Generalized Newtonian fluid

In fluid mechanics, 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:

\tau = \mu_{\rm eff}( \dot{\gamma} ) \dot{\gamma}

where \tau is the shear stress, and \dot{\gamma} is the shear rate. The quantity \mu_{\rm 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:

• 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.