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Kinetic Theory of Soft Matter. The Penetrable-Sphere Model

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 $ϕ(r)=ε>0$ if the two spheres are overlapped ($r<σ$) and $ϕ(r)=0$ otherwise ($r>σ$). 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.