Minimal quantum viscosity from fundamental physical constants

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Science Advances  24 Apr 2020:
Vol. 6, no. 17, eaba3747
DOI: 10.1126/sciadv.aba3747


  • Fig. 1 Viscosity and kinematic viscosity of fluids.

    Experimental viscosity η (A) and kinematic viscosity ν (B) of noble, molecular, and network liquids (15) showing minima. η for H2, H2O, and CH4 are shown for pressure P = 50, 100, and 20 MPa, respectively. η for He, Ne, Ar, and N2 are shown at two pressures each: 20 and 100 MPa for He, 50 and 300 MPa for Ne, 20 and 100 MPa for Ar, and 10 and 500 MPa for N2. The minimum at higher pressure is above the minimum at lower pressure for each fluid.

  • Fig. 2 Elementary viscosity of fluids.

    νm calculated from experimental kinematic viscosity (15) for H2 (A), He (B), and H2O (C) below and above the critical pressure Pc. Pc = 1.3 MPa for H2, 0.23 MPa for He, and 22 MPa for H2O. The smallest value of νm, ι, is consistent the lower bound (Eq. 18).


  • Table 1 Calculated and experimental νm.

    νm (calc.)νm (exp.)
    ×108 m2/s×108 m2/s
    Ar (20 MPa)3.45.9
    Ar (100 MPa)3.47.7
    Ne (50 MPa)4.84.6
    Ne (300 MPa)4.86.5
    He (20 MPa)10.75.2
    He (100 MPa)10.77.5
    N2 (10 MPa)4.16.5
    N2 (500 MPa)4.112.7
    H2 (50 MPa)15.216.3
    O2 (30 MPa)3.87.4
    H2O (100 MPa)5.112.1
    CO2 (30 MPa)3.28.0
    CH4 (20 MPa)5.411.0
    CO (30 MPa)4.17.7

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