Universal correlation of self-diffusion coefficients of model and real fluids based on residual entropy scaling law

• Published in: Chemical engineering science 2012-09, Vol.79, p.153-162
• Main Authors: Vaz, Raquel V., Magalhães, Ana L., Fernandes, Daniel L.A., Silva, Carlos M.
• Format: Article
• Language: English
• Subjects: Applied sciences; Chemical engineering; Computational fluid dynamics; Correlation; Deviation; Diffusion; Entropy; Entropy scaling law; equations; Exact sciences and technology; Fluid flow; Fluids; Heat and mass transfer. Packings, plates; Mass transfer; Mathematical modelling; Mathematical models; Model reduction; Simulation; temperature
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2012.05.006

In this work, the entropy based scaling laws of Rosenfeld, Dzugutov and Bretonnet, which connect reduced self-diffusion coefficients (D⁎) with residual entropy (named excess entropy in this field), were analysed in order to test their attributed universal character. With this purpose, an extensive database with 1727 molecular dynamic and experimental values was compiled for hard-sphere (HS), Lennard-Jones (LJ), hard-sphere chain (HSC), and real (polar, nonpolar, symmetrical and asymmetrical) fluids. It was shown that these equations fail when tested over the entire range of density and temperature (through residual entropy), even for atomic and simple fluids (e.g., HS and LJ) for which they have been originally proposed. Furthermore, the dependence of the self-diffusivities upon both residual entropy and a molecular chain length parameter (r) was clearly found on the basis of HSC and real data. Accordingly, a new universal correlation for the estimation of D⁎ as function of residual entropy and r was obtained, giving rise to an average absolute relative deviation of 9.13% for all database. It was also devised a very simple and accurate entropy based equation for spherical systems (HS and LJ) which provides only 4.61% of error. The original Rosenfeld, Dzugutov and Bretonnet's expressions attain deviations that are several orders of magnitude higher than our values. ► The self-diffusion coefficient (D11) is studied by entropy scaling law's approach. ► One shows that well know entropy scaling laws of the literature are not universal. ► One shows that D11 depends upon both residual entropy & chain length parameter. ► Universal D11 correlation is proposed for model & real fluids (9.13%, 1724 points). ► A simple equation is proposed specifically for HS and LJ fluids (4.61%, 659 points).