Characterization particle size distribution

This is the special form which f. in Eq. (10) must take for y. to be constant during diffusion-limited growth. It corresponds to a unimodal particle size distribution characterized by the two constants k/B and A/B. ... 

Other statistical measurements used in geology for particle size distribution characterization (moment, quartile and others) have been defined [135,136]. 

J. de Graaf, A.J. van Dillen, K.P. de Jong, and D.C. Koningsberger, Preparation of Highly Dispersed Pt Particles in Zeolite Y with a Narrow Particle Size Distribution Characterization by Hydrogen Chemisorption, TEM, EXAFS Spectroscopy, and Particle Modeling. J. Catal., 2001, 203, 307-321. 

The Rosin-Rammler fimction is widely used in particle size distribution characterization. It was introduced in comminution studies in 1933 (Harris, 1971/1972), but was also used to describe the particle size distribution of moon dust (Allen, 1981). Usually, it is a two-parameter function given as a cumulative percentage undersize (Svarovsky, 2000) ... 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

A fundamental requirement in powder processing is characterization of the as-received powders (10—12). Many powder suppHers provide information on tap and pour densities, particle size distributions, specific surface areas, and chemical analyses. Characterization data provided by suppHers should be checked and further augmented where possible with in-house characterization. Uniaxial characterization compaction behavior, in particular, is easily measured and provides data on the nature of the agglomerates in a powder (13,14). 

The characteristics of a powder that determine its apparent density are rather complex, but some general statements with respect to powder variables and their effect on the density of the loose powder can be made. (/) The smaller the particles, the greater the specific surface area of the powder. This increases the friction between the particles and lowers the apparent density but enhances the rate of sintering. (2) Powders having very irregular-shaped particles are usually characterized by a lower apparent density than more regular or spherical ones. This is shown in Table 4 for three different types of copper powders having identical particle size distribution but different particle shape. These data illustrate the decisive influence of particle shape on apparent density. (J) In any mixture of coarse and fine powder particles, an optimum mixture results in maximum apparent density. This optimum mixture is reached when the fine particles fill the voids between the coarse particles. 

Suspension Polymers. Methacrylate suspension polymers are characterized by thek composition and particle-size distribution. Screen analysis is the most common method for determining particle size. Melt-flow characteristics under various conditions of heat and pressure are important for polymers intended for extmsion or injection molding appHcations. Suspension polymers prepared as ion-exchange resins are characterized by thek ion-exchange capacity, density (apparent and wet), solvent sweUing, moisture holding capacity, porosity, and salt-spHtting characteristics (105). 

The most commonly measured pigment properties ate elemental analysis, impurity content, crystal stmcture, particle size and shape, particle size distribution, density, and surface area. These parameters are measured so that pigments producers can better control production, and set up meaningful physical and chemical pigments specifications. Measurements of these properties ate not specific only to pigments. The techniques appHed are commonly used to characterize powders and soHd materials and the measutiag methods have been standardized ia various iadustries. 

Aerosol Dynamics. Inclusion of a description of aerosol dynamics within air quaUty models is of primary importance because of the health effects associated with fine particles in the atmosphere, visibiUty deterioration, and the acid deposition problem. Aerosol dynamics differ markedly from gaseous pollutant dynamics in that particles come in a continuous distribution of sizes and can coagulate, evaporate, grow in size by condensation, be formed by nucleation, or be deposited by sedimentation. Furthermore, the species mass concentration alone does not fliUy characterize the aerosol. The particle size distribution, which changes as a function of time, and size-dependent composition determine the fate of particulate air pollutants and their... 

Brown et al. [494] developed a method for the production of hydrated niobium or tantalum pentoxide from fluoride-containing solutions. The essence of the method is that the fluorotantalic or oxyfluoroniobic acid solution is mixed in stages with aqueous ammonia at controlled pH, temperature, and precipitation time. The above conditions enable to produce tantalum or niobium hydroxides with a narrow particle size distribution. The precipitated hydroxides are calcinated at temperatures above 790°C, yielding tantalum oxide powder that is characterized by a pack density of approximately 3 g/cm3. Niobium oxide is obtained by thermal treatment of niobium hydroxide at temperatures above 650°C. The product obtained has a pack density of approximately 1.8 g/cm3. The specific surface area of tantalum oxide and niobium oxide is nominally about 3 or 2 m2/g, respectively. 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

H. E., and Crommelin, D. J. A., Characterization of liposomes (1987). The influence of extrusion of multilamellar vesicles through polycarbonate membranes on particle size, particle size distribution and number of bilayers, Int. J. Pharm.. 35, 263-274. 

Not all reference materials producers currently employ the various techniques that would characterize materials for microanalytical use. Such techniques include measurement of particle size distribution, particle composition, and the determination of component homogeneity with microanalytical techniques. Nevertheless, some... 

In order to evaluate the extent of attrition and its impact on the particle size distribution, there is a need of a qualitative and quantitative characterization. This, however, is not as simple as it may seem at first. There are many different properties, parameters and effects that manifest themselves and could be measured. In addition, as will be shown, the choice of the assessment procedure is strongly connected with the definition of attrition which, on its part, depends on the degradation mechanism that is considered to be relevant to the process. Hence there are a lot of procedures and indices to characterize the process of particle attrition. Section 3 deals with those which are relevant to fluidized beds and pneumatic conveying lines. 

H. N. Frock, in Particle Size Distribution Assessment and Characterization, T. Provder, ed., American Chemical Society, Washington, D.C., 1987, pp. 146-160. 

Catalytic reactions in fluidized-bed reactors often involve the use of catalyst particles of different sizes, which may be characterized by a particle-size distribution. Consider the reaction A(g) -> products, for which the following data are available ... 

Characterization of wastewater organic matter in terms of particle size distribution has been provided by Levine et al. (1985), Logan and Jiang (1990) and Levine et al. (1991) (Figure 3.5). 

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