Dispersions.* When particles are added to a liquid, the viscosity is
increased. Near a particle the flow is disturbed, which causes the velocity
gradientCto be locally increased. Because the energy dissipation rate due to
flow equalsZC^2 , more energy is dissipated, which becomes manifest as an
increased macroscopic viscosity. The ‘‘microscopic’’ viscosity, as sensed by
the particles, remains that of the solvent (pure liquid)Zs. For very dilute
dispersions of solid spherical particles, Einstein derived
Z¼Zsð 1 þ 2 : 5 jÞð 5 : 6 Þa very simple relation. Note that only the volume fractionjof the particles,
not their size, affects viscosity (provided that the size is significantly larger
than that of the solvent molecules). If the volume fraction becomes larger
than about 0.01, the flow disturbances caused by the particles start to
overlap. Consequently, the viscosity increases more withjthan predicted
by Eq. (5.6). This is illustrated in Figure 5.5. The particles themselves now
also sense a greater stress, because the local velocity gradient is increased.
- It may be helpful for understanding the following part of the present section to consult first
some parts of Chapter 9, especially where it concerns particles.
FIGURE5.5 Example of the effect of concentration on viscosity. The relativeðZrelÞ
and the reduced viscosityðZredÞof dispersions of spherical particles are given as a
function of volume fractionðjÞ.