Carreau fluid

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


\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, \mu_{\operatorname{\inf}}, \lambda and n are material coefficients.

\mu_0 = viscosity at zero shear rate (Pa.s)

\mu_{\operatorname{\inf}} = viscosity at infinite shear rate (Pa.s)

\lambda = relaxation time (s)

n = power index


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

The model was first proposed by Pierre Carreau.

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