Kinetic Theory of Soft Matter. The Penetrable-Sphere Model

TL;DR

This paper analyzes the kinetic theory of penetrable-sphere models in soft matter, focusing on how their transport properties like viscosity and diffusion vary with temperature, and applies findings to hydrodynamic flow profiles.

Contribution

It provides the first detailed evaluation of shear viscosity, thermal conductivity, and self-diffusion coefficients for a dilute gas of penetrable spheres, revealing temperature-dependent collision behavior.

Findings

Collision frequency peaks at intermediate temperatures.

Transport coefficients exhibit non-monotonic temperature dependence.

Hydrodynamic profiles are modeled for steady Fourier and Couette flows.

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 $\phi(r)=\epsilon>0$ 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.