Free Volume Power Law for Transport Properties of Hard Sphere Fluid

TL;DR

This study introduces a power law relating transport properties to free volume in dense hard sphere fluids, validated by simulations and connecting thermodynamic and geometric free volumes, resolving longstanding controversies.

Contribution

It proposes a new power law model linking transport properties to free volume using a generic distribution function and thermodynamic relations, validated against simulation data.

Findings

Power law accurately models viscosity, diffusivity, and thermal conductivity.

The model reproduces various existing equations and scaling laws.

The approach resolves the Cohen-Turnbull-Doolittle free volume controversy.

Abstract

This paper presents a study on the relationship between transport properties and geometric free volume for hard sphere (HS) system in dense fluid region. Firstly, a generic free volume distribution function is proposed based on recent simulation results for the HS geometric free volume by Maiti et al. [1,2] Combining the new distribution function with a local particle transportation model, we obtain a power law for the HS transport properties. Then a relation between the geometric free volume and thermodynamic free volume is established, which makes it possible to use well-developed equations of state (EoS) for the expressions of the geometric free volume. The new power law models are tested with molecular dynamic (MD) simulation results for HS viscosity, diffusivity and thermal conductivity, respectively and the results are very satisfactory. Using the power law we are able to reproduce several equations obtained from different approaches, such as the entropy scaling laws [3], mode coupling theory [4] or empirical correlations [5]. In particular, A long-standing controversy regarding the well known Cohen-Turnbull-Doolittle free volume model [6,7] is resolved by using the power law combined with an EoS.