Chemistry Reference
In-Depth Information
where
A
is the initial shear stress (where
t
=
1 second in Equation 7.15
and
t
t
m
in Equation 7.16) and
B
is the time coefficient of thixotropic
breakdown. The parameter B corresponds to the rate of the breakdown
of thixotropic structure during agitation at a constant rate of shear (Welt-
mann, 1943). Note that a zero-time stress is nonexistent in the Weltmann
model (
=
reaches infinity as time approaches zero). The
t
m
in Equation
7.16 is the time at maximum observed shear stress, corresponding to
the starting point of the stress decay or structural breakdown process.
The modified Weltmann model assumes the semi-solid structure starts
to breakdown after shear stress reaches a certain value of
A
. The param-
eters
A
and
B
are dependent on the applied shear rate and temperature.
Ramaswamy and Basak (1992) applied the modified Weltmann model
to fit the shear stress decay data and compared the parameters
A
and
B
for two yoghurt samples. The
A
(or
B
) values for the two samples
were similar at low shear rates but showed dissimilarity at high shear
rates. At a certain shear rate, these parameters decreased with increas-
ing temperature in a linear pattern, suggesting less time dependency of
the flow behaviour. Ramaswamy and Basak (1992) described the rela-
tionship between
A
σ
is the applied shear
rate, and temperature using the Arrhenius equation (Equation 7.13),
which shows that the
E
a
values gradually decreased as the shear rate
increased. This is similar to their observations in the hysteresis loop
test and suggests that the temperature effect on the flow behaviour is
less significant at a higher shear rate (Ramaswamy and Basak, 1991).
Tarrega
et al
. (2004) fitted the shear stress decay data to the Weltmann
model for the Spanish dairy dessert samples and compared the results
with those from the hysteresis loop test. The parameters
A
and
B
showed
lower values at higher temperature and corresponded to less hysteresis
areas, suggesting a slower rate of structure breakdown (Tarrega
et al
.,
2004).
Other models have also been used to describe the time dependency of
semi-solid dairy products (O'Donnell and Butler, 2002; Camacho
et al
.,
2005). A common one is the structural kinetic model (Equation 7.17)
proposed by Dzuy Nguyen
et al
. (1998). The structural kinetic model
postulates that the change in time-dependent flow properties is due to
shear-induced breakdown of the internal structure. This is represented
by the kinetics of the process of going from the structured state (apparent
viscosity of
/
γ
˙
(viscosity, Pa
·
s), where ˙
γ
η
0
) to the non-structured state (apparent viscosity of
η
∞
)
(Abu-Jdayil, 2003):
The structural kinetic model is
(
1
−
n
η
−
η
∞
)
η
0
−
η
∞
1)
kt
(7.17)
−
1
=
(
n
−
