Cross fluid

In fluid dynamics, a Cross fluid is a type of generalized Newtonian fluid whose viscosity depends upon shear rate according to the Cross Power Law equation:

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

where $\mu _{\mathrm {eff} }({\dot {\gamma }})$ is viscosity as a function of shear rate, $\mu _{\infty }$ is the infinite-shear-rate viscosity, $\mu _{0}$ is the zero-shear-rate viscosity, $m$ is the time constant, and $n$ is the shear-thinning index.

The zero-shear viscosity $\mu _{0}$ is approached at very low shear rates, while the infinite shear viscosity $\mu _{\infty }$ is approached at very high shear rates.^[1]

When $\mu _{0}$ > $\mu _{\infty }$ , the fluid exhibits shear thinning (pseudoplastic) behavior where viscosity decreases with increasing shear rate; when $\mu _{0}$ < $\mu _{\infty }$ , the fluid displays shear thickening (dilatant) behavior where viscosity increases with shear rate.

It is named after Malcolm M. Cross who proposed this model in 1965.^[2]^[3]

References

^ Cunningham, Neil. "Making Use Of Models: The Cross Model". www.rheologyschool.com. Retrieved 2018-02-28.
^ Cross, Malcolm M. (1965-06-01). "Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems". Journal of Colloid Science. 20 (5): 417–437. doi:10.1016/0095-8522(65)90022-X. ISSN 0095-8522.
^ Galindo-Rosales, F. J.; Rubio-Hernández, F. J.; Sevilla, A.; Ewoldt, R. H. (2011-12-01). "How Dr. Malcom M. Cross may have tackled the development of "An apparent viscosity function for shear thickening fluids"". Journal of Non-Newtonian Fluid Mechanics. 166 (23): 1421–1424. doi:10.1016/j.jnnfm.2011.08.008. ISSN 0377-0257.

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

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

[2] Cross, Malcolm M. (1965-06-01). "Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems". Journal of Colloid Science. 20 (5): 417–437. doi:10.1016/0095-8522(65)90022-X. ISSN 0095-8522.

[3] Galindo-Rosales, F. J.; Rubio-Hernández, F. J.; Sevilla, A.; Ewoldt, R. H. (2011-12-01). "How Dr. Malcom M. Cross may have tackled the development of "An apparent viscosity function for shear thickening fluids"". Journal of Non-Newtonian Fluid Mechanics. 166 (23): 1421–1424. doi:10.1016/j.jnnfm.2011.08.008. ISSN 0377-0257.

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Non-Newtonian fluids
Effects	Barus Self-siphoning Kaye Toms Weissenberg
Properties	Viscoelastic materials Kelvin–Voigt Maxwell Time-dependent viscosity Rheopecty Thixotropy Non-Newtonian viscoelasticity Shear thinning Shear thickening
Generalized Newtonian fluids	Bingham Carreau Cross Herschel–Bulkley Newtonian Ideal Power-law

Fahrer / Team für die Suche eingeben:

Fahrer / Team für die Suche eingeben:

Langbahn Team – Weltmeisterschaft

Cross fluid

See also

References