This paper presents a study on the relationship between transport properties and geometric free volume for dense hard sphere (HS) systems. Firstly, a generic free volume distribution function is proposed based on recent molecular dynamic (MD) simulations for the HS geometric free volume1,2. 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 obtain the expressions of the geometric free volume. The new models are tested with MD results for HS viscosity, diffusivity, respectively and the results are very satisfactory. Using the power law we are able to reproduce equations obtained from different approaches, such as the entropy scaling laws3, mode coupling theory4 or empirical correlations5. In particular, A long-standing controversy regarding the Cohen-Turnbull-Doolittle free volume model6,7 is resolved.

In vapor liquid equilibrium (VLE) calculations with a cubic equation of state (EoS), exact solution has to be carried out numerically with an iterative approach [1,2]. This causes significant wastes of repetitive efforts and computing resources. Based on a recent study [3] on the van der Waals EoS [4,5], here we propose a procedure for analytically approximate solutions to the VLE calculation with the Soave-Redlich-Kwong (SRK) EoS [6] for the entire coexistence curve. This procedure can be applied to any cubic EoS. A simple databank can be built containing only the coefficients of a newly defined function and other thermodynamic properties will be obtained with analytical forms. For each system there is only a one-time effort. We also show that for exact solutions, the VLE problem with any cubic EoS can be reduced to solving a transcendental equation with one unknown, which can significantly simplify the methods currently employed [2,7].