Carreau fluid

Carreau fluid is a type of generalized Newtonian fluid where viscosity, μ eff {displaystyle mu _{operatorname {eff} }} , depends upon the shear rate, γ ˙ {displaystyle {dot {gamma }}} , by the following equation: Carreau fluid is a type of generalized Newtonian fluid where viscosity, μ eff {displaystyle mu _{operatorname {eff} }} , depends upon the shear rate, γ ˙ {displaystyle {dot {gamma }}} , by the following equation: 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}} = viscosity at zero shear rate (Pa.s) μ inf {displaystyle mu _{operatorname {inf } }} = viscosity at infinite shear rate (Pa.s) λ {displaystyle lambda } = relaxation time (s) n {displaystyle n} = power index At low shear rate ( γ ˙ ≪ 1 / λ {displaystyle {dot {gamma }}ll 1/lambda } ) a Carreau fluid behaves as a Newtonian fluid with viscosity μ 0 {displaystyle mu _{0}} . At intermediate shear rates ( γ ˙ ≳ 1 / λ {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 {displaystyle n} and the infinite shear-rate viscosity μ inf {displaystyle mu _{operatorname {inf } }} , a Carreau fluid behaves as a Newtonian fluid again with viscosity μ inf {displaystyle mu _{operatorname {inf } }} . The model was first proposed by Pierre Carreau.