Kinetic Theory of Soft Matter. The Penetrable-Sphere Model

Abstract

The penetrable-sphere model has been introduced in the literature to describe the peculiar thermodynamic behavior of some colloidal systems. In this model the interaction potential is $\varphi (r)=\epsilon >0$ if the two spheres are overlapped ($r<\sigma$) and $\varphi (r)=0$ otherwise ($r>\sigma$). In this paper the shear viscosity, thermal conductivity, and self-diffusion coefficients of a dilute gas of penetrable spheres are evaluated. It is found that the effective collision frequency $\nu (T^{\ast })$ grows as $\sqrt{T^{\ast }}$ up to $T^{\ast }\equiv k_{B}T/\epsilon \simeq 0.25$, reaches a maximum at $T^{\ast }\simeq 0.415$ and then decays as ${T^{\ast }}^{-3/2}\log T^{\ast }$ for large temperatures. The results are applied to the hydrodynamic profiles in the steady Fourier and Couette flows.

6 pages, 4 figures; to appear in Rarefied Gas Dynamics: 24th International Symposium (AIP Conference Proceedings)

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