in which: K is the flow consistency stock (SI units Pa•sⁿ), ∂u/∂y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s^-1), and north is the flow behaviour stock (dimensionless).

A quantity

is an apparent or even efficacious viscosity as a function of the shear rate (SI unit Pa•s).

As well referred to as a Ostwald-de Waele stevens' power law, this mathematical relationship is useful because of its simplicity, but only more or less describes the behaviour of a really non-Newtonian fluid. For instance, whenever n were less than the single, the stevens' power law predicts that a effectual viscousness would decrease by owning increasing shear rate indefinitely, requiring a fluid using infinite viscousness at rest & zero viscousness when the shear rate approaches eternity, however a really fluid has two a minimum & the utmost effectual viscousness that depend on the physical chemistry at the molecular level. For this understanding, a stevens' law is sole a good description of fluid behaviour through a range of shear rates to which a coefficients were fitted. There are a total of more system that better describe a entire flow behaviour of shear-dependant water, however it wash sol at a expense of simplicity, then the stevens' law is however wont to describe fluid behaviour, permit mathematical predictions, & correlate experimental information.

Power-law water may be subdivided into deuce-ace different types of juice according to a value of their flow behaviour stock:

Pseudoplastic fluids
Pseudoplastic, or even shear-thinning juice have a moo apparent viscousness at higher shear rates, & come unremarkably solutions of large, polymeric molecules in the solvent by owning little molecules. These are typically supposed that a big molecular chains tumble indiscriminately & affect big volumes of fluid under moo shear, however that it step by step align themselves in the counsel of increasing shear & create less trend lines.

The most common personal case of the strongly shear-thinning fluid is styling gel, which primarily composed of the lake & the fixative like a vinyl acetate/vinylpyrrolidone copolymer (PVP/PA). inside case 1 were to hang on to the sample of hair gel in the single h& and a sample of corn syrup or glycerine in the other, it would locate that a hair gel is lot harder to pour off the fingers (a moo shear application), however that it produces great deal less trend lines whilst rubbed between the fingers (a high shear application).

Newtonian fluids
The Newtonian fluid is a power-law fluid with a behaviour stock of One, in which the shear stress is directly proportional to the shear rate:

These juice have a constant viscousness, μ, through completely shear rates & include numerous of the usual a stream, like water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.

Dilatant fluids
Dilatant, or shear-thickening juice increase within apparent viscousness at higher shear rates. It is seldom found, however 1 most common case is an uncooked paste of cornstarch and water. Under high shear a water supply is squeezed out from either between a starch molecules, which are suspire to interact other strongly.

See Also

Navier-Stokes equations Fluids First-Order Fluid Cross fluid Carreau fluid Generalized Newtonian fluids