Single particle size shape

Measurements taken from a series of different ct arrived at in situ by dilution in specially designed viscometers comprise the capillary viscometry technique known as dilution viscometry. Neither single-point nor dilution viscometry is suitable for suspensions, because of the unreliability of their , resulting from heterogeneities of particle size, shape, and interaction. Variations in t- are conducive to slippage, wall effects, and turbulence. 

Shapespeare Corporation s Juliet features single particle size and shape measurement together with fractal analysis as well as conventional classical measurements. It also measures size and shape distributions for sets of particles with image manipulation and data graphing capability. 

An ideal study of support effects requires model catalysts with metal particles that are identical in size and shape (so that only the support oxide varies). This is difficult to achieve for impregnated catalysts, but identical metal particles can be prepared via epitaxial model catalysts [36]. Well-faceted Rh nanocrystals were grown on a 100-cm area NaCl(OOl) thin film at 598 K. One half of a Rh/NaCl sample was covered with Al Oj, and the other half with TiO. The preparation of Rh particles for both Al Oj- and TiO -supported model catalysts in a single step prevents any differences in particle size, shape, and surface structure which could occur if the samples were prepared in separate experiments. Three model catalysts were prepared, with a mean Rh particle size of 7.8, 13.3, and 16.7 mn (the films were finally removed from the NaCl substrate by flotation in water). Activation was performed by O /H treatments, with the structural changes followed by TEM (Fig. 15.6). Oxidation was carried out in 1 bar O at 723 K prodncing an epitaxially grown rhodium oxide shell on a Rh core (cf Fig. 15.5e), whereas the hydrogen reduction temperature was varied. 

Rarely will a single adsorbent be optimal in all of these respects. Frequently it will be possible to narrow the choice to one or two classes of adsorbents, leaving a vast array of possible particle sizes, shapes, pretreatment conditions, and so forth. Final decisions should always be based on data. To make budget estimates, however, a number of different approaches can be derived from rules of thumb to provide quick experimental feasibility tests. Potential sources of such information are adsorbent or equipment vendors, published or commercial databases, and in-house or external laboratories. 

The total fraction remaining, F, calculated from the volume of HC1 added is given as a function of dimensionless time, t/t50, where t50 is the time required to dissolve 50% of the CaC03. Calculated curves are also given using the simplified mass transfer model with a single particle size (monodisperse) and with the actual polydisperse size distribution (Table 2). The polydisperse model fits the shape of the curve very well at all times. The monodisperse model is only satisfactory for t/t50 less than 1. 

The grade efficiency has become a very useful definition, since most industrial powders consist of an infinite number of differently sized particles. Thus, a single particle size really corresponds to a range of particles having almost similar sizes. Therefore, the gradeefficiency of most separation equipments is a continuous function of x. This function is seldom expressed analytically but graphically. An S-shaped curve is usually obtained for separators in which inertial or gravity body forces perform the separation. 

This ideal case is rarely if ever encountered in practice in general there will be a distribution of particle sizes rather than a single size, and in addition there will usually be a range of particle shapes, many of them highly irregular. 

To measure the strength of the forces exerted on particles, various analytical techniques have been developed [6, 7]. Unfortunately, since most of these techniques are based on hydrodynamics, assumption of the potential profiles is required and the viscosities of the fiuid and the particle sizes must be precisely determined in separate experiments, for example, using the viscous flow technique [8,9] and power spectrum analysis of position fluctuation [10]. Furthermore, these methods provide information on ensemble averages for a mass of many particles. The sizes, shapes, and physical and chemical properties of individual particles may be different from each other, which will result in a variety of force strengths. Thus, single-particle... 

Structure sensitivity is not a single phenomenon but can often be regarded as a set of independent, but interlinked mechanisms. At the very beginning it is important to realize that the term particle size effect (PSE) not only refers to the size of active component particles but moreover comprises effects deriving from peculiarities in their morphology, that is, their shape and structure. 

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