[1][2] This mathematical relationship is useful because of its simplicity, but only approximately describes the behaviour of a real non-Newtonian fluid.
Therefore, the power law is only a good description of fluid behaviour across the range of shear rates to which the coefficients were fitted.
There are a number of other models that better describe the entire flow behaviour of shear-dependent fluids, but they do so at the expense of simplicity, so the power law is still used to describe fluid behaviour, permit mathematical predictions, and correlate experimental data.
Power-law fluids can be subdivided into three different types of fluids based on the value of their flow behaviour index: Pseudoplastic, or shear-thinning are those fluids whose behaviour is time independent and which have a lower apparent viscosity at higher shear rates, and are usually solutions of large, polymeric molecules in a solvent with smaller molecules.
It is generally supposed that the large molecular chains tumble at random and affect large volumes of fluid under low shear, but that they gradually align themselves in the direction of increasing shear and produce less resistance.
A common household example of a strongly shear-thinning fluid is styling gel, which is primarily composed of water and a fixative such as a vinyl acetate/vinylpyrrolidone copolymer (PVP/PA).
If one were to hold a sample of hair gel in one hand and a sample of corn syrup or glycerine in the other, they would find that the hair gel is much harder to pour off the fingers (a low shear application), but that it produces much less resistance when rubbed between the fingers (a high shear application).
In these cases, large molecules or fine particles form loosely bounded aggregates or alignment groupings that are stable and reproducible at any given shear rate.
But these fluids rapidly and reversibly break down or reform with an increase or decrease in shear rate.
Pseudo plastic fluids show this behavior over a wide range of shear rates; however often approach a limiting Newtonian behavior at very low and very high rates of shear.
Typical examples include oil films in automotive engine shell bearings and to a lesser extent in geartooth contacts.
Dilatant, or shear-thickening fluids increase in apparent viscosity at higher shear rates.
Under high shear rates, the water is squeezed out from between the starch molecules, which are able to interact more strongly, enormously increasing the viscosity.