Carreau fluid

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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: $μ 0$ , $λ$ 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.