Thixotropy. In most systems the latter effect is not directly
reversible: at constant strain rateZatends to decrease with time, and it
gradually increases again when flow is stopped (aggregates then are formed
again). Such behavior is called thixotropy. Many thick liquid foods are
thixotropic; a good example is tomato ketchup. For such systems, the
apparent viscosity observed will depend not only on the shear rate applied
but also on the time during which it is sheared. Moreover, agitation applied
to the sample before measurement may have markedly decreased the
apparent viscosity, especially when measured at low strain rate.
Question
Consider (a) an oil-in-water emulsion of monodisperse droplets,joil¼ 0 :6; and (b)
the same emulsion but atjoil¼ 0 :5, to which an amount of a globular protein has
been added atjprotein¼ 0 :2. Which system would have the higher viscosity?
Answer
For these systems we can presumably apply Eq. (5.11). In (a) we havej¼ 0 :6; since
the particles are spheres,½Z¼ 2 :5; and because the spheres are monodisperse,jmax
would be about 0.65. This yieldsZrel¼65. In (b)jis higher, i.e., 0.7, butjmaxwill
also be higher. Even if the oil droplets touch one another, the very much smaller
protein molecules can fit in the gaps between the drops. Presumably,jmaxwill be
about 0.85. Also½Zmay be taken at 2.5, since most globular proteins are fairly
spherical particles. Equation (5.11) then yieldsZrel&40; forjmax¼ 0 :82, we obtain
Zrel¼51. Consequently, despite the higher volume fraction in (b), its viscosity would
be lower.
Note The validity of Eq. (5.11) may be questioned for such a strongly
bimodal particle size distribution. Another approach is first to calculate the
viscosity of the protein solution (withj¼ 0 :4 andjmax¼ 0 :65), which
yieldsZrel¼ 4 :7. Subsequently, this value is taken forZsin Eq. (5.11) for the
emulsion (withj¼ 0 :5 andjmax¼ 0 :65), which also yieldsZrel¼51.5.1.3 Viscoelasticity
Figure 5.8 illustrates what can happen when an amount of material is put
under a given stress for some time. Envisage, for instance, a cheese cube
onto which a weight is placed and after some time removed. In (a) the
stress–time relation applied is shown, and in (b) we see the response of a