Particle contact

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

There are three types of Hquid content in a packed bed (/) in a submerged bed, there is Hquid filling the larger channels, pores, and interstitial spaces (2) in a drained bed, there is Hquid held by capillary action and surface tension at points of particle contact, or near-contact, as weU as a zone saturated with Hquid corresponding to a capillary height in the bed at the Hquid discharge face of the cake and (3) essentially undrainable Hquid exists within the body of each particle or in fine, deep pores without free access to the surface except perhaps by diffusion or compaction. 

Theoretical Strength of Agglomerates. Based on statistical-geometrical considerations, Rumpf developed the following equation for the mean tensile strength of an agglomerate in which bonds ate localized at the points of particle contact (9) ... 

In processes where new powder feed has a much smaller particle size than the smallest granular product, the feed powder can be considered as a continuous phase which can nucleate to form new granules [Sastry Fuerstenau, Powder Tech., 7, 97 (1975)]. The size of the nuclei is then related to nucleation mechanism. In the case of nucleation by spray, the size of the nuclei is of the order of the droplet size and proportional to cos0, where 0 is binder fluid-particle contact angle (see Fig. 20-67 of Wetting section). 

This fitted the data well up to volume fractions of 0.55 and was so successful that theoretical considerations were tested against it. However, as the volume fraction increased further, particle-particle contacts increased until the suspension became immobile, giving three-dimensional contact throughout the system flow became impossible and the viscosity tended to infinity (Fig. 2). The point at which this occurs is the maximum packing fraction, w, which varies according to the shear rate and the different types of packings. An empirical equation that takes the above situation into account is given by [23] ... 

Logtenberg, S. A., Nijemeisland, M., and Dixon, A. G., Computational fluid dynamics simulations of fluid flow and heat transfer at the wall-particle contact points in a fixed-bed reactor, Chem. Eng. Sci. 54, 2433-2439 (1999). 

Polarization in the point dipole model occurs not at the surface of the particle but within it. If dipoles form in particles, an interaction between dipoles occurs more or less even if they are in a solid-like matrix [48], The interaction becomes strong as the dipoles come close to each other. When the particles contact each other along the applied electric field, the interaction reaches a maximum. A balance between the particle interaction and the elastic modulus of the solid matrix is important for the ER effect to transpire. If the elastic modulus of the solid-like matrix is larger than the sum of the interactions of the particles, the ER effect may not be observed macroscopically. Therefore, the matrix should be a soft material such as gels or elastomers to produce the ER effect. 

Electrode pressure on the sample material approximately corresponded to the pressure used in a practical EC in its operational mode and was equal to 8 kgf-cm 2 (this pressure was applied for purposes of minimization of particle contact resistance). 

The heat transfer from tubes in the freeboard was also measured for the 20 MW model. Figure 45 shows a comparison of the measured overall heat transfer coefficient in the 20 MW pilot plant versus that predicted from the scale model test. When the bed height is lowered, uncovering some tubes, the heat transfer is reduced because there are fewer particles contacting the tube surface. Although the scale model did not include proper scaling for convective heat transfer, the rate of change of the overall heat transfer should be a function of the hydrodynamics. 

Oguchi, U., and Kubo, J., Liquid-Solid Particles or Liquid-Gas-Solid Particle Contacting Method, U.S. Patent 3,754,993 (1973)... 

Electrolyte mixing is necessary to maintain the particles in suspension, unless the particles are neutrally buoyant, and to transport the particles to the surface of the electrode. The hydrodynamics of the electrodeposition system control the rate, direction, and force with which the suspended particles contact the electrode surface. Bringing the particles in contact with the electrode is a necessary step for the incorporation of particles into the metal matrix, although particle-electrode contact does not guarantee incorporation of the particle. Of course, an increase in flow can increase the plating rate as the thickness of the diffusion layer at the electrode surface decreases. 

In order to generate information on the mechanism of flocculation by polymers it is, however, necessary to correlate flocculation with various system properties, particularly adsorption. Thus, if particle/polymer-polymer/particle contact is the aggregation mechanism, the flocculation responses should be expected to continuously increase with surface coverage. On the other hand, if particle/polymer-particle contact is predominant and if the polymer adsorption is essentially irreversible, maximum flocculation might be expected under submonolayer conditions. In order to determine the nature of this relationship for the present systems, selected flocculation responses are plotted in Figures 8 and 9 as a function of surface coverage for the nonionic and the anionic polymer respectively. The assumptions involved in the computation of the surface coverage are to be noted at this point ... 

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