# 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:

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

Where: $\mu_0$, $\mu_{\operatorname{\inf}}$, $\lambda$ and $n$ are material coefficients.

$\mu_0$ = viscosity at zero shear rate (Pa.s)

$\mu_{\operatorname{\inf}}$ = viscosity at infinite shear rate (Pa.s)

$\lambda$ = relaxation time (s)

$n$ = power index

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.