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:

:$\backslash tau\; =\; \backslash mu\_\{\backslash operatorname\{eff\}\}(\; \backslash dot\{\backslash gamma\}\; )\; \backslash dot\{\backslash gamma\}$

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

The most commonly used types of generalized Newtonian fluids are:{{cite book|last=Kennedy|first=Peter|title=Flow analysis of injection molds|year=1995|publisher=Hanser u.a.|location=Munich u.a.|isbn=1-56990-181-3}}

• 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.{{Cite journal|last1=Pritchard|first1=David|last2=Duffy|first2=Brian|last3=Wilson|first3=Stephen|date=2015|title=Shallow flows of generalised Newtonian fluids on an inclined plane|journal=Journal of Engineering Mathematics|language=en-US|volume=94|issue=1 |pages=115–133|doi=10.1007/s10665-014-9725-2|bibcode=2015JEnMa..94..115P |s2cid=254473611 |url=https://strathprints.strath.ac.uk/48744/9/Pritchard_etal_JEM2014_shallow_flows_generalised_newtonian_fluids.pdf }}{{Cite journal|last=Hinton|first=Edward|date=2022|title=Inferring rheology from free-surface observations|journal=Journal of Fluid Mechanics|language=en-US|volume=937|doi=10.1017/jfm.2022.157|s2cid=246634281 |arxiv=2202.02893|bibcode=2022JFM...937R...4H }}