volume fraction. The extent to which a substance can increase viscosity is
expressed in the intrinsic viscosity (relative increase of viscosity per unit
solute, extrapolated to zero concentration). The maximum volume fraction
possible for the particles present also affects viscosity, as the latter becomes
infinite at the said maximum.
In a Newtonian liquid the viscosity does not depend on the stress or
the strain rate applied, but many liquids are non-Newtonian. Many liquid
dispersions are strain rate thinning, i.e., the ‘‘apparent’’ viscosity decreases
with increasing strain rate. Some of these dispersions are also thixotropic:
the apparent viscosity decreases during flow at constant strain rate and
slowly increases again after flow has stopped.
Viscoelasticity. Some strain rate thinning liquids, especially
polymer solutions, are also viscoelastic. This means that after exerting a
stress on the liquid, it deforms at first elastically and then starts to flow;
upon release of the stress it regains part of the original shape.
If a given deformation is applied to a viscoelastic material, the stress
slowly relaxes; the characteristic time for this is called the relaxation time.
The Deborah number (De) is defined as the ratio of this relaxation time over
the observation time. For a solid De is very large, for a liquid very small,
and for a viscoelastic material of order unity. It thus depends on the time
scale of observation whether we call a material solid or liquid. Several foods
appear to be solid at casual observation, but show flow during longer
observation.
Another phenomenon is that a material may turn out to have solid
properties if a small stress is applied, but starts to flow above a certain stress,
called the yield stress. Its magnitude varies widely among foods, some
apparently true liquids having a small yield stress and some apparently rigid
solids flowing above a large stress. Its magnitude also depends on the time
scale, being smaller for a longer observation time.
Viscoelastic materials are often studied by means of dynamic, i.e.,
oscillatory, rheological tests. These yield a complex shear modulus, the
resultant of a (real) elastic or storage modulus and a (imaginary) viscous or
loss modulus. The ratio of loss over storage modulus is called the loss
tangent; the higher it is, the more liquidlike the material is. The loss tangent
generally depends on the time scale of the deformation, i.e., on the
oscillation frequency.
Diffusion. Molecules show heat motion, and this has some
consequences: (a) particles in a liquid undergo Brownian motion, in fact
the equivalent of molecular motion at a slower rate; (b) if concentration
gradients exist, these are evened out by diffusion, and (c) the same applies to