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where
t
is time (second),
n
is the kinetic order and
k
is the model param-
eter, representing the rate of the structural breakdown during shearing
(Abu-Jdayil, 2003). Tarrega
et al
. (2004) applied this model to fit the ex-
perimental data of a shear stress decay test, assuming a kinetic order of
n
2. The viscosity of semi-solid dairy dessert samples decreased
rapidly with time within the first 300 seconds of shearing and ap-
proached a constant value, which was used as
=
η
∞
(Tarrega
et al
., 2004).
The η
0
/
η
∞
ratio was lower at a higher temperature for all samples,
suggesting a lower extent of the structure breakdown; however, the tem-
perature effect on the
k
values was not the same for different samples,
possibly due to the differences of the structure responsible for the effect
of temperature on the rate of thixotropic breakdown (Tarrega
et al
.,
2004).
7.4.2
Yield stress
Yield stress is frequently detected for semi-solid dairy products. It can
be measured as the initial stress value for the upward shear-rate flow
curve in a hysteresis loop, which is the minimum stress required to
make the sample flow (Fig. 7.8a). In this case, Herschel-Bulkley and
Casson models are usually used to fit the rheological data (Ramaswamy
and Basak, 1991; Tarrega
et al
., 2004). Yield stress was assigned to
the maximum value of the flow curve for some semi-solid samples,
such as cream cheese in Sanchez
et al
. (1994) (Fig. 7.8b). Kealy (2006)
determined yield stress of cream cheese samples using a controlled stress
rheometer. Shear stress was gradually increased and the deformation
(shear strain) was measured. The yield stress was determined at the
intersection of two linear regions in the displacement profile (Fig. 7.8c),
at which the reversible deformation has ended and the material has
begun to flow (Kealy, 2006). Measurements with the 'vane' device in
low shear conditions also provided a way to estimate yield stress, at rest
and after shearing (Breidinger and Steffe, 2001; Doublier and Durand,
2008). The maximum stress value in shear stress-time curve is taken
as yield stress (Fig. 7.8d). Note that a pre-shear process can destroy the
weak gel structure of a semi-solid product and significantly decrease the
stress (Fig. 7.8d).
Barnes and Walters (1985) suggested that yield stress does not exist
except in a few limited circumstances. The creep behaviour for solids,
soft solids and structured liquids at low stresses can be described by
a Newtonian-plateau viscosity (Barnes, 1999). Tarrega
et al
. (2005)
obtained the zero-shear viscosity by fitting the experimental data to
Carreau model (Equation 7.6). Their results suggest that semi-solid
sample can flow even under a very small stress (close to zero), since no
yield stress exists; however, it may take an extremely long time for the
