Dairy Systems - Practical Food Rheology - page 135

s n )and n is the
dimensionless flow behaviour index. Milk products usually show shear-
thinning (pseudoplastic) behaviour with flow behaviour indexes of
0

where K is the consistency coefficient (unit of Pa ·

< n < 1. Apparent viscosity ( η ) can be calculated (Equation 7.3) for

a shear-thinning fluid as:

η = σ ˙

n − 1

Apparent viscosity = K ˙ γ (7.3)

γ

The flow behaviour index indicates the deviation from Newtonian be-
haviour ( n 1), which reflects the changing rate of fluid viscosity with

shear rate. For a shear-thinning fluid ( n

=

1), a lower value of the flow
behaviour index suggests a faster decrease of the apparent viscosity
with increasing shearing rate. A higher consistency coefficient does not
necessarily guarantee a higher viscosity, which is also dependent on the
flow behaviour index and shear rate for shear-thinning fluids. Velez-
Ruiz and Barbosa-Canovas (1998, 2000) found Newtonian behaviours
for milks with

<

22.3% solid contents and shear-thinning behaviours for
concentrated milks with solid contents between 22.3 and 30.5%. The
flow behaviour index of concentrated milk decreased with increasing
solid content, showing a larger magnitude of shear-thinning behaviour
(Velez-Ruiz and Barbosa-Canovas, 1998, 2000). Shear-thinning be-
haviour was explained based on asymmetric molecules aligning with
the shear planes and thereby reducing frictional resistance (Tung, 1978).
The consistency coefficient of concentrated milk increased markedly
with solid content (Velez-Ruiz and Barbosa-Canovas, 1998, 2000). The
transition of milk flow behaviour from Newtonian to non-Newtonian
with increasing solid content has been reported by other groups but with
different critical solid concentrations, such as 25% by Chang and Hartel
(1997) and 15% by Solanki and Rizvi (2001). This most probably re-
flects differences in milk composition combined with processing effects.
An increase in milk viscosity as a function of storage time has been
reported as the so-called 'age-thickening' process (Snoeren et al ., 1984;
Velez-Ruiz et al ., 1998; Bienvenue et al ., 2003). This is proposed to
be due to changes such as structural transformations in casein micelles
and whey proteins (Snoeren et al ., 1984); however, the precise physico-
chemical changes involved in age thickening are unknown.
Yield stress is observed for concentrated milks and is associated
with the high amounts of solids, allowing for weak gel formation. In
these cases, the Bingham (Equation 7.4) or Herschel-Bulkley models
(Equation 7.5) describe the rheological characteristics of milks (Velez-
Ruiz and Barbosa-Canovas, 1998; Bienvenue et al ., 2003):

<

Bingham model σ = σ 0 + η pl ˙ γ (7.4)

n

Herschel-Bulkley model σ = σ 0 + K ˙ γ (7.5)