Cross fluid

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

${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }})=\mu _{\infty }+{\frac {\mu _{0}-\mu _{\infty }}{1+(k{\dot {\gamma }})^{n}}}}$

where ${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }})}$ is viscosity as a function of shear rate, ${\displaystyle \mu _{\infty }}$, ${\displaystyle \mu _{0}}$, ${\displaystyle k}$ and n are coefficients.

The zero-shear viscosity ${\displaystyle \mu _{0}}$ is approached at very low shear rates, while the infinite shear viscosity ${\displaystyle \mu _{\infty }}$ is approached at very high shear rates.^[1]

See also

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

References

1. Cunningham, Neil. "Making Use Of Models: The Cross Model". www.rheologyschool.com. Retrieved 2018-02-28.

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