Nonspherical particles suspension viscosity

According to the Einstein theory, the intrinsic viscosity of a spherical particle suspension is 2.5. However, for a colloidal suspension of nonspherical particles, [r ] > 2.5. Jeffery [112] obtained the viscosity of an ellipsoidal particle suspension under shear. Incorporating Jeffery s results of velocity fields around the particle, Simha [113] obtained expressions for two explicit limiting cases of ellipsoids. Kuhn and Kuhn [114] also obtained an expression for intrinsic viscosity for the full range of particle aspect ratio (p) by taking an approach similar to Simha s method. 

If the particles are not spherical, even in the very dilute limit where the translational Brownian motion would still be unimportant, rotational Brownian motion would come into play. This is a consequence of the fact that the rotational motion imparts to the particles a random orientation distribution, whereas in shear-dominated flows nonspherical particles tend toward preferred orientations. Since the excess energy dissipation by an individual anisotropic particle depends on its orientation with respect to the flow field, the suspension viscosity must be affected by the relative importance of rotational Brownian forces to viscous forces, although it should still vary linearly with particle volume fraction. 

The Andreasen pipette introduced in the 1920s is perhaps the most popular manual apparatus for sampling from a sedimenting suspension. Determination of the change in density of the sampled particle suspension with time enables the calculation of size distribution of the particles. As Stokes law applies only to spherical particles, the nonspherical particles give a mean diameter referred to as Stokes equivalent diameter. The size range measurable by this method is from 2 to 60 pm (8). The upper limit depends on the viscosity of liquid used while the lower limit is due to the failure of very small particles to settle as these particles are kept suspended by Brownian motion. 

Suspensions of noninteracting rigid spheres are Newtonian up to volume fractions of ca. 25%.Interacting spheres, nonspherical particles, and polymer solutions frequently show non-Newtonian behavior at lower volume fractions, sometimes well below 5%. Most non-Newtonian behavior is shear-thinning, in that viscosity decreases with shear rate. The reverse effect, known as shear-thickening, is sometimes observed at higher shear rates in concentrated dispersions of relatively uniform particles. 

In principle, some types of nonspherical particles could be packed more tightly than spheres, although they would start to interact at lower concentrations. In reality, higher viscosities are normally found with nonspherical particles. The concentration law is approximately exponential at low to moderate concentrations, but equations similar to eq. 10.5.1 can still be used as well. The empirical value of 4>m can be much smaller than that for spherical particles (e.g., 0.44 for rough crystals with aspect ratios close to unity Kitano et al., 1981). If fibers are used, this value drops even further, down to 0.18 for an aspect ratio of 27 (see also Metzner, 1985). The decrease with aspect ratio seems to be roughly linear. Homogeneous suspensions of fibers with large aspect ratios are difficult to prepare and handle. As in dilute systems, the type of flow will determine the extent of the shape effect. Extensional flows are discussed below. 

The representation of the dispersion viscosity given above related to suspensions of particles of spherical form. Upon a transition to anisodiametrical particles a number of new effects arises. The effect of nonsphericity is often discussed on the example of model dispersions of particles of ellipsoidal form. An exact form of particles to a first approximation is not very significant, the degree of anisodiametricity is only important, or for ellipsoidal-particles, their eccentricity. 

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