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:

${\displaystyle \tau =\mu _{\operatorname {eff} }({\dot {\gamma }}){\dot {\gamma }}}$

where ${\displaystyle \tau }$ is the shear stress, and ${\displaystyle {\dot {\gamma }}}$ is the shear rate. The quantity ${\displaystyle \mu _{\operatorname {eff} }}$ represents an apparent viscosity or effective viscosity as a function of the shear rate.

The most commonly used types of generalized Newtonian fluids are:^[1]

• 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.^[2][3]

• Navier–Stokes equations