Particle rotation, effective volume fraction

Effect of Particle Rotation on the Effective Volume Fraction The rotation of particles cause the effective volume fraction of an anisotropic particle to be much laiger than that of the volume fraction of the particle itself. For example, the volume of the effective sphere of revolution divided by the particle volume is given by... 

The situation for non-interacting anisometric aggregates is more complicated, because such particles can rotate in a shear gradient and their effective volume fraction is therefore much larger than the volume of the micelles, even if their hydration shell is taken into account. Such solutions are also Newtonian liquids, although their viscosities are higher than the viscosities of spheres with the same concentrations. For such systems, the Simha equation has been derived, as follows ... 

In suspensions of particles with an aspect ratio (length to diameter) greater than 1, particle rotation during flow results in a large effective hydrodynamic volume, and Kh > 2.5 (see Figure 4.7). At particle volume fractions above about 5-10%, interaction between particles during flow causes the viscosity relationship to deviate from the Einstein equation. In such instances, the reduced viscosity is better described by the following relationship ... 

When the particles in suspension are non-spherical, the rotation of the particles due to Brownian motion results in an excluded volume, which is higher than the volume-fraction of the particles. As the degree of anisotropy increases, the effects become more dramatic. Figure 9.6 shows the volume-fraction dependence of the viscosity of silicon nitride, alumina and silicon carbide whisker (SiCw) suspensions. The experimental points were fitted to a modified Krieger-Dougherty equation ... 

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