Carreau fluid
In fluid dynamics, a Carreau fluid is a type of generalized Newtonian fluid (named after Pierre Carreau) where viscosity, μ eff {\displaystyle \mu _{\operatorname {eff} }} , depends upon the shear rate, γ ˙ {\displaystyle {\dot {\gamma }}} , by the following equation: μ eff ( γ ˙ ) = μ inf + ( μ 0 − μ inf ) ( 1 + ( λ γ ˙ ) 2 ) n − 1 2 {\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: μ 0 {\displaystyle \mu _{0}} , μ inf {\displaystyle \mu _{\operatorname {\inf } }} , λ {\displaystyle \lambda } and n {\displaystyle n} are material coefficients: μ 0 {\displaystyle \mu _{0}} is the viscosity at zero shear rate (Pa.s), μ inf {\displaystyle \mu _{\operatorname {\inf } }} is the viscosity at infinite shear rate (Pa.s), λ {\displaystyle \lambda } is the characteristic time (s) and n {\displaystyle n} power index. The dynamics of fluid motions is an important area of physics, with many important and commercially significant applications.