Cross fluid

A Cross fluid is a type of generalized Newtonian fluid whose viscosity depends upon shear rate according to the following equation:

$\mu_{\operatorname{eff}}(\dot \gamma) = \frac {\mu_0}{1 + ({\frac {\mu_0 \dot \gamma} {\tau ^ *}})^{1-n} }$

where

$\mu_{\operatorname{eff}}(\dot \gamma)$ is viscosity as a function of shear rate,

$\mu_0$, $\tau ^ *$ and n are coefficients.

At low shear rate (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \mu_0 \dot \gamma \ll \tau^* ), cross fluids behave as Newtonian fluids and at high shear rate (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \mu_0 \dot \gamma \gg \tau^* ) as power-law fluids.

See also

• Navier-Stokes equations
• Fluid
• Carreau fluid
• Power-law fluid
• Generalized Newtonian fluid

References

• Kennedy, P. K., Flow Analysis of Injection Molds. New York. Hanser. ISBN 1-56990-181-3