Since most materials are non-Newtonian, non-linear models are needed to describe the change in viscosity as a function of shear. The power law equation is the simplest of the available models. The viscosity (either Newtonian or apparent) is replaced by a consistency coefficient, k.
Based upon the power law index, n, the power law model describes three basic types of flow:
n=1 Newtonian behavior
n<1 Shear thinning (or Pseudoplastic)
n>1 Shear thickening
Most materials are shear thinning and can be represented by the power law over a limited range of shear. Dispersions with a high volume fraction may exhibit shear-thickening behavior. Often, a volumetric increase may also take place and this is referred to as dilatancy.
Over a sufficiently wide shear range, the power law does not accurately describe the materials behavior and more complex models must then be used.
