Particle crowds

We have already indicated that the coefficient kx in Equation (42) has been calculated for spheres by various theoretical models. While this coefficient is a measure of concentration effects, we do not pursue its derivation. Instead, we qualitatively examine the effect of particle crowding as the origin of the positive deviations from the Einstein theory that inevitably set in at higher concentrations, as seen in Figures 4.10 and 4.11. 

FIG. 4.11 The effect of particle crowding on viscosity. The solid line is drawn according to Equation (48) the points are experimental results. (Data from R. Roscoe, Br. J. Appl. Phys., 3, 267(1952).)... 

In impinging streams particle crowds exhibit two important contradictory behaviors as follows ... 

Beyond question, residence time distribution is one of the most important behaviors of particle crowds in impinging streams. This will be discussed in detail in the next chapter as it involves many complex problems. 

The movement and collisions of particle crowds in impinging streams are very complex and have great randomicity. Many researchers have devoted themselves to the... 

In nature, residence time distribution is an important behavior of particle crowds because of its complexity, it will be subject of focus in this chapter. 

But what we have the intention to consider is not a mass thus disseminated it is a coherent mass of water, whose various parts are adjacent to each other, which forms a continuous whole, limited by a certain surface this mass evidently cannot be considered as being in the same state as the preceding we may not say whether disseminating the particles crowded together or closing in the scattered parts is an operation which does not modify our mass of water. 

Figure 15.3 indicates that for the silica microspheres, the potential and viscosity both follow the expected behavior predicted by the classical DLVO theory. On the other hand, the nanosize fnmed silica exhibits a discrepancy between the expectation of DLVO theory and the experimental results that is, as the of the nanosize fumed silica increases, viscosity sharply increases. Hence factors such as particle crowding, particle ordering, and electroviscous effects will also impact viscosity, in addition to aggregate or network formation. 

Figure 9. Schematic of a two-particle crowded system. Key r, particle radius 8, diffusion layer thickness and 2,, interparticle distance.

In 1974, Tunstall and Hird (87) published a paper entitled "Effect of Particle Crowding on Scattering Power of Titanium Pigments" in which they agreed with Stieg s 1959 interpretation of... 

Suspensions can show varying rheological, or viscosity, behaviors. Sometimes these properties are due to stabilizing agents in the suspension. However, typically particle-particle interactions are sufficient to cause the suspension viscosity to increase because of electrostatic interactions or simply particle crowding. ... 

Particle Crowding" Effect. The growth of a crystal in a suspension can be influenced by the presence of other crystals when the crystal number concentration (number/volume) exceeds a certain level so that the interparticle distance becomes smaller than 20 particle diameters. For most precipitation systems, the crystal number concentration is typically higher than lO" per cm, and the interparticle distances are normally less than 15 times the crystal size. In such a crowded system, the diffusion fields around the individual crystals begin to influence one another and one may expect some interparticle effects on crystal growth. 

Sedimentation or free settling refers to the sinking of solid particles in a volume of liquid which is large with respect to the total volume of particles, hence particle crowding is a neg-Hgible phenomena. Usually, free setthng predominates when the mass fraction of solids is less than 15 wt.%. 

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