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The penetrable-square-well (PSW) pair interaction potential is defined as$\phi (r)=\epsilon_r$ if the two interacting particles are overlapped($r<\sigma$), $\phi(r)=-\epsilon_a$ inside a corona ($\sigma <r<\lambda$), and$\phi(r)=0$ otherwise ($r>\lambda$). Thus, the potential reduces to theconventional square-well (SW) one in the limit $\epsilon_r\to\infty$ and to thepenetrable-sphere (PS) potential if $\epsilon_a\to0$ or $\lambda\to\sigma$.This paper aims at studying the temperature dependence of the Navier--Stokestransport coefficients of a dilute gas of particles interacting via the PSWmodel. By exploiting the fact that the PSW scattering process is analogous tothat of a light ray passing through two concentric spherical media withdifferent refractive indices, the scattering angle is analytically derived as afunction of the impact parameter and the relative velocity of the collidingparticles; depending on the values of those two quantities, collisions can besoft, hard, or grazing. Next, by standard application of known general resultsfrom the Chapman--Enskog method, the Navier--Stokes transport coefficients inthe first-order approximation are numerically evaluated. It is found that thePSW coefficients are practically indistinguishable from the SW ones fortemperatures low enough ($k_BT\lesssim 0.2 \epsilon_r$), there exists atransition regime ($0.2 \epsilon_r\lesssim k_BT\lesssim 10\epsilon_r$) wherethe transport coefficients interpolate between the SW and the PS ones, andfinally the PSW coefficients are comparable to the PS ones for high enoughtemperatures ($k_BT\gtrsim 10\epsilon_r$). The results are applied to thetemperature profiles of the planar Fourier flow.

Kinetic Theory of Soft Matter. The Penetrable-Square-Well Model