# Carreau fluid

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

${\displaystyle \mu _{\operatorname {eff} }({\dot {\gamma }})=\mu _{\operatorname {\inf } }+(\mu _{0}-\mu _{\operatorname {\inf } })\left(1+\left(\lambda {\dot {\gamma }}\right)^{2}\right)^{\frac {n-1}{2}}}$

Where: ${\displaystyle \mu _{0}}$, ${\displaystyle \mu _{\operatorname {\inf } }}$, ${\displaystyle \lambda }$ and ${\displaystyle n}$ are material coefficients.

${\displaystyle \mu _{0}}$ = viscosity at zero shear rate (Pa.s)

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

${\displaystyle \lambda }$ = relaxation time (s)

${\displaystyle n}$ = power index

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

The model was first proposed by Pierre Carreau.