Bulk particle properties

Expressions for minimum fluidizing velocify can be derived by examining fhe relationship between the velocity of a fluid passing through a packed bed of particles and the resultant pressure drop across the bed. Consequently it is necessary to define a number of bulk particle properties which influence fluidized bed behaviour. 

The solids density Ps is the density of fhe solid material from which fhe parficle is made and excludes any pore spaces within the particle. It can be measured using a specific gravity bottle and a liquid in which the particle does not dissolve. The envelope density of a particle is that which would be measured if an envelope covered the external particle surface, i.e. it is equal to the particle mass divided by the external volume. In most analyses the envelope and solids densities are assumed to be equivalent. The bulk density of a powder ps is the effective density of the particle bed defined by 

The bulk density will be considerably smaller than the solids density because the bed volume includes the volume of the spaces between particles. 

Intraparticle porosity refers to the fraction of the particle volume which is occupied by internal pores most manufactured food particles are porous. However, it is important to distinguish this quantity from bed voidage. The interparticle voidage e is the fraction of the packed bed occupied by the void spaces between particles and is defined as 

Volume is inversely proportional to density and therefore equation 1.20 becomes 

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The basis of all bulk conveyor engineering is the precise definition and accurate classification of materials according to individual characteristics under a specific combination of handling conditions (1). Since the late 1960s there has been an extraordinary growth in research into the fundamental properties and behavior of particulate soHds. However, as of this writing, it is not possible to predict the handling behavior of a bulk soHds material relevant to conditions in a specific conveyor, merely on the basis of the discrete particle properties. 

B bulk property d deactivation e effective property G gas phase i component index i reaction index L liquid phase p catalyst particle property equilibrium conditions... 

Evaluation of the morphology of a pharmaceutical solid is of extreme importance, since this property exerts a significant influence over the bulk powder properties of the material. In addition to providing insights into the micromeritic properties of the solid, microscopy can also be used to develop preliminary estimations of the particle-size distribution. A determination can be easily made regarding the relative crystallinity of the material, and it is often possible to deduce crystallographic information as well. Unknown particulates can often be identified solely on the basis of their microscopic characteristics, although it is useful to obtain confirmatory support for these conclusions with the aid of microscopically assisted techniques. 

In the present work, such a systematic approach to the physical characterization of pharmaceutical solids is outlined. Techniques available for the study of physical properties are classified as being associated with the molecular level (properties associated with individual molecules), the particulate level (properties pertaining to individual solid particles), and the bulk level (properties associated with an ensemble of particulates). Acquisition of this range of physical information yields a total profile of the pharmaceutical solid in question, whether it is an active drug, an excipient, or a blend of these. The development of a total profile is a requirement for successful manufacture of any solid dosage form. 

The accessibility of new techniques such as EXAFS brings researchers a powerful tool for unambiguous determination of the true core metallic framework of such systems. Thus, the relationship between the parent carbonyl precursor, the support and the final metal-supported particles has been studied at the structural atomic level in some cases. This can allow differentiation of the catalytic behavior of supported metal particles with bulk-like properties from that of supported metal clusters, opening the way to understanding the mechanism of metal-catalyzed reactions and extending the concept of sensitive or insensitive structure reactions from metal aggregates to clusters. 

Solidification of the particles may not be the final step in the formation process of solid lipid particles. Lipidic materials exhibit rich polymorphism [69,70], which may also occur in the dispersed state. In nanoparticles, the polymorphic behavior of the matrix lipids may, however, differ distinctly from that in the bulk material. Polymorphic transitions are usually accelerated in the nanoparticles compared with the bulk lipids [2,62]. In some cases, polymorphic forms not observable in the corresponding bulk materials were detected in lipid nanoparticles [1,65]. Because polymorphism can affect pharmaceutically relevant properties of the particles, such as the drug incorporation capacity [65], corresponding investigations should also be included in the characterization process. As long as polymorphic or other crystalaging phenomena have not terminated, the particle matrix cannot be regarded as static, and alterations of the particle properties may still occur. 

Volume-normalized extinction is plotted in Fig. 11.2 as a function of photon energy for several polydispersions of MgO spheres both scales are logarithmic. For comparison of bulk and small-particle properties the bulk absorption coefficient a = Airk/X is included. Some single-particle features, such as ripple structure, are effaced by the distribution of radii. The information contained in these curves is not assimilated at a glance they require careful study. 

