Grain size distribution scale effects

Although the powders in general consist of particles of irregular size and shape, the simplistic approach that considers isodiametric spherical particles makes a useful semi-quantitative analysis possible. 

The flow rate de/dt is inversely proportional to the viscosity t] and proportional to the stress, whose form (see equation [3.1]) is fu, where u is the radius of the sintering neck. The duration 8t of the transport of a given quantity of matter is inversely proportional to the speed, therefore  

The radius of the neck u, is in a certain ratio k with the radius of the particles x = kr. For a system that grows homothetically, particles p times coarser imply neck radii p times larger. Therefore, for this system that is p times larger  

This result shows that the duration is proportional to the size r of the particles and therefore that the sintering time necessary to obtain a certain degree of consolidation varies inversely to the size of the particles for example, dividing the size of the particles by ten reduces the duration of the sintering in the same ratio. 

We suppose that the spherical particles are covered with a thin film of liquid, with a thickness of ej. The matter flow is  

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Construction of levee material used by this study, were no major differences in the grain size distribution. However, differences the collapse time and the breach widening process. In the future, it is necessary to study characteristics of the soil in more detail such as adhesive strength. It is important to examine the scale effect of the model by comparing with the other researchers results in a field or large scale experiment. 

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