Chemistry Reference
In-Depth Information
1000.0
100.0
10.0
1.0
G
′ ϕ
= 0.348
G
′
ϕ
= 0.348
′
G
′ ϕ
= 0.455
G
′
ϕ
= 0.455
′
0.1
0.001
0.01
0.1
1
strain
Figure 6.5
A plot of the apparent storage and loss moduli as a function of strain for
volume
fractions of dispersions of
silica particles.
(a
¼
150 nm
c
¼
10
3
M.).
stress-controlled instrument must maintain a rapid and constant feedback
between the torque applied and the subsequent displacement achieved in the
measuring geometry. If the sample responds rapidly and can undergo changes
more rapidly than the feedback and accompanying instrumental inertia allows,
then the instrument will fail to maintain the correct strain. In the nonlinear
regime where the non-Maxwell processes can be very rapid, strain control can
fail spectacularly. It is a useful design option but should be used, as with so
many rheological measurements, with care.
In conclusion, a treatise on the phenomenological approach to nonlinear
responses is limited only by the amount of space available and the patience of
both the author and the reader.
10
Simple equations for characterising data
curves are useful tools. They allow you to reduce a complex set of data to a few
parameters. Trends can often be more easily discerned from the parameters
than from the original data. This is particularly the case for experiments where
we are unable to hold all the chemical variables constant and just adjust one.
The chemical engineer also finds simple models useful when solving heat- and
mass-transfer problems. They can be used in finite-element method calculations
without the need for recourse to the molecular details underlying the system.
This can, on occasion, provide cold comfort when a process fails and we need to
establish the chemical origin. Then, the connection must be made between
simple models and nonlinear flow behaviour. In the following sections this issue
will be addressed.
