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.
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
Hellenica World - Scientific Library
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