On the ratio of the shear viscosity to the density of entropy of the rare gases and H2,N2,CH4, and CF4

•The shear viscosity to density of entropy ratio is minimal at the critical point.•The minimal ratio obeys the conjecture proposed by Kovtun, Son and Starinets.•The minimal ratio depends on mass and collision diameter of atoms and molecules.

The ratio κ of the shear viscosity η to the volume density of entropy s,κ=η/s, of the rare gases He, Ne, Ar, Kr, and Xe and the molecules H2,N2,CH4, and CF4 is studied in the critical region. It is shown that the minimum value κm of η/s is observed in the vicinity of the critical point. In addition the universal inequality κ⩾ℏ/(4πk) proposed by Kovtun et al. (2005) holds for these gases. For the rare gases and 6Li κm depends linearly on m1/2σ2, where m is the mass and σ defined via the potential energy function as U(σ)=0. κm of the molecules H2,N2,CH4, and CF4 falls on the same straight line provided that the vibrational and rotational contributions to the entropy density s are removed.

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