Carreau¶

Module: fluid

Category: materialprop

Type string: "Carreau"

Parameters¶

Name	Description	Default	Units
`mu0`	zero shear rate viscosity	0	[P.t]
`mui`	infinite shear rate viscosity	0	[P.t]
`lambda`	relaxation time	0	[t]
`n`	power index	1	[]

The material type for a Carreau model ¹ is Carreau.

The viscous shear stress for this material model is

\[ \boldsymbol{\tau}=2\mu\mathbf{D} \]

where

\[ \mu=\mu_{\infty}+\left(\mu_{0}-\mu_{\infty}\right)\left(1+\left(\lambda\dot{\gamma}\right)^{2}\right)^{\left(n-1\right)/2} \]

Here, \(\dot{\gamma}=\sqrt{2\mathbf{D}:\mathbf{D}}\) is the engineering shear rate.

Example:

<viscous type="Carreau">
    <mu0>0.056</mu0>
    <mui>0.0035</mui>
    <lambda>3.3</lambda>
    <n>0.36</n>
</viscous>

Cho, Y I and Kensey, K R, "Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows", Biorheology 28, 3-4 (1991), pp. 241-62. ↩