Physics:Generalized Newtonian fluid

A generalized Newtonian fluid is an idealized fluid for which the shear stress is a function of shear rate at the particular time, but not dependent upon the history of deformation. Although this type of fluid is non-Newtonian (i.e. non-linear) in nature, its constitutive equation is a generalised form of the Newtonian fluid. Generalised Newtonian fluids satisfy the following rheological equation:

[math]\displaystyle{ \tau = \mu_{\operatorname{eff}}( \dot{\gamma} ) \dot{\gamma} }[/math]

where [math]\displaystyle{ \tau }[/math] is the shear stress, and [math]\displaystyle{ \dot{\gamma} }[/math] the shear rate. The quantity [math]\displaystyle{ \mu_{\operatorname{eff}} }[/math] represents an apparent or effective viscosity as a function of the shear rate.

The most commonly used types of generalized Newtonian fluids are:

• Power-law fluid
• Cross fluid
• Carreau fluid
• Bingham fluid

It has been shown that Lubrication theory may be applied to all Generalized Newtonian fluids in both two and three dimensions.

See also

• Navier–Stokes equations