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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 ($${\displaystyle {\dot {\gamma }}\ll 1/\lambda }$$ ) a Carreau fluid behaves as a Newtonian fluid with viscosity $$\mu_0$$ . At intermediate shear rates ( $${\displaystyle {\dot {\gamma }}\gtrsim 1/\lambda }$$), a Carreau fluid behaves as a Power-law fluid. At high shear rate, which depends on the power index n and the infinite shear-rate viscosity $${\displaystyle \mu _{\operatorname {\inf } }}$$, a Carreau fluid behaves as a Newtonian fluid again with viscosity $${\displaystyle \mu _{\operatorname {\inf } }}$$.

The model was first proposed by Pierre Carreau.

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

Physics Encyclopedia

World

Index