Packing size of a non-spherical

Determination of the Packing Size of a Non-spherical Particle An Emperical Approach... 

The equivalent packing diameter of a non-spherical particle should be a function of its size and shape. Probably the so-called concept packing size was first used by Meloy who also felt that it should be possible to quantify the packing size of a non-spherical particle from its shape analysis. However, at least to our knowledge, to date there have been no publications dealing with this problem in the literature. In fact, it is very difficult, if not impossible, to develop such a method. Therefore, we have here proposed an alternative approach to this problem. As discussed below, the resultant equivalent packing diameter of a non-spherical particle can be readily related to its geometric size and shape. 

It is highly desirable to relate the packing size of a non-spherical particle to its size and shape analysis. For this purpose, the packing of fiber-sphere (cylinder-sphere) binary mixtures , as it has been extensively investigated, is worthwhile being examined further. 

The purpose of this paper is to propose an empirical approach to the characterization of the padang size of a non-spherical particle with our present knowledge of the packing of solid particles. 

However, it should be noted that the present work is based on the limited quantitative data available in the literature. For example, eqn.(5) was only partially verified (see Figure 7). Furthermore, the proposed approach is to a great degree established based on the results of fiber-sphere binary mixtures. The effect of other shapes on the porosities of non-spherical particle mixtures should be investigated. Therefore, it is considered that in order to characterize the packing size of a particle and hence the structural properties of particle mixtures properly, it seems that much more experimental work needs to be done in order to obtain the required store of quantitative data, especially for the packing of particles with low sphericities. 

In general, the Ergun equation for flow through a packed bed of non-spherical and polydisperse-sized particles becomes ... 

Bon and coworkers carried out a study on the fate of the nanoparticles throughout solids-stabilized emulsion polymerization [119], A quantitative method based on disk centrifugation was developed to monitor the amount of nanoparticles present in the water phase in solids-stabilized emulsion polymerizations of vinyl acetate, methyl methacrylate, and butyl acrylate. The concentration profile of nanoparticles in the water phase as a function of monomer conversion agreed with theoretical models developed for the packing densities in these systems [120]. Noteworthy was that in the case of silica-nanoparticle-stabilized emulsion polymerization of vinyl acetate, the event of late-stage limited coalescence, leading to small armored non-spherical clusters, could be predicted and explained on the basis of the concentration profiles and particle size measurements. Adjusting the amount of silica nanoparticles prevented this phenomenon. 

Furthermore, an icosahedron composed of 12 spherical (identical or non-identical subunits) lipid A-phosphate clusters can be constructed and arranged around a central sphere. The sphere was surrounded by a second icosahedral shell twice the size of the first. The shell contained 42 spheres one layer to the next one. This implies in light of multiple lipid A-phosphate molecules packed as deformable spheres that the adoption of an HCP arrangement was only possible for the high volume fractions mentioned... 

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