Physics: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:
- [math]\displaystyle{ \tau = \mu_{\operatorname{eff}}( \dot{\gamma} ) \dot{\gamma} }[/math]
where [math]\displaystyle{ \tau }[/math] is the shear stress, and [math]\displaystyle{ \dot{\gamma} }[/math] the shear rate. The quantity [math]\displaystyle{ \mu_{\operatorname{eff}} }[/math] represents an apparent 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
References
- ↑ Kennedy, Peter (1995). Flow analysis of injection molds. Munich u.a.: Hanser u.a.. ISBN 1-56990-181-3.
- ↑ Pritchard, David; Duffy, Brian; Wilson, Stephen (2015). "Shallow flows of generalised Newtonian fluids on an inclined plane" (in en-US). Journal of Engineering Mathematics 94 (1): 115–133. doi:10.1007/s10665-014-9725-2. Bibcode: 2015JEnMa..94..115P. https://strathprints.strath.ac.uk/48744/9/Pritchard_etal_JEM2014_shallow_flows_generalised_newtonian_fluids.pdf.
- ↑ Hinton, Edward (2022). "Inferring rheology from free-surface observations" (in en-US). Journal of Fluid Mechanics 937. doi:10.1017/jfm.2022.157. Bibcode: 2022JFM...937R...4H.
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