title: Generalized Newtonian fluid
text: # 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.
  
  