Kinetic Theory of Soft Matter. The Penetrable-Sphere Model

Details Kinetic Theory of Soft Matter. The Penetrable-Sphere Model Kinetic Theory of Soft Matter. The Penetrable-Sphere Model

2005-01-05

arxiv.org/abs/cond-mat/0501068v1

Rarefied Gas Dynamics: 24th International Symposium on Rarefied Gas Dynamics, M. Capitelli, ed. (AIP Conference Proceedings, 2

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1063/1.1941550

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 $\phi(r)=\epsilon>0$ if the two spheres are overlapped ($r<\sigma$) and $\phi(r)=0$ 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 $\nu(T^*)$ grows as $\sqrt{T^*}$ up to $T^*\equiv k_BT/\epsilon\simeq 0.25$, reaches a maximum at $T^*\simeq 0.415$ and then decays as ${T^*}^{-3/2}\log T^*$ for large temperatures. The results are applied to the hydrodynamic profiles in the steady Fourier and Couette flows.

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