Chemistry Reference
In-Depth Information
where
η
∞
is the Newtonian limiting viscosity, and the Casson equation,
which is useful, for example, in establishing the flow characteristic of
chocolate flow behaviour (Steffe, 1996; Aguilera and Stanley, 1999):
1
/
2
1
/
2
σ
=
k
0
+
k
1
˙
γ
(2.6)
The power law, Bingham, Herschel-Bulkley and Casson models ef-
fectively describe the rheology of a wide variety of foodstuffs (Steffe,
1996).
2
.
4
.
1
.
2
Time-dependent flow models
In addition to the non-ideal behaviour described previously, many ma-
terials exhibit time-dependent effects, which have more complex re-
sponses. There are two types of time-dependant flow: thixotropy and
rheopexy. If the viscosity of the material decreases with time, when
sheared at a constant shear rate, this behaviour is termed as thixotropy.
On the other hand, if the viscosity of the material increases with time,
again when sheared at a constant shear rate, this behaviour is called as
rheopexy. These effects can occur in materials with or without yield
stress. Rheopexy is a rare phenomenon, but thixotropic materials are
common. Examples of thixotropic materials are starch pastes, gelatine
and mayonnaise (Steffe, 1996).
Irreversible changes, such as cross-linking, coagulation, degradation
and mechanical instabilities, cause the time-dependent behaviour, and
so the sample does not recover when the stress is removed. However,
if reversible changes occur, for example, the breakage and reformation
of colloidal aggregates, the material can recover if left at rest. Mod-
els describing time-dependent behaviour are less satisfactory and more
controversial than those of shear-dependent behaviour (Prentice, 1984).
Experimentally, it can be difficult to detect differences between a
shear-thinning fluid, in which the viscosity decreases with increasing
shear, and a thixotropic material, in which the viscosity decreases with
time, because of the combined shear and time effects that occur during
measurement. This is especially true if only a small number of data
points are collected. In addition, most materials which are thixotropic
are also shear thinning. In fact, one definition suggests that for a material
to be described as thixotropic, its viscosity should be a function of both
shear rate and time (Donald and Gary, 1971; Aral and Kalyon, 1994).
Constitutive models such as the Herschel-Bulkley equation may
be adapted to allow for thixotropic effects by introducing a structural
parameter
λ
(Steffe, 1996):
)
n
)
σ
=
λ
(
τ
y
+
K
(˙
γ
(2.7)
