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:
<math display=block>\tau = \mu_{\rm eff}( \dot{\gamma} ) \dot{\gamma} </math>
where <math>\tau</math> is the shear stress, and <math>\dot{\gamma}</math> is the shear rate. The quantity <math>\mu_{\rm eff}</math> represents an apparent viscosity 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.
See also
- Navier–Stokes equations