The complexity of calculations for high order virial coefficients of ellipsoids makes it difficult to obtain accurate analytical high order coefficients and equation of state for such systems. Using analytical method, the virial coefficients up to third order are calculated. For higher ones, the numerical values were taken from publications of other researchers, based on Monte Carlo integration method. By fitting the available numerical virial coefficients, sixth to eighth order, the two shape parameter analytical expressions of the hard convex molecules are obtained. Using these available data, up to eighth order, we have obtained the approximate one shape parameter analytical expressions of the hard prolate and oblate ellipsoid molecules. The fitted virial coefficients are in agreement with the simulation results. Moreover, the approximate analytical expressions for the equation of state of isotropic hard ellipsoid fluids are proposed. The proposed equations of state are in good agreement with the simulations up to medium elongations. In addition, our equations show a better agreement comparing to other works. Also, the newest equation is used for both prolate and oblate ellipsoid fluids and is convenient for elongations, k<10.0.
| Published in | Chemical and Biomolecular Engineering (Volume 2, Issue 1) |
| DOI | 10.11648/j.cbe.20170201.15 |
| Page(s) | 27-40 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Virial Coefficients, Equation of State, Hard Ellipsoid, Isotropic Fluid, Prolate Molecule, Oblate Molecule
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APA Style
Maryam Hashemi, Abolghasem Avazpour, Shaker Hajati. (2017). Analytical Virial Coefficients and New Equations of State of Hard Ellipsoid Fluids. Chemical and Biomolecular Engineering, 2(1), 27-40. https://doi.org/10.11648/j.cbe.20170201.15
ACS Style
Maryam Hashemi; Abolghasem Avazpour; Shaker Hajati. Analytical Virial Coefficients and New Equations of State of Hard Ellipsoid Fluids. Chem. Biomol. Eng. 2017, 2(1), 27-40. doi: 10.11648/j.cbe.20170201.15
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Download@article{10.11648/j.cbe.20170201.15,
author = {Maryam Hashemi and Abolghasem Avazpour and Shaker Hajati},
title = {Analytical Virial Coefficients and New Equations of State of Hard Ellipsoid Fluids},
journal = {Chemical and Biomolecular Engineering},
volume = {2},
number = {1},
pages = {27-40},
doi = {10.11648/j.cbe.20170201.15},
url = {https://doi.org/10.11648/j.cbe.20170201.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbe.20170201.15},
abstract = {The complexity of calculations for high order virial coefficients of ellipsoids makes it difficult to obtain accurate analytical high order coefficients and equation of state for such systems. Using analytical method, the virial coefficients up to third order are calculated. For higher ones, the numerical values were taken from publications of other researchers, based on Monte Carlo integration method. By fitting the available numerical virial coefficients, sixth to eighth order, the two shape parameter analytical expressions of the hard convex molecules are obtained. Using these available data, up to eighth order, we have obtained the approximate one shape parameter analytical expressions of the hard prolate and oblate ellipsoid molecules. The fitted virial coefficients are in agreement with the simulation results. Moreover, the approximate analytical expressions for the equation of state of isotropic hard ellipsoid fluids are proposed. The proposed equations of state are in good agreement with the simulations up to medium elongations. In addition, our equations show a better agreement comparing to other works. Also, the newest equation is used for both prolate and oblate ellipsoid fluids and is convenient for elongations, k.},
year = {2017}
}
TY - JOUR T1 - Analytical Virial Coefficients and New Equations of State of Hard Ellipsoid Fluids AU - Maryam Hashemi AU - Abolghasem Avazpour AU - Shaker Hajati Y1 - 2017/02/22 PY - 2017 N1 - https://doi.org/10.11648/j.cbe.20170201.15 DO - 10.11648/j.cbe.20170201.15 T2 - Chemical and Biomolecular Engineering JF - Chemical and Biomolecular Engineering JO - Chemical and Biomolecular Engineering SP - 27 EP - 40 PB - Science Publishing Group SN - 2578-8884 UR - https://doi.org/10.11648/j.cbe.20170201.15 AB - The complexity of calculations for high order virial coefficients of ellipsoids makes it difficult to obtain accurate analytical high order coefficients and equation of state for such systems. Using analytical method, the virial coefficients up to third order are calculated. For higher ones, the numerical values were taken from publications of other researchers, based on Monte Carlo integration method. By fitting the available numerical virial coefficients, sixth to eighth order, the two shape parameter analytical expressions of the hard convex molecules are obtained. Using these available data, up to eighth order, we have obtained the approximate one shape parameter analytical expressions of the hard prolate and oblate ellipsoid molecules. The fitted virial coefficients are in agreement with the simulation results. Moreover, the approximate analytical expressions for the equation of state of isotropic hard ellipsoid fluids are proposed. The proposed equations of state are in good agreement with the simulations up to medium elongations. In addition, our equations show a better agreement comparing to other works. Also, the newest equation is used for both prolate and oblate ellipsoid fluids and is convenient for elongations, k. VL - 2 IS - 1 ER -
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