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:


 * $$\tau = \mu_{\operatorname{eff}}( \dot{\gamma} ) \dot{\gamma} $$

where $$\tau$$ is the shear stress, and $$\dot{\gamma}$$ the shear rate. The quantity $$\mu_{\operatorname{eff}}$$ 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.