Yield Stress. Curve (c) is characteristic for many viscoelastic
materials. At small stress, the material behaves elastically, as shown in
Figure 5.8b. Above a given stress, however, it starts to flow, and its behavior
is like that in Figure 5.8d. This critical stress is called theyield stress. Beyond
ty, the liquid is strain rate thinning. The magnitude of the yield stress varies
widely, and values from 10^5 Pa (some fruit juices) to over 10^5 Pa (some
butters) have been observed. Ifty<10 Pa, the yielding behavior tends to go
unnoticed at casual observation. (Can you explain this?) Thus the existence
of a yield stress does not mean that a high stress is needed to cause a certain
flow rate. A high-viscosity Newtonian liquid, like curve (d), may have a
much higher apparent viscosity, at least at highs.
The yield stress is not a clear-cut material property, since its magnitude
generally depends on time scale, often markedly so. If the applied stress lasts
longer, a lower yield stress is commonly observed. In other words, the
Deborah number determines whether or not yielding occurs at a given
stress.
A material with a finite yield stress that is made to flow, say in a pipe,
may show quite irregular behavior. Near the wall, the velocity gradient,
hence the stress, tends to be greatest. This may then imply that near the wall
the stress is larger than the yield stress, but further to the center of the tube it
is not. In this way, plug flow arises: a high velocity gradient near the wall
and a (very) small one in most of the tube. In extreme cases, one speaks of
slip: the material does not flow, except in a very thin layer near the wall. This
can readily occur in several kinds of rheometers. In such a case the results of
the test will then merely characterize the strongly altered material near the
wall rather than the whole specimen.
Question 1
To check whether an egg is boiled, you can put it on a plate and then set it spinning.
If boiled, the egg goes on spinning for a fairly long time; if unboiled, it soon stops.
Can you explain this? Can you roughly calculate the time needed for the unboiled egg
to stop spinning?
Answer
The inside of an unboiled egg is liquid. In a spinning egg the moving shell will
transfer its momentum to the liquid, and a velocity gradient is formed. This means
that viscous energy dissipation occurs, thereby decreasing the kinetic energy of the
spinning egg. A (hard-)boiled egg is virtually an elastic solid, and a velocity gradient
cannot form; the egg merely loses kinetic energy by friction with the plate and the air.