Packings aspect ratio

Particle shape also affects the sintering of a powder compact. Jagged or irregular shaped particles, which have a high surface area to volume ratio, have a higher driving force for densification and sinter faster than equiaxed particles. High aspect ratio platey particles, whiskers, and fibers, which pack poorly, sinter poorly. 

It may be that the extent of dispersion is to be determined from correlations rather than by direct experimental means. Suitable correlations based on large quantities of data exist for common reactor geometries, i.e. tubular reactors, both empty and packed, fluidised beds or bubble columns. Some of these are expressed in graphical form in, for instance, refs. 17, 21 and 26. Most forms of correlation give the intensity of dispersion D/ud as a function of Reynolds and/or Schmidt numbers if this intensity is multiplied by an aspect ratio, i.e. djL for a tubular reactor, then the dispersion number is obtained. 

The coercive force of a powder is an extrinsic property, which is influenced by many factors such as size and shape and packing density. Maghemite particles prepared from directly precipitated spindle-type hematite particles showed a tendency of increase in coercive force with decrease in particle size, and increase in their aspect ratios (31). However, a quantitative relationship between the coercive force and size and/or aspect ratio is still not available. 

There is no radial velocity, and the axial velocity across the radius of the packed bed is uniform. Schwartz and Smith (1953) found that the velocity across the diameter of a packed bed is not uniform for radial aspect ratios (tube-to-particle diameter) less than about 30, due to the significant effect of the increased void space near the wall where the particles are locally ordered. This result has been verified by Hoiberg et al. (1971) for a packed bed reactor with radial aspect ratio about 50. They considered a radial velocity variation suggested by experimental observations with a sharp peak about 15% greater than the mean fluid velocity situated close to the wall. Simulations using their model showed results virtually identical to those obtained with a uniform velocity profile.3... 

Pressure Drop, Mass and Heat Transfer Pressure drop is more important in reactor design than in analysis or simulation. The size of the compressor is dictated by pressure drop across the reactor, especially in the case of gas recycle. Compressor costs can be significant and can influence the aspect ratio of a packed or trickle bed reactor. Pressure drop correlations often may depend on the geometry, the scale, and the fluids used in data generation. Prior to using literature correlations, it often is advisable to validate the correlation with measurements on a similar system at a relevant scale. 

Intalox Snowflake packing (Fig.. 4e). The low aspect ratio (height to diameter), even lower than that of CMR , orients the Snowflake- par-... 

Kitano et al.61 also conducted a study on suspensions of elongated particles Fig. 4.9. Aspect ratios ranged from 1 (for spheres) to 27 (for carbon fibers). The results of this study are similar to those obtained for spherical particles. However, the larger the aspect ratio, the lower the volume fraction of solid at which the packing threshold is reached. The viscosity of the suspensions follow Eqn. (2), with a constant 0 that depends on the aspect ratio see Table 4.1. 

If the flow rate is sufficiently high to create turbulent flow, then Pe is a constant and the magnitude of the right-hand side of the equation is determined by the aspect ratio, L/d. By solving Equation, (8.4.12) and comparing the results to the solutions of the PER [Equation (8.4.3)], it can be shown that for open tubes, L/d, > 20 is sufficient to produce PER behavior. Likewise, for packed beds, L/d, > 50 (isothermal) and L d, >150 (nonisothermal) are typically sufficient to provide PER characteristics. Thus, the effects of axial dispersion are minimized by turbulent flow in long reactors. 

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