Kinetic theory of soft matter. The penetrable-square-well model

摘要

The penetrable-square-well (PSW) pair interaction potential is defined as Φ(r) = ε_r if the two interacting particles are overlapped (r < σ), Φ(r) = ε_a inside a corona (σ < r < λ), and Φ(r) = 0 otherwise (r > λ). Thus, the potential reduces to the conventional square-well (SW) one in the limit ε_r → ∞ and to the penetrable-sphere (PS) potential if ε_a → 0 or λ → σ. This paper aims at studying the temperature dependence of the Navier-Stokes transport coefficients of a dilute gas of particles interacting via the PSW model. By exploiting the fact that the PSW scattering process is analogous to that of a light ray passing through two concentric spherical media with different refractive indices, the scattering angle is analytically derived as a function of the impact parameter and the relative velocity of the colliding particles; depending on the values of those two quantities, collisions can be soft, hard, or grazing. Next, by standard application of known general results from the Chapman-Enskog method, the Navier-Stokes transport coefficients in the first-order approximation are numerically evaluated. It is found that the PSW coefficients are practically indistinguishable from the SW ones for temperatures low enough (k_BT approx.< 0.2ε_r), there exists a transition regime (0.2ε_r approx.< k_BT approx.< 10ε_r) where the transport coefficients interpolate between the SW and the PS ones, and finally the PSW coefficients are comparable to the PS ones for high enough temperatures (k_BT approx.> 10ε_r). The results are applied to the temperature profiles of the planar Fourier flow.