Physics:Cross fluid

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

[math]\displaystyle{ \mu_\mathrm{eff}(\dot \gamma) = \mu_\infty + \frac {\mu_0-\mu_\infty}{1 + (k\dot{\gamma})^n} }[/math]

where [math]\displaystyle{ \mu_\mathrm{eff}(\dot \gamma) }[/math] is viscosity as a function of shear rate, [math]\displaystyle{ \mu_\infty }[/math], [math]\displaystyle{ \mu_0 }[/math], [math]\displaystyle{ k }[/math] and n are coefficients.

The zero-shear viscosity [math]\displaystyle{ \mu_0 }[/math] is approached at very low shear rates, while the infinite shear viscosity [math]\displaystyle{ \mu_\infty }[/math] 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