Cross fluid

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

${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }})={\frac {\mu _{0}}{1+\left({\frac {\mu _{0}{\dot {\gamma }}}{\tau ^{*}}}\right)^{1-n}}}}$

where

${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }})}$ is viscosity as a function of shear rate,

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

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