Carreau fluid

Carreau fluid is a type of generalized Newtonian fluid where viscosity, ${\displaystyle \mu _{\operatorname {eff} }}$, depends upon the shear rate, ${\dot {\gamma }}$, 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: $\mu _{0}$, ${\displaystyle \mu _{\operatorname {\inf } }}$, $\lambda$ and $n$ are material coefficients.

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

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

$\lambda$ = relaxation time (s)

$n$ = 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.

See also

• Navier-Stokes equations
• Fluid
• Cross fluid
• Power-law fluid
• Generalized Newtonian fluid

References

• Kennedy, P. K., Flow Analysis of Injection Molds. New York. Hanser. ISBN 1-56990-181-3

External links