Physico-chemical Properties of Milk - Advanced Dairy Chemistry - page 709

due only to cold agglutination. Relative viscosity at g ¼1 was related to fat
content in this range by the equation

ln rel ; g ¼1 ¼ ln g ¼1

2 : 5 fat
1 1 : 165 fat skim ¼

(26)

The rheological properties of cream containing > 40% fat were influ-
enced also by the tendency of fat globules to become orientated by shearing.
The relationship between relative viscosity and fat content, for fat contents in
the range 40-70% (w/w), was

rel ; g ¼1 ¼ 1 þ 2 : 5 fat þ 4 : 55 fat þ 13 : 45 fat þ 100 : 6 fat (27)

The temperature dependence of skim in the temperature range 5-408C
was accounted for by the equation

skim ¼ 5 : 0213 10 7 exp ð 2398 = T Þ (28)

where T is absolute temperature (K). Randhahn and Reuter (1978) pointed
out that the viscosity of raw cream depends to some extent also on tempera-
ture history, possibly owing to temperature-dependent characteristics of milk
proteins.
Randhahn and Reuter (1978) found that the Cross equation (29), which
relates apparent viscosity to shear rate, exactly described the pseudoplastic
nature of raw cream:

app ¼ g ¼1 þ g ¼ 0 g ¼1
1 þ bg m

(29)

where app is the apparent viscosity at g s 1 , g ¼ 0 and g ¼1 are the apparent
viscosities at g ¼ 0s 1 and g ¼1 , respectively, found by extrapolation, and b,
m are constants. The factors g ¼ 0 , g ¼1 , b and m are each dependent on
temperature and fat content. The applicability of the Cross equation implies
that a state of equilibrium exists during flow between the size and number of
fat globule clusters and shear rate.
Homogenization of milk results in an increase in viscosity at high shear
rates. The increase is inversely related to fat globule size (Reuter and Randhahn,
1978). Reuter and Randhahn (1978) found that for raw milk the relative
viscosity at g ¼1 depends on the mean distance between fat globules:

1

a 1

ln rel ¼ð 4 : 7 fat 0 : 1 Þ þ ln rel ; R (30)

a R