Particle size distribution cumulative

For pumoses of calculating size selectivity from cumulative particle size distribution data, Eq. (20-16) can be expressed in incremental form as follows ... 

A.J. O Neil, R.D. Jee and A.C. Moffat, Measurement of the cumulative particle size distribution of microcrystalline cellulose using near infrared reflectance spectroscopy. Analyst, 124, 33-36 (1999). 

First the particle size and shape should mentioned. As columns packed with nominally 5 or 10 pm particles are used most commonly in HPLC, the particle size distribution has become an important characteristic of the packing because with such small particles it is difficult to obtain a monodisperse product. Size distribution of the particles can be represented in many different ways. Most commonly the cumulative particle size distribution curve obtained with an instrument such as the... 

Figure 9 Cumulative particle size distribution of the agglomerates at a fixed normalized amount n (=0.62) of granulating liquid for different ratios of the binary powder mixture lactose/corn starch.

FIGURE 17 Cumulative particle size distribution in 5% dextrose solutions for injection ( ) product 2AL packed in 500-mL glass containers with lacquer-coated rubber stopper (o) product 2G packed in 500-mL plastic bags (smooth curve), BP specification [80]. 

Figure 40. Cumulative particle size distribution curve of a normal (705) and a mi-cronized (705 LS) iron blue pigment of equal primary particle size LS = Luftstrahlmiihle (air jet mill)...

Figure D3.4.7 Change in cumulative particle size distribution of a 20% (w/v) oil-in-water emulsion stabilized by 2% (w/v) Tween 20 at the lower port (A) and upper port (B). (C) Change in mean droplet diameter and volume fraction of the emulsions as a function of time.

FIGURE 20.5 Cumulative particle size distribution pt= 0.62 for different ratios of the binary mixture lactose (L)/corn starch (MS). The granule diameter is critically linked to the concentration ratio (percolation effect ). (From Leuenberger, H., Usteri, M., Imanidis, G, and Winzap38ll,. Chem. Farrn 128, 54-61... 

Figure 3-2. Example of cumulative particle size distribution of HPLC packing materials (Waters p-Bondapack). Average particle size is 10pm (inflection point). (Reprinted from reference 8, with permission.)...

Often it is convenient to plot the results of experimental measurements as a cumulative particle size distribution (Figure 14.3a). 

Figure 14.3. Particle size distribution, (a) Discrete and continuous cumulative particle size distribution, (b) Discrete and continuous particle size distribution, (c) Volume distribution plotted in accordance with equation 3. (d) Particle size distributions at four depths in a calcareous sediment from west equatorial Pacific Ocean, 1°6.0 S, 161 36.6 E, box core No. 136, water depth 3848 m. (From Lerman, 1979.)...

O Neil et al. [55] measured the cumulative particle size distribution of microcrystalline cellulose with diffuse reflectance NIR. Both MLR and PCA were used for the work. The results were consistent with those obtained by forward-angle laser light scattering. 

Figure 3. Cumulative particle-size distribution of the mineral constituents of oil shales (by low-temperature ashing). Particle size by Coulter counter.

One can distinguish between the differential and integral (or cumulative) particle size distribution functions. These two types of functions are related to each other by the differentiation and integration operations, respectively. The adequate description of distribution function must include two parameters the object of the distribution (i.e. what is distributed), and the parameter with respect to which the distribution is done. The first parameter may be represented by the number of particles, their net weight or volume10, their net surface area or contour lengthen some rear cases). The second parameter typically characterizes particle size. It can be represented as a particle radius, volume, weight, or, rarely, surface area. Consequently, the differential function of the particle number distribution with respect to their... 

Fig. 6.1-S Comparison of typical cumulative particle size distributions after crushing solids in a single-stage roller mill and an MPE Cran-U-Lizer with three sets of rollers. Note the much reduced amount of oversize (shaded area) and the almost unchanged amount of fines (courtesy Modern Process Equipment, Inc. (MPE), Chicago, IL, USA)...

What is a normal particle si/e distribution What is a cumulative particle size distribution ... 

Rhodes and Haag [52] studied the particle size distribution of Y203-stabi-lized (6 mol%) Zr02, and typical cumulative particle size distribution curves for two different batches of powders are shown in Fig. 15, which is a common... 

Parameter Estiiiiation results. The dispersion model including the growth and nucleation models was applied to the experimental precipitation data in the dispersion range. Typical fit of the calculated cumulative particle size distribution and the experimental values for these data are presented in Figure 10. Calculated values and experimental data are in agreement within 15%. Details can be found in (13). 

Figure 18.19 illustrates how blend ingredients are evaluated for physical compatibility according to cumulative particle-size distribution. 

In table 1 to 3 the results for the experiments in the semi batch reactor are shown. For each precursor the time t after that the gel was taken from the reactor and the temperature T in the reactor is indicated. The cumulative particle size distribution (PSD) is shown for the dried precursor and for some calcined catalysts. The X5, X50 and X90 values are presented. For example X50 = 3 pm means 50 % of the particles have a volume based size smaller than 3 pm (table 1 catalyst RF 4/89). The next column demonstrates the BET surface area of the precursors and of some calcined catalysts (values in brackets) In addition the densities for some precursors and the rates for the formation of methanol for some catalysts are shown. The precursors prepared with ultrasound of low intensity (ultrasonic bath) in general have low BET surface areas. The precursors prepared with ultrasound of high intensity in general show high BET surface areas. The calcination affects the surface area dramatically. 

Ilari et al. [85] used scatter correction to determine the particle sizes of materials. Particle sizes of both organic and inorganic materials were determined by this technique. O Neil et al. [86] measured the cumulative particle size distribution of microcrystalline cellulose with diffuse reflectance NIR. Both multiple linear regression (MLR) and PCA were used for the work. The results were consistent with those obtained by forward-angle laser light scattering. Rantanen and Yliruusi [87] predicted... 

The so-called analytical cut size Xa is the size such that ideally the feed solids would be split according to size (with no misplaced material) in the proportions given by the total efficiency Ej. In other words the analytical cut size corresponds to the percentage equal to on the cumulative particle size distribution oversize F x) of the feed material (see Figure 3.5a), i.e. 

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