The state of the art in friction and wear of PTFE-filled rubbers include the effects of many important system parameters, such as the composition of the rubber formulation, particle dispersion, bulk mechanical properties, ability of transfer film formation, and the chemistry between PTFE powder and the rubber matrix. Although the present study has explicitly highlighted the potential of PTFE powder in rubber matrixes with significant property improvements in the friction, wear, and physical properties, it has simultaneously opened a new field regarding the use of PTFE powder in rubber compounds, with some challenging tasks for chemists, engineers, and material scientists. 

The properties of any material are dependent on the particles present and the forces operating on the particles. Since these forces are different at the frontier than the forces in the bulk, the properties of the frontier region, the interphase region, will differ from the bulk properties. Thus, the uniform properties of the electrolyte are perturbed in the interphase region by the presence of another phase. 

The measurement of residual stresses is usually associated with the analysis of mechanical properties, and not microstructure. However, residual stress fields in nanocomposites depend directly on microstructural parameters (particle size, position and spacing), as well as bulk material properties, such as differences in the coefficient of thermal expansion. 

One of the most important properties of a material is its density, for which there are several expressions, namely, bulk, particle, and skeletal densities. The bulk density of solids is the overall density of the material including the interparticle distance of separation. It is defined as the overall mass of the material per unit volume, which can be determined by simply pouring a preweighed sample of particles into a graduated cylinder and measuring the volume occupied. The material can become denser with time and settling, and its bulk density reaches a certain limiting value, known as the tapped or packed bulk density. 

These questions lead on to further fundamental questions concerning the shapes and properties of small metal particles. For example, what is the stable shape for a small metal particle How is this affected by size, method of preparation, temperature, gaseous environment, precursor compound, support morphology, etc. Do small metal particles have different electronic properties from bulk metal Do surface electronic properties depend on particle size, and if so, do they vary in the same way as bulk electronic properties When, indeed, is a particle small enough to have unusual properties ... 

All the experimental results summarized in this section have been interpreted in the original papers as evidence that there is a change in electronic properties of small metal particles due to their size. Most researchers agree that upwards of 150 atoms is required to attain bulk-like properties. The narrowing of the electron bands is attributed to the fact that in a small crystal there are fewer molecular orbitals which go to make up the electron band. This particular point is not in dispute. However, what has been challenged is the interpretation of shifts in the position of the centroid of the d-band, or... 

Bulk electronic properties are observed for particles containing about 150 atoms, corresponding to diameters in the range 1.5-2.0 nm. On the other hand, surface electronic properties typical of bulk metal are observed with much smaller particles. Only about 25 atoms are required in a particle for the adsorption to the be characteristic of the bulk metal. 

Thermodynamics deals with relations among bulk (macroscopic) properties of matter. Bulk matter, however, is comprised of atoms and molecules and, therefore, its properties must result from the nature and behavior of these microscopic particles. An explanation of a bulk property based on molecular behavior is a theory for the behavior. Today, we know that the behavior of atoms and molecules is described by quantum mechanics. However, theories for gas properties predate the development of quantum mechanics. An early model of gases found to be very successftd in explaining their equation of state at low pressures was the kinetic model of noninteracting particles, attributed to Bernoulli. In this model, the pressure exerted by n moles of gas confined to a container of volume V at temperature T is explained as due to the incessant collisions of the gas molecules with the walls of the container. Only the translational motion of gas particles contributes to the pressure, and for translational motion Newtonian mechanics is an excellent approximation to quantum mechanics. We will see that ideal gas behavior results when interactions between gas molecules are completely neglected. 

Analytical characterization includes measurement of absolute sizes and concentrations of species present in the catalyst. For the purpose of clarity, these techniques have been organized, starting with the bulk macroscopic properties, down to the component, microscopic features. The underlying goal of analytical characterization is to provide information about the sample which will allow research personnel to relate the properties measured to some aspect of a catalyst s performance, either in the field or in the evaluation laboratory. Macroscopic characterization includes both chemical compositions and physical properties such as particle size, density and total surface area. Chemical analysis techniques are well... 

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