Kinetic Theory of Soft Matter. The Penetrable-Sphere Model
arXiv:cond-mat/0501068 · doi:10.1063/1.1941550
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 $Ï(r)=ε>0$ if the two spheres are overlapped ($r<Ï$) and $Ï(r)=0$ otherwise ($r>Ï$). 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 $ν(T^*)$ grows as $\sqrt{T^*}$ up to $T^*\equiv k_BT/ε\simeq 0.25$, 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.
6 pages, 4 figures; to appear in Rarefied Gas Dynamics: 24th International Symposium (AIP Conference Proceedings)