Cross fluid

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

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

where

<math> \mu_{\operatorname{eff}}(\dot \gamma) </math> is viscosity as a function of shear rate,

<math> \mu_0 </math>, <math> \tau ^ * </math> and n are coefficients.

At low shear rate (<math> \mu_0 \dot \gamma \ll \tau^* </math>), cross fluids behave as Newtonian fluids and at high shear rate (<math> \mu_0 \dot \gamma \gg \tau^* </math>) 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 1569901813