Types of particle size distribution

2 particle size distribution by length (not used in practice)/l(x)  

These distributions are related but conversion from one to another is possible only when the shape factor is constant, i.e. the particle shape is independent of 

The following relationships show the basis of such conversions  

The constants k2 and ks contain a shape factor which may often be particle-size-dependent this makes an accurate conversion impossible without a full quantitative knowledge of the shape factor s dependence on particle size. If the shape of the particles does not vary with size, the constants 

If the data are in a cumulative form, as cumulative percentage undersize or oversize (see section 2.5), conversions between the different particle size distributions can be made without having to differentiate the curves to obtain the size frequencies, as follows. 

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Most systems of fine particles have the log-normal type of particle size distribution. That is, with the logarithm of the particle size, the particle size distribution follows the normal or Gaussian distribution in semilog scales. Therefore, the density function for the log-normal distribution can be expressed by... 

Many properties of disperse systems, such as those described above and those analyzed in subsequent chapters, are defined by the degree to which substance is dispersed and by the type of particle size distribution. Various methods for the investigation of dispersion composition of dispersed phase (idispersion analysis) have been developed. Many of these methods utilize the concepts of transfer phenomena discussed in previous sections of this chapter. 

Initial reaction rate, Vo 10, S- Volume fraction of dispersed phase, % Type of particle size distribution Average size of particles, D, pm... 

The different types of particle size distributions have been discussed extensively in Chapter 2. No single distribution applies equally well to all comminuted products, particularly in the range of coarser particle sizes. For finer particles, however, the most commonly found distribution follows a log-normal function (Herdan, 1960), which is the most useful one among the different types of functions (Beddow and Meloy, 1980). 

Statistical properties of ID measurements for various types of particle size distribution randomly dispersed are given in Figure 3.10 and for flocculated dispersion in Figure 3.11. Summary statistics for IDs are listed in Table 3.2. The normalized ID (Figure 3.10) is given by... 

For a given particulate matter, four different types of particle size distribution are defined (see Figure 2.2a). These are ... 

Emulsion and microsuspension processes will be considered together in that they both generate aqueous latices. The latices are usually dried before processing. However the particle size and size distribution of the latex particles play an important role in subsequent processing, particularly when the dried powder is dispersed in a plasticiser to form a so-called plastisol or paste. The types of particle size distribution produced commercially are reviewed, and poljmierisation techniques to produce stable latices at high solids content are discussed. 

Different types of particle size distributions are used for forming ceramics. Batch composition gives the proportions of the constituents. Many parameters determine the consistency of a batch. They are ... 

Table 1 shows that catalysts prepared on the same type of support have about the same particle size distribution (PSD). Table 1 also shows that the newly developed CPS4 supported catalysts have the smallest span of particle size distribution, therefore, it has the fastest filtration rate. Filtration rate is measured by measuring the filtration time of 350 ml of 4-benzyloxyphenol debenzylation products. 

P.Y.139 is a reddish yellow pigment, used in plastics, paints, and printing inks. The commercial types exhibit a wide variety of particle size distributions and accordingly demonstrate very different coloristic properties, which is especially true for the hiding power. The opaque version is considerably redder. Incorporated in a paint, it is less viscous, which makes it possible to increase the pigment concentration without affecting the gloss of the product. 

The 7-crystal modification of P.V.19 affords bluish red shades which are much yellower than those obtained by the (3-modification. Commercial types of 7-P.V.19 show a wide range of particle size distributions. The specific surface areas vary accordingly, they range from approximately 30 to 70 m2/g. 

Aniline Black provides a deep, neutral shade of black. Extensive absorption and little scattering make for good hiding power. The commercial grades cover a comparatively wide range of particle size distributions. The types with fine particle sizes in particular provide characteristically dull, velvety effects in finishes and... 

Fig. 3.10 Comparison of particle size distributions between types of atomizers...

Montmorillonite has some important characteristics that justify its use as a model substance for the study of the interfacial processes of rocks and soils. It is a dioctahedral three-layer clay (2 1 clays, TOT) an A10(0H) octahedral sheet is between two tetrahedral Si04 layers (Chapter 1, Table 1.2). The distance between the layers is not fixed (—O—O-bonds) the layers can be expanded. Because of the layered structure, it has two surface types external and internal surfaces. The external surface is the surface of the particles (edge surface), and its size depends on particle size distribution. Its area can be measured by the BET method, usually by the adsorption of nitrogen gas at the temperature of liquid nitrogen (Chapter 1, Section 1.1.3). The internal surface is the surface between the layers (interlayer surface), and its size can be determined by introducing substances into the interlayer space (e.g., water) (Chapter 1, Section 1.1.3). The internal surface area is independent of particle size distribution. 

Equation (5.41) assumes that the gas is of a uniform composition throughout the reactor at all times. If the gas composition changes with the time or position within the reactor, a different equation must be used. To account for the effect of particle size distribution in addition to the residence time distribution is difficult because different size particles can remain in the reactor for different periods of time. To account for these effects completely a population balance must be performed, where the conversion is an internal variable (see Chapter 3). This type of treatment is beyond the scope of this chapter. A simplified method of accounting for the effects of a particle size distribution, mQt), on the mean conversion, is by... 

It is axiomatic in the use of filter aids that the ability of the filter aid to remove small particles of suspended matter decreases as the particle size, and thus the flow rate, increases. Conversely, as filter aid particle size, and therefore the flow rate, decreases, the ability of the filter aid to remove small particles of suspended matter increases. The extent to which this takes place will depend very much on the type and particle size distribution of the undissolved solids being removed. 

Precipitate detection methods typically use light scattering techniques such as nephelometry, flow cytometry, and turbidity measurements to determine the amount of the precipitate formed during the incubation process. A major advantage with these types of techniques is the availability of particle size distribution and aggregation information. 

The same type of problem is encountered in the definition of particle size distribution since the starting assumption is that all particles have the same shape. In this case, the particle size distribution is defined as the relationship between a given particle size and the frequency, or number of particles, with that certain diameter or size. Matyi et al. (143a) discuss in detail for a given particle size distribution the several features that can be interpreted as the average size. We refer the reader to this review article. 

Figure 15.2 Influence of particle size distribution on activity and filtration behavior for three different types of wood-based activated carbons.

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