ART

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]

See also

Navier-Stokes equations
Fluid
Carreau fluid
Power-law fluid
Generalized Newtonian fluid

References

Cunningham, Neil. "Making Use Of Models: The Cross Model". www.rheologyschool.com. Retrieved 2018-02-28.

Kennedy, P. K., Flow Analysis of Injection Molds. New York. Hanser. ISBN 1-56990-181-3

Physics Encyclopedia

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Hellenica World - Scientific Library

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