Physics:Cross fluid

A Cross fluid is a type of generalized Newtonian fluid whose viscosity depends upon shear rate according to the following equation:

${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}(\dot{\gamma })={\mu }_{\mathrm{\infty }}+\frac{{\mu }_0-{\mu }_{\mathrm{\infty }}}{1+(k\dot{\gamma }{)}^n}$

where ${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}(\dot{\gamma })$ is viscosity as a function of shear rate, ${\mu }_{\mathrm{\infty }}$, ${\mu }_0$, $k$ and n are coefficients.

The zero-shear viscosity ${\mu }_0$ is approached at very low shear rates, while the infinite shear viscosity ${\mu }_{\mathrm{\infty }}$ is approached at very high shear rates.

See also

• Navier-Stokes equations
• Fluid
• Carreau fluid
• Power-law fluid
• Generalized Newtonian fluid

References

• Kennedy, P. K., Flow Analysis of Injection Molds. New York. Hanser. ISBN:1-56990-181-3