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# Carreau fluid

Carreau fluid is a type of generalized Newtonian fluid where viscosity, $\mu_{\operatorname{eff}}$, depends upon the shear rate, $\dot \gamma$, by the following equation:

$\mu_{\operatorname{eff}}(\dot \gamma) = \mu_0 \left(1+\left(\lambda \dot \gamma\right) ^2 \right) ^ {\frac {n-1} {2}}$

Where: μ0, λ and n are material coefficients.

At low shear rate ($\dot \gamma \ll 1/\lambda$) Carreau fluid behaves as a Newtonian fluid and at high shear rate ($\dot \gamma \gg 1/\lambda$) as a power-law fluid.

The model was first proposed by Pierre Carreau.

## References

• Kennedy, P. K., Flow Analysis of Injection Molds. New York. Hanser. ISBN 1569901813