Physics:Generalized Newtonian fluid

Short description: Extended mathematical model of a 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:

$$\tau ={\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}(\dot{\gamma })\dot{\gamma }$$

where $\tau$ is the shear stress, and $\dot{\gamma }$ is the shear rate. The quantity ${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ 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