Chemistry Reference
In-Depth Information
where
is the coefficient of viscosity of the milk product (Pa s),
0
is the
coefficient of viscosity of the portion of the product consisting of water and
low-molecular-weight substances other than lactose (Pa s),
i
is the volume
fraction of a dispersed component with a particle size at least an order of
magnitude greater than the size of the water molecule, (
i
)
¼
fat
+
cas
+
wp
+
l
,wherefat
¼
milk fat, cas
¼
casein, wp
¼
whey proteins and l
¼
lactose, and
max
is the assumed value of (
i
) for maximum packing of all dispersed particles
(0.9 for fluid milk products).
max
may be somewhat higher than 0.9 for evapo-
rated milk and somewhat lower for high-fat cream (Walstra and Jenness, 1984).
The volume fraction of an individual component is given by
i
¼
V
i
c
v
;
i
(23)
where V
i
is the voluminosity of component i (m
3
kg
1
of dry component) and
c
v,i
is the volume concentration of the component in the product (kg m
3
of
product). Walstra and Jenness (1984) give the following values of volumin-
osity (V):
Fat globules
1.11
10
-3
m
3
kg
1
of lipid in fat globules
Casein
3.9
10
-3
m
3
kg
1
of dry casein
Whey proteins
1.5
10
-3
m
3
kg
1
of dry protein
Lactose
1.0
10
-3
m
3
kg
1
of lactose
Voluminosity and volume fraction pertain to hydrodynamic volume
and thus account for particle shape and water of hydration as well as volume
per se (Walstra and Jenness, 1984).
Equation 22, for (
i
)
!
0, reduces to the well-known Einstein equa-
tion for the viscosity of a very dilute solution of hard spheres:
¼
0
ð
1
þ
2
:
5
Þ
(24)
Einstein's equation assumes no particle-particle interaction (
<
0.05;
Hinrichs, 1999). Eilers's equation accounts both for the presence of the
dispersed phase and for hydrodynamic interaction between particles during
flow.
Van Vliet and Walstra (1980) showed that the volume fractions of all
the dispersed species and dissolved lactose must be included in the (
i
) term
in Eilers's equation (Equation 22); the equation will, for example, under-
estimate the viscosity of cream if
fat
is substituted for (
i
) and
skim
(taken
as being the same as
plasma
) for
0
.
The volume fraction of the casein (
cas
) in milk is the main determinant
of (
i
) and thus of viscosity. Large differences in viscosity between different
milks are almost certainly attributable to differences in
cas
, which depend, in
