Carreau fluid

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Carreau fluid in physics 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)

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

${\displaystyle n}$ = power index

The dynamics of fluid motions is an important area of physics, with many important and commercially significant applications.

Computers are often used to calculate the motions of fluids, especially when the applications are of a safety critical nature.