Viscosity of Moderately Dense Gases

Abstract

At moderate densities the viscosity of a gas may be represented by a virial expansion in density η=η₀+bρ+···, and we present a calculation of the contribution of triple collisions to the coefficient b. We approximate three‐body encounters by two‐body collisions between a single molecule and a dimer. We derive the equilibrium constant for dimers, according to classical statistical mechanics for spherically symmetric short‐range potentials, which include bound, metastable, and orbiting pairs. Numerical results are obtained for the Lennard‐Jones (6–12) potential and the equilibrium constant is found to be approximately proportional to $T^{-\frac{3}{2}}$ . We then apply the Chapman—Enskog theory of the viscosity of a binary mixture of dilute gases, one component being the monomer, the other the dimers. Collisional transfer in binary collisions is not taken into account. The analysis based on this simple model yields substantial agreement with experiment, in particular the temperature dependence of b∼T⁻¹ at high reduced temperature, and the near invariance of b with T at moderate reduced temperatures. In comparison, Enskog's theory of hard spheres predicts b∼T^½ and the anomalous behavior at high reduced temperature is not removed by ad hoc variation of the hard‐sphere diameter with temperature. For given parameters (σ, ε) of the Lennard‐Jones intermolecular potential, good agreement with experiment is obtained, if the monomer—dimer interaction is represented by a similar potential with parameters 1.02σ, 1.23ε. The results are essentially independent of the use of other potential parameters which maintain the magnitude of the attractive potential. We conclude that the physical origin of the initial density dependence of viscosity requires consideration of not only repulsive but also attractive forces between molecules.