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 ($\mu _{0}{\dot {\gamma }}\ll \tau ^{*}$), cross fluids behave as Newtonian fluids and at high shear rate ($\mu _{0}{\dot {\gamma }}\gg \tau ^{*}$) 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