Individual packing fractions

Flow of any concentrated suspension will become impossible when the solid particles can form a continuous three-dimensional network of contacts throughout the sample. This so-called maximum packing fraction 4> depends mainly on the particle size distribution and the particle shape. Broader particle size distributions result in lower values of 4>m, because the smaller particles can fill the gaps between the bigger ones, and a deviation from spherical shape results in lower values of 4>m due to steric hindrance of packing. Also flocculation will result in a decrease in the value of 4>in, because the individual floes are only loosely packed. 

Figure 17.33 Distance between individual 7 xm diameter carbon fiber filaments in a regular hexagonal array at different packing fractions.

The size of the ionic radii and the character of their interactions, dependent on the metal type, is reflected in the space packing density. Knowing the values of ionic radii one can calculate the p>acking density of ions in individual oxides. The relation between the packing fraction of ions and the metal ion radius is presented in Fig.lO. The relative metal ion radii were used and the oxygen ion radius was assumed to be 0.14 nm. The packing fraction was calculated as the ratio of the volume occupied by ions (Vai) to the volume of the unit cell calculated from lattice parameters (Vx). 

Foams and emulsions soften as their packing fraction decreases—their shear modulus gets smaller and ultimately vanishes continuously at the critical packing fraction Hence, the collective response of a foam or emulsion can be much softer than its individual contacts. 

An on-line supercritical fluid chromatography-capillary gas chromatography (SFC-GC) technique has been demonstrated for the direct transfer of SFC fractions from a packed column SFC system to a GC system. This technique has been applied in the analysis of industrial samples such as aviation fuel (24). This type of coupled technique is sometimes more advantageous than the traditional LC-GC coupled technique since SFC is compatible with GC, because most supercritical fluids decompress into gases at GC conditions and are not detected by flame-ionization detection. The use of solvent evaporation techniques are not necessary. SFC, in the same way as LC, can be used to preseparate a sample into classes of compounds where the individual components can then be analyzed and quantified by GC. The supercritical fluid sample effluent is decompressed through a restrictor directly into a capillary GC injection port. In addition, this technique allows selective or multi-step heart-cutting of various sample peaks as they elute from the supercritical fluid... 

Coupled columns packed with different stationary phases can be used to optimize the analysis time (71, 75). In this approach the different columns are connected in a series or in parallel. liie sample mixture is first fractioned on a relatively short column. Subsequently the fractions of the partially separated mixture are separated on other columns containing the same or other stationary phases in order to obtain the individual components. Columns differing in length (number of theoretical plates), adsorptive strength or phase ratio (magnitude of specific surface area), and selectivity (nature of the stationary phase) can be employed, whereas, the eluent composition remains unchanged. Identification of the individual sample components via coupled column technique requires a careful optimization of each column and precise control of each switching step. 

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