# Is supercritical CO$_2$ a newtonian fluid?

Is supercritical CO$_2$ a newtonian fluid?

I can't seem to find any articles describing the stress-strain relationship for carbon-dioxide in a supercritical state (high temperature/pressure combination). I know it's newtonian in its gaseous state and I presume that being in a supercritical state would not alter its stress-strain relationship, but I can't find any references stating one way or the other. Any help would be greatly appreciated! :)

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Any small molecule fluid is Newtonian. This is clear theoretically, so that people do not even bother to say that CO2 is Newtonian. The non-Newtonian fluids are relatively long polymers, so that the physical interactions have extra degrees of freedom describing how the polymers are tangled up and slide past each other. When there are no polymers, the x,y,z components of the fluid momentum are each locally doing independent diffusion at small scales, just on general principles of physics, any long-range random drift of a conserved quantity is diffusive by the laws of large numbers.

This is generally stated as a form of the central limit theorem--- when you have a conserved quantity moving from point to point at random, the quantity is doing diffusion at long distance scales. Diffusion of momentum is Newtonian viscosity. But of course it helps to have experimental data to make sure you aren't missing something, which akhmeteli provided.

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In the article: J. of Supercritical Fluids 56 (2011) 144–151, "Viscosity of pure carbon dioxide at supercritical region: Measurement and correlation approach", the authors conclude: "Viscosities of pure CO2 have been measured for the temperature range from 313.15K to 523.15K and pressure range between 7.7MPa and 81.1MPa using rolling body viscometer. A gas booster system is also used to compress the gases to pressures required in this research. Easy-to-use correlation, which is simpler than current available models, has been developed to accurately predict the pure CO2 viscosity just by using operating pressure and temperature." The last phrase seems to imply that supercritical CO2 is a Newtonian liquid.

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How do you gather that from the last statement? –  Paul Sep 29 '12 at 5:20
@Paul: "For Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure (and also the chemical composition of the fluid if the fluid is not a pure substance), not on the forces acting upon it." (en.wikipedia.org/wiki/Newtonian_fluid ). Also: "The viscosity of Newtonian fluids is affected by temperature, pressure, and, in the case of solutions and mixtures, by composition." (columbia.edu/itc/ldeo/lackner/E4900/Themelis3.pdf ). See also some information on supercritical CO2 in the latter source, also implying that it's a Newtonian fluid. –  akhmeteli Sep 29 '12 at 6:44