Cross fluid

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

${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }})=\mu _{\infty }+{\frac {\mu _{0}-\mu _{\infty }}{1+(k{\dot {\gamma }})^{n}}}}$

where ${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }})}$ is viscosity as a function of shear rate, ${\displaystyle \mu _{\infty }}$, ${\displaystyle \mu _{0}}$, ${\displaystyle k}$ and n are coefficients.

The zero-shear viscosity ${\displaystyle \mu _{0}}$ is approached at very low shear rates, while the infinite shear viscosity ${\displaystyle \mu _{\infty }}$ is approached at very high shear rates.