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, \( {\displaystyle \mu _{\infty }}\) , \( \mu_0\) , k and n are coefficients.

The zero-shear viscosity \( \mu_0 is approached at very low shear rates, while the infinite shear viscosity \( {\displaystyle \mu _{\infty }} \) is approached at very high shear rates.[1]