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:

$${\displaystyle \tau =\mu _{\rm {eff}}({\dot {\gamma }}){\dot {\gamma }}}$$

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

The most commonly used types of generalized Newtonian fluids are: ^[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

References

1. Kennedy, Peter (1995). Flow analysis of injection molds. Munich u.a.: Hanser u.a. ISBN   1-56990-181-3.
2. Pritchard, David; Duffy, Brian; Wilson, Stephen (2015). "Shallow flows of generalised Newtonian fluids on an inclined plane" (PDF). Journal of Engineering Mathematics. 94 (1): 115–133. Bibcode:2015JEnMa..94..115P. doi:10.1007/s10665-014-9725-2. S2CID   254473611.
3. Hinton, Edward (2022). "Inferring rheology from free-surface observations". Journal of Fluid Mechanics. 937. arXiv: 2202.02893 . Bibcode:2022JFM...937R...4H. doi:10.1017/jfm.2022.157. S2CID   246634281.