Cross¶
Module: fluid
Category: materialprop
Type string: "Cross"
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] |
m |
power | 2 | [] |
Description¶
The material type for a Cross model 1 is Cross.
The viscous shear stress for this material model is
\[
\boldsymbol{\tau}=2\mu\mathbf{D}
\]
where
\[
\mu=\mu_{\infty}+\left(\mu_{0}-\mu_{\infty}\right)\frac{1}{1+\left(\lambda\dot{\gamma}\right)^{m}}
\]
Here, \(\dot{\gamma}=\sqrt{2\mathbf{D}:\mathbf{D}}\) is the engineering shear rate.
Example:
<viscous type="Cross">
<mu0>0.056</mu0>
<mui>0.0035</mui>
<lambda>1.0</lambda>
<m>1.0</m>
</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. ↩