Sphericity of the particle

The bed geometry defines the scale factor and ( is the sphericity of the particles. By matching this set of parameters hydrodynamic similarity is almost obtained as has been confirmed by several experimental investigations (4). 

Here VP, SP, and s are the volume, the effective surface area, and the sphericity of the particle, respectively. 

There are a number of procedures for determining the particle size of the latex polymer. Transmission electron microscopy (TEM) has been used for some time. The method is necessary to confirm the sphericity of the particles. Since a microscopist selects the images for further study, and the number of slides to be taken is limited for practical reasons, the statistical randomization of the measurements is somewhat questionable. Results, by the latter technique have actually been surprisingly good. 

Flow through packed beds of solids is usually analyzed by considering such characteristics as the porosity of the bed and the sphericity of the particles, and Section 7.5.4.1 shows that the analysis of a filter is helped by considering how the deposit of precipitated solids changes those characteristics. In the other filters, the solids deposit as a cake on the filter medium. The resistances of the filter cake and medium are then additive. When the resistivity, or the resistance per unit thickness, of the cake remains constant throughout operation, the specific resistance increases linearly with the amount of solid deposited. Analytical solutions for the filtration rate are then possible. In the constant-rate case, the pressure drop encountered can be expressed as a function of time (Section 7.5.4.2). 

Figure 6.10 Packing density versus the reciprocal of the standard deviation for particles with a log normal size distribution. The parameter is a measure of the sphericity of the particles and is equal to the reciprocal of the shape factor. (From Ref. 9.)...

It must be noted that the Archimedes number Ar T is based on the Sauter diameter referring to Equations (3.81) and (3.69) and y/ denotes the dimensionless sphericity of the particles. 

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