Fracture particle

Fine Size Limit (See also Single-Particle Fracture above.)... 

The manner in which a particle fractures depends on (i) the nature of the particle and (ii) the manner in which the fracture force is applied. A number of terms have been used to describe the different mechanisms of single particle fracture. The different terms considered here are abrasion, cleavage, shatter, and chipping. It may be pointed out that in practice these events do not occur in isolation. Real breakage involves a combination of these processes, with the proportions changing, depending on the equipment, and on the manner each particle is stressed within it. 

Because of the random motion of the solids, some abrasion of the surface occurs in the bed. However, this abrasion is very small relative to the particle breakup caused by the high-velocity jets at the distributor. Typically, particle abrasion (fragmentation) will amount to about 0.25 to 1 percent of the solids per day. In the area of high gas velocities at the distributor, greater rates of attrition will occur because of fracture of the particles by impact. As mentioned above, particle fracture of the grid is reduced by adding shrouds to the gas distributor. 

Nonetheless, mathematical analyses of milling operations, particularly for ball mills, roller mills, and fluid energy mills, have been moderately successful. There continues to be a pronounced need for more complete understanding of micromeritic characteristics, the intrinsic nature of the milling operation itself, the influence of fines on the milling operation, and phenomena including flaw structure of solids, particle fracture, particulate flow, and interactions at both macroscopic and microscopic scales. 

Elastic deformation is a reversible process, whereby, if the applied load is released before the elastic yield value is reached, the particles will return to their original state. Plastic deformation and brittle fragmentation are non-reversible processes that occur as the force on the particles is increased beyond the elastic yield value of the materials. Brittle fragmentation describes the process where, as the force is increased, particles fracture into smaller particles, exposing new, clean surfaces at which bonding can occur. For plastically deforming materials, when the force is removed, the material stays deformed and does not return to its original state. Plastic materials are also known as time-dependent materials because they are sensitive to the rate of compaction. We can also speak of viscoelastic-type materials which stay deformed when the force is removed, but will expand slowly over time. 

The same considerations apply to the making of a foam by dispersion of gas bubbles into water, assuming constant gas volume fraction. When dispersing particles by subdivision energy is still required, but the situation is somewhat different in that particles fracture rather than deforming and pinching off, as is the case with droplets and bubbles. 

Circulation and stirring conditions. This must be done on an individual basis. If the particles in the API exist as single crystals, aggressive settings should be avoided to prevent particle fracture. 

A third type of negative electrode is based on an alloy of the negative electrode active material with one or more other metals [22], Such anodes offer only limited rechargeability as the alloys lose their dimensional stability over long term cycling due to particle fracture induced by large volume changes encountered... 

Figure 8-40 Relationship Between Particle Size and System Properties. D = particle deposition in fibrous fillers, F = adhesion force, H = homogeneity of a particle, Sv = surface area per unit volume, W = particle weight, Vg = terminal setting rate, as = particle fracture resistance. Source From H. Schubert, Food Particle Technology. Part 1 Properties of Particles and Particulate Food Systems, J. Food Eng., Vol. 6, pp. 1-32, 1987, Elsevier Applied Science Publishers, Ltd.

Since the development of the equation, it has been tried to derive further information from it. Rees and Rue [129] determined the area under the Heckel plot. Duberg and Nystrom [137] used the nonlinear part for characterization of particle fracture. Paronen [138] deduced elastic deformation from the appearance of the Heckel plot during decompression. Morris and Schwartz [139] analyzed different phases of the Heckel plot. Imbert et al. [134] used, in analogy to Leuenberger and Ineichen [14], percolation theory for the compression process as described by the Heckel equation. Based on the Heckel equation, Kuentz and Leuenberger [135,140] developed a new derived equation for the pressure sensitivity of tablets. 

Figure 6. Electron micrograph of a CTBN-toughened epoxy resin with small particles—fracture through a shear band (X5200)...

Single-Particle Fracture The key issue in all breakage processes is the creation of a stress field inside the particle that is intense enough to cause breakage. The state of stress and the breakage reaction are affected by many parameters that can be grouped into both particle properties and loading conditions, as shown in Fig. 21-58. 

Fine Size Limit (See also Single-Particle Fracture above.) It has long been thought that a limiting size is attainable, and, in fact, it is almost a logical necessity that grinding cannot continue down to the molecular level. Nonetheless, recent results suggest that stirred... 

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