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Analytical Virial Coefficients and New Equations of State of Hard Ellipsoid Fluids

Received: 2 January 2017     Accepted: 19 January 2017     Published: 22 February 2017
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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<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), 2017. Published by Science Publishing Group

Keywords

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

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    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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    AMA 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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  • @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}
    }
    

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  • 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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Author Information
  • Department of Physics, Yasouj University, Yasouj, Iran

  • Department of Physics, Yasouj University, Yasouj, Iran

  • Department of Physics, Yasouj University, Yasouj, Iran

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