gradient (or strain rate) applied, or on the stress applied. The ratio of stress
over strain rate then is called theapparent viscosity, symbolZa. In most
cases,Zadecreases with increasing value ofsorC, as illustrated in Figure
5.7. Such liquids are commonly called shear thinning, butstrain rate thinning
is a better term. First, the dependency of viscosity on the velocity gradient is
not restricted to shear flow; it also occurs in elongational flows. Second, a
material may become more resistant to deformation as the strain on it
increases—a phenomenon called strain hardening—while at the same time
the value ofZadecreases with increasingCvalue (at the same strain), which
means that the material is strain rate thinning. Some doughs and batters
show such a combination of properties.
Several types of dispersions show strain rate thinning, and a
quantitative explanation is not easily given. We will briefly consider two
cases. The first one concerns shear flow. As discussed (above, Factor 4),
anisometric particles show rotational diffusion and thereby increase
viscosity. This effect will be smaller for a higher shear rate: when the
shear-induced rotation is much faster than the diffusional rotation, the latter
will have no effect anymore. The shear rate thinning effect is completely
reversible. Something comparable happens in polymer solutions (Section
6.2.2).
Another situation arises when attractive forces cause particle
aggregation (see Factor 2). A shear or elongational stress may now break
down the aggregates, the more so for a higher strain rate. This then will lead
to a decrease in effective volume fraction, hence to a decrease inZa.
FIGURE5.7 Examples of the relations between strain rate (C,ins^1 ), stress (s,in
Pa), and (apparent) viscosity (Za,inPa?s) in flow of a Newtonian liquid (N) and one
showing fairly strong strain rate thinning (T); logarithmic scales. Note that most of
the decrease inZaoccurs over about one decade ins, and over about three decades in
C.