Dairy Systems - Practical Food Rheology - page 144

of the suspended particles is more meaningful than concentration when
considering the effects of particles to the microstructure and viscosity of
milk. Einstein equation describes a relationship between the viscosity
of a dilute dispersion (milk) and the volume fraction of hard spheres (fat
globules and macromolecules) in a continuous phase of known viscosity
(water) (Dewan et al ., 1973):

η = η + . φ

Einstein equation c (1 2 5 ) (7.11)

where η c are the viscosities of the dispersion (milk) and continuous

(water) phase and

η and

is the volume fraction of the hard spheres. However,
the Einstein equation fails in more concentrated systems; in these cases,
the viscosity can be better described by Eilers equation (Dewan et al .,
1973):

φ

1 2

η
η

1 . 25 φ

Eilers equation η =

c =

+ (7.12) rel

− φ/φ

1 max

where φ max is the hypothetical maximum volume fraction that could

be occupied by the close packing of the representative particles and
accounts for the interactions among particles. The φ max depends on the

shape of the particles and their size distribution. van Vliet and Walstra
(1980) described the relationship between the viscosity of milk and
cream and the fat content using Eilers equation. They used the total
volume fraction of fat, proteins, and lactose instead of that for fat alone
in their model, and the volume fractions of proteins and lactose were
assumed to be constants. Snoeren et al . (1982) showed that the Eilers
equation described concentrated skim milk viscosity as a function of
volume fraction occupied by the macromolecular materials. The effects
of the voluminosities of constitutes (casein micelles, whey proteins,
fat globules, fat-protein complexes) on milk viscosity are accounted
for in Eilers model by using the volume fraction instead of weight
concentration (Griffin et al ., 1989; Solanki and Rizvi, 2001; Anema
et al ., 2004).
More complicated models involving viscosity of the particles have
been applied to describe the relationship between milk viscosity and
the volume fraction of fat globules (Kyazze and Starov, 2004). This ap-
proach demonstrated the importance of cluster formation of fat globules
on the viscosity of concentrated milk.

7 . 2 . 3 . 3 Temperature

The effect of temperature on Newtonian viscosity, apparent viscos-
ity or the consistency coefficient (if the flow behaviour index is not