Madelung constant

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

${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}(\dot{\gamma })=\frac{{\mu }_0}{1+(\frac{{\mu }_0\dot{\gamma }}{{\tau }^{*}}{)}^{1-n}}$

where

${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}(\dot{\gamma })$ 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