW, which should be lower than 2.5 for the chromatographic application dp,xt (dpV t) equals the value at 90% (10%) of the cumulative size distribution. Figure 3.24a and b visualize the effect of size classification and effident removal of fine particles. 

The population balance approach to measurement of nucleation and growth rates was presented by Randolph and Larson (1971, 1988). This methodology creates a transform called population density [n(L)], where L is the characteristic size of each particle, by differentiating the cumulative size distribution N versus L. shown in Fig. 4-22, where N is the cumulative number of crystals smaller than L. Per unit volume, the total number of particles, total surface area, and total volume/mass are calculated as the first, second, and third moments of this distribution. 

It is not possible to assess the effect of the substrate surface independently however, the powder can be characterized with respect to effective size by means of a simple sieve analysis that can be used to get a cumulative size distribution. If the total fraction that passes each size sieve is plotted against the sieve opening on normal probability paper, the mean weight-diameter from the 50% point is obtained and the standard deviation from the sizes corresponding to the 13% and/or 83% diameter. The effective (surface mean) particle diameter can then be calculated by means of the equation given by Orr and Dallavalle [66] ... 

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