Chemistry Reference
In-Depth Information
If we compare the shear stress versus shear rate, it can be practically dicult
to distinguish between plastic and pseudoplastic behaviour. However, when the
same data is represented on a log
log plot clear differences emerge. The low-
shear viscosity begins to reduce the stress significantly. The application of a
shear in the nonlinear regime can give rise to forces normal to the shear
direction. Flow instabilities can develop due to the viscoelastic behaviour of the
samples at finite strains to the extent where the sample cannot be constrained
by the measuring geometry. Changes in the volume of material under deforma-
tion are commonly encountered. An example of this is when walking along a
damp sandy beach and the sand around your footprint seems to dry as you
walk. In a sense this is actually what happens. The deformation applied by your
foot causes the sand grains to rearrange from the close-packed structure
produced by the water motion, take up a greater volume, ''sucking-in'' the
liquid in the process. The phenomena of volume changes under a shearing field
is called dilatancy. The formation of structural order caused by deforming
strains can result in some interesting effects. For example, at high frequencies,
compression waves can be used to induce nucleation in supersaturated electro-
lyte solutions. For systems with slower diffusion dynamics than those of ions, a
gentler lower-frequency oscillation can induce gelation. This effect is called
rheopexy. This phenomena is time dependent, and the shear equations in this
section form constitutive equations that provide no information on this time-
dependent behaviour.
There is a relationship that is used to cross between time and shear rate
dependence regimes and that is the Cox-Merz rule.
5
The dynamic viscosity
Z*(o), when plotted as a function of frequency, has a similar form to a
pseudoplastic curve although not necessarily displaying a high shear rate
plateau. These observations apply, for example, to reasonably concentrated
homopolymers. In the linear viscoelastic limit for a liquid, the complex
viscosity equates with the low-shear-rate viscosity, Z*
ð
o
!
0
Þ¼
Z
ð
g
!
0
Þ
.
For some materials this rule can be extended into the nonlinear response
regime equating the dynamic viscosity as a function of frequency,
Z*
ð
ao
Þ¼
Z
ð
g
Þ
. The term a can be adapted to improve the agreement between
the two sets of data. It would seem unlikely at first sight that an oscillating
shear response would be comparable to a non-Newtonian finite strain response
since the nature of the deformation is very different. However, good agreement
is sometimes observed. It should be emphasised that, in general, whilst the form
of the experimental data can be similar, Z*(o) is a measurement that can be
made with a linear system and as such is consistent with the mathematics of
linear viscoelasticity, whereas shear thinning is very much a nonlinear response.
6.2.2 Time Dependence in Flow and the Boltzmann Superposition Principle
The application of a shear rate to a linear viscoelastic liquid will cause the
material to flow. The same will happen to pseudoplastic material and to a
plastic material once the yield stress has been exceeded. The stress that would
result from the application of the shear rate would not necessarily be achieved
