Hongqin Liu

Unified approach to the self-diffusion coefficients of dense fluids over wide ranges of temperature and pressure—hard-sphere, square-well, Lennard–Jones and real substances

Abstract In this work a physically sound approach for calculation of the self-diffusion coefficient of model and real fluids is presented. After carrying out a systematic study focused on the equations and molecular dynamic data available in the literature concerning the self-diffusivities of the hard-sphere (HS), square-well (SW) and Lennard–Jones (LJ) fluids, new models are proposed to represent this transport property. First of all, a free-volume-based equation with only one parameter is used to reproduce the recently published data for the HS fluid. Then it is demonstrated that reasonable models for the SW and LJ systems are liable to arise from the HS model by just introducing an attractive contribution. Finally, it is shown that it is possible to describe the self-diffusivities of real substances in terms of the equations devised for the SW and LJ fluids, which give rise to two-parameter models. These parameters are the diameter and the energy of the considered potential function. Reliable representation is accomplished with the proposed LJ model, the results (AAD=5.45%) being well comprised by the experimental accuracy. The validation involved the largest database ever used (2514 data points).

Models for self-diffusion coefficients of dense fluids, including hydrogen-bonding substances

Abstract This work comprises two main and independent purposes: 1. A new four-parameter model is proposed for the description of self-diffusion coefficients of polar, nonspherical and even hydrogen-bonding substances. It gives accurate results over wide ranges of temperature and pressure (AAD=4.45%; 2471 data points). This equation is devised from an extension of a Lennard–Jones fluid model embodying the van der Waals model approach. 2. Generalized correlations are suggested for the estimation of the Lennard–Jones force constants (energy and diameter) of a two-parameter equation. From these it is possible to predict tracer diffusivities with satisfactory results, by means of simple combining rules.

Generalised free-volume theory for transport properties and new trends about the relationship between free volume and equations of state

Abstract In this work, a new generalised model for transport properties is given, the theoretical background of some free-volume equations is revealed and the analysis of various free-volume expressions in the literature is presented. Firstly, we develop the free-volume equation for the self-diffusion coefficient, which embodies the hybrid principles of the real fluids, since it considers both the concepts of molecular free volume and activation energy. Secondly, it is shown that the relevant expressions presented in the literature are particular cases of our generalised equation. With this it is possible to clarify their validity and range of applicability, since the expressions arise by introducing approximations duly established in the fundamental model. Moreover, the relationship between free-volume expressions and the equations of state (EoS) of van der Waals (vdW) type is discussed. Some representative free-volume expressions are given and compared according to the effects of density, temperature and molecular shape. Following this comparison, some expressions are recommended.

Accurate correlations for the self-diffusion coefficients of CO2, CH4, C2H4, H2O, and D2O over wide ranges of temperature and pressure

Abstract In this work, two models are proposed for the correlation of self-diffusivities over the entire ranges of gas and liquid phases. The first model is an empirical equation containing 12 adjustable parameters and is based on the density expansion for self-diffusivities presented by Kawasaki and Oppenheim. The second model is a modification of the free-volume expression by Macedo and Litovitz, with seven adjustable parameters. Self-diffusion coefficient data for CO2, CH4, C2H4, H2O, and D2O, which are known to be very important supercritical fluids employed in extraction processes, were correlated with the proposed equations. The average absolute deviations obtained are smaller than 5% for wide ranges of both temperature and pressure. Therefore, these equations can be recommended for accurate predictions of self-diffusivities for these substances in the covered density ranges.

Thermodynamic modelling of near-critical solutions

Abstract The challenge of modeling the properties of near-critical systems requires the use of different approaches in order to describe their strong variations with conditions, the variety of different and complex substances that can be present, and the difficulty of obtaining reliable data. This paper describes some approaches that lead to relatively simple descriptions for phase equilibrium and volumetric properties at low solute concentrations as well as suggests methods for solute–solute effects based on Fluctuation Solution Theory.