Viscosity of Diluted Liquid Dispersions

The presence of (colloidal) particles in a liquid medium always increases the viscosity of the system. The reason is that the particles interrupt the stream lines (i.e., inside the particles there is no or less shear) so that a higher stress is required to achieve the same shear rate. 

The most simple situation is that of incompressible, impermeable, noninteracting particles dispersed in a fluid continuum. For such (hypothetical) systems Einstein derived that the viscosity TJs increases proportionally with the volume fraction O of 

Tio is the viscosity of the medium k a constant depending on the shape of the particles 

FIGURE 17.9 The value of k (Equation 17.7) for ellipsoidal particles as a function of then-shape. 

Because of the underlying assumption that the particles are noninteracting, which implies here that the flow pattern around any particle is not affected by the presence of the others, Equation 17.7 applies to very dilute dispersions only. Roughly speaking, Equation 17.7 is valid for rij/rio 1.03. For more concentrated systems, t s can be approximated in an expansion of powers of O  

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