Chemistry Reference
In-Depth Information
log
10
k
¼
log
¼
3
:
82
ð
i
Þ
3
:
35
(48)
where the units of k and
are Pa s
n
and n
¼
1.
Hinrichs (1999) found that shear thinning behaviour occurs at (
i
)
>
0.5.
This critical value of
is close to the theoretical maximum value of 0.52 that
could exist in an ideal monodisperse suspension in which the suspended
particles are in contact but able to move in straight lines in the direction of
flow. The dependence of k (at 208C) on (
i
) at
>
0.5 is greater than that
expressed by Equation 48 and can be estimated approximately from Hinrichs'
data to be
log
10
k
¼
10
:
15
ð
i
Þ
6
:
51
(49)
Interestingly, Hallstr om and Dejmek (1988a) found that for ultrafiltra-
tion skim milk concentrates, a similar double linear relationship existed
between k
relative
and (
i
) (expressed as
p
), also with a critical value of
(
i
) of about 0.5, at which the slope changed to a higher value. k
relative
was
defined by the equation
k
permeate
k
relative
¼
(50)
where
permeate
was taken as being the viscosity of the continuous phase of the
concentrates. The relationship between k
relative
and (
i
) was independent of
temperature, pH and preheat treatment of the original whole milk prior to
separation.
Horne (1993) found that the shear thinning behaviour of fresh skim milk
concentrates (made by thermal evaporation and concentrated up to 6.22-fold)
could be described by the Bingham equation. Suitable manipulation of
pl
data
for low concentrations (
<
1.5-fold) gave a value of
cas
of 3.85
10
3
m
3
kg
1
,
a figure close to the values of 3.57
10
3
and 3.9
10
3
given by Walstra and
Jenness (1984) and Snoeren et al. (1982), respectively.
Horne (1993) treated skim milk concentrates as dispersions of casein
micelles in a continuous phase. He found by further manipulation of his
data that the viscosity of the continuous phase was numerically the same as
that of a 4% lactose solution.
pl
expressed as viscosity relative to this
continuous phase viscosity was uniquely related to
cas
when
max
was
taken as 0.66
0.02. (The volume fraction of the whey proteins was appar-
ently not considered explicitly.)
Yield stress (t
0
) was found to increase steeply with
cas
above 0.3 and to
scale with
cas
to the power 4.1. The value of this exponent was close to the
value of 3.85 exhibited by weakly flocculated latex suspensions, implying that
concentrated milks are themselves weakly flocculated suspensions. Horne
