The Empirical Enskog-Like Approximation of Shear Viscosity in the Penetrable-Sphere Model

摘要

The so-called penetrable-sphere (PS) interaction potential is defined as u~(PS) (r) = {ε, r < σ/0, r > σ (1) where σ is the diameter penetrable sphere, and ε (> 0) is the strength of the repulsive energy barrier between two overlapping spheres when they penetrate each other. The PS system simply reduces to the hard-sphere (HS) model in the zero-temperature limit, i.e., T*(≡ k_BT/ε) → 0, or ε*(≡ k_BT/ε) → 0, or ε*(≡ ε/k_BT) → ∞, where k_B is the Boltzmann constant, and T the temperature. In the opposite high-temperature limit T* → ∞, or the high-penetrability limit ε* → 0, the PS system becomes a collisionless ideal gas. For the PS system, in principle, the overlapping penetrability allows any possible value of the nominal packing fraction φ (= (π/6)ρ*), where ρ*(=Nσ3/V) is the reduced number density. Note that the maximum packing fraction in the pure HS system is 2 π/6 (≈ 0.7405) from the face-centered cubic structure.