Cross fluid explained

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

where

is viscosity as a function of shear rate, , , and n are coefficients.

The zero-shear viscosity

is approached at very low shear rates, while the infinite shear viscosity is approached at very high shear rates.^[1]

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

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.

Notes and References

1. Web site: Making Use Of Models: The Cross Model. Cunningham. Neil. www.rheologyschool.com. en. 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 . 10.1016/0095-8522(65)90022-X . 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 . 10.1016/j.jnnfm.2011.08.008 . 0377-0257.