Generalized Newtonian fluid explained

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) \dot

where

\tau is the shear stress, and • \gamma is the shear rate. The quantity \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]}

See also

• Navier–Stokes equations

Notes and References

1. Book: Kennedy, Peter. Flow analysis of injection molds. 1995. Hanser u.a.. Munich u.a.. 1-56990-181-3.
2. Pritchard. David. Duffy. Brian. Wilson. Stephen. 2015. Shallow flows of generalised Newtonian fluids on an inclined plane. Journal of Engineering Mathematics. en-US. 94. 1 . 115–133. 10.1007/s10665-014-9725-2. 2015JEnMa..94..115P . 254473611 .
3. Hinton. Edward. 2022. Inferring rheology from free-surface observations. Journal of Fluid Mechanics. en-US. 937. 10.1017/jfm.2022.157. 246634281 . 2202.02893. 2022JFM...937R...4H .