Effective particle concept

For liquids, there is no complete theory of multicomponent diffusion yet available. For this reason only rough theoretical approaches, as used for the description of mass transport in the porous particles filled with a liquid are discussed. The effective diffusivity concept just described is the only known approach and... 

A general transient model of diffusion-reaction that uses the effective diffusivity concept described for gas-solid catalytic reactions can be derived here as well, e.g., for a spherical particle ... 

Intraparticle diffusion resistance may become important when the particles are larger than the powders used in slurry reactors, such as for catalytic packed beds operating in trickle flow mode (gas and liquid downflow), in upflow gas-liquid mode, or countercurrent gas-liquid mode. For these the effectiveness factor concept for intraparticle diffusion resistance has to be considered in addition to the other resistances present. See more details in Sec. 19. 

Example 11-5 Vycor (porous silica) appears to have a pore system with fewer interconnections than alumina. The pore system is monodisperse, with the somewhat unusual combination of a small mean pore radius (45 A) and a low porosity 0.31. Vycor may be much closer to an assembly of individual voids than to an assembly of particles surrounded by void spaces. Since the random-pore model is based on the assembly-of-particles concept, it is instructive to see how it applies to Vycor. Rao and Smith measured an effective diffusivity for hydrogen of 0.0029 cm /sec in Vycor. The apparatus was similar to that shown in Fig. 11-1, and data were obtained using an H2-N2 system at 25°C and 1 atm. Predict the effective diffusivity by the random-pore model. 

Thus electrons behave in some respects like particles and in other respects like waves. We are faced with the apparently contradictory wave-particle duality of matter (and of light). How can an electron be both a particle, which is a localized entity, and a wave, which is nonlocalized The qpswer is that an electron is neither a wave nor a particle, but something else. An accurate pictorial description of an electron s behavior is impossible using the wave or particle concept of classical physics. Hie concepts of classical physics have been developed from experience in the macroscopic world and do not properly describe the microscopic world. Evolution has shaped the human brain to allow it to understand and deal effectively with macroscopic phenomena. The human nervous system was not developed to deal with phenomena at the atomic and molecular level, so it is not surprising if we cannot fully understand such phenomena. 

The first reduction of the two-scale model that we consider is already included in the equations from Table 3.1 and refers to the reaction-diffusion problem inside catalytic particles. The treatment of this question based on the effectiveness factor concept (rf) is widely generalized in the literature, after the seminal works of Damkohler [77], Thiele [78], and Zeldovitch [79]. It may be defined for a reaction j with respect to the conditions prevailing at the pellet surface by Ref. [80] ... 

While there is no precise definition, nano-fillers can be considered as particles which, when dispersed in polymers, are very small in at least one dimension. This concept is pushed quite far in some of the literature, with particles of up to at least a hundred nanometers being described as nano-particles. A reasonable working definition would seem to be that at least one dimension of the effective particle, when dispersed in a polymer matrix, should be no more than 20 nm, or 200 A. As a result, the specific surface area, which plays a significant role in the effects observed, will be at least 150 m /g. The term effective particle is used to eliminate fillers, such as carbon blacks, where the primary particle could be in the specified range, but are strongly aggregated into larger structures, that become the effective particles. 

One of the principal difficulties is due to the ability of many fillers to exhibit a variety of particle shapes and sizes depending on the work done in dispersing them. Their effective shape and size can therefore vary at any stage of composite formation and use. In principle one would like to characterise them in situ. This is, however, far less easy than characterising the initial particulate material itself and one is usually reduced to trying to carry out measurements under conditions that will represent as near as possible those encountered in use. In this context, the concept of effective particle, which is the size and shape achieved in the actual application, is a very useful one to keep in mind and is returned to later in this chapter. 

It has already been observed that spin-charge inversion is one of the remarkable features of a conjugational defect in poly acetylene charged defects are spinless neutral defects carry a magnetic moment. This inversion is related to fractionized charges, which also occur in elementary-particle physics and in the fractionized quantum Hall effect [107]. Spin-charge inversion is a symmetry property of the system, it makes use of the quasi-particle concept, but non-dispersive motion is not essential in this respect. 

Effects of the project week (approximately 120 students participating) were investigated by means of the following design (Figure 5). At the beginning of the year, a pre-test was administrated which included a questionnaire on the idea of particles. Concept maps were also used to measure students conceptions about the micro-world. 

After the project week, the desired positive effects became evident in all areas of the particle conception and were highly significant The learning effects with regard to the thinking about models suggested that students advanced from a naive-realistic conception to a hypothetical-realistic position. Moreover, flie results of the analysis of scales elucidated that students were more careful not to apply macroscopic characteristics directly to the smallest particles. The same pertained to ascribing macroscopic behaviour. 

Where d is the particle surface charge density. The effective particle radius should lead to the concepts of the effective particle volume fraction, (t>eff, the effective inter-particle spacing, IPSeff, the effective free volume of... 

It also was found experimentally, in accordance with theoretical predictions, that the jamming coverage of hard spheres adsorbed irreversibly (in the limit of negligible electrostatic interactions) approached 55%. This value strongly decreases for lower ionic strength, hilly in accordance with the effective hard-particle concept. This hnding conhrmed the decisive role of the lateral electrostatic interactions in irreversible adsorption of colloid particles. 

These preliminary results are a first demonstration that the shape-selected particles concept may work in a realistic fuel cell environment. Future research will focus on degradation and stability tests of the novel materials as well as their application in other fuel cell types, as for instance direct methanol fuel cells and high-temperature pol)uner electrolyte membrane fuel cells. Moreover, the effect of the surfactant requires special attention, as the surfactant molecules may also influence the electrocatalysis by a ligand effect or an ensemble effect directing the adsorption of reactants to specific surface sites. 

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