A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-Alkanes
The Density Gradient Theory (DGT) permits obtaining the surface tension by using an equation of state and the so-called influence parameter. Different correlations of the influence parameter versus temperature have been proposed, with the two-coefficient ones from Zuo and Stenby (full temperature ra...
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2024-11-01
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| author | Isidro Cachadiña Ariel Hernández Ángel Mulero |
| author_facet | Isidro Cachadiña Ariel Hernández Ángel Mulero |
| author_sort | Isidro Cachadiña |
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| description | The Density Gradient Theory (DGT) permits obtaining the surface tension by using an equation of state and the so-called influence parameter. Different correlations of the influence parameter versus temperature have been proposed, with the two-coefficient ones from Zuo and Stenby (full temperature range) and Miqueu et al. (valid for the lower temperature range) being widely used. Recently, Cachadiña et al. applied the DGT with the Peng-Robinson Equation of State to esters. They proposed a new two-coefficient correlation that uses a universal exponent related to the critical exponent associated with the dependence of coexistence densities on temperature near the critical point. When applied to <i>n</i>-alkanes, it is shown that the Cachadiña et al. correlation must be modified to improve the lower temperature range behavior. The proposed modification results in a three-coefficient correlation that includes the triple point temperature as an input parameter and incorporates the Zuo and Stenby and Miqueu et al. correlations as particular cases. Firstly, the correlation coefficients for each of the 32 <i>n</i>-alkanes considered are obtained by fitting the selected values for the surface tension obtained from different databases, books, and papers. The results obtained are comparable to other specific correlations reported in the literature. The overall mean absolute percentage deviation (OMAPD) between the selected and calculated data is just <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.79</mn><mo>%</mo></mrow></semantics></math></inline-formula>. Secondly, a general correlation with three adjustable coefficients valid for all the <i>n</i>-alkanes is considered. Despite the OMAPD of 4.38% obtained, this correlation is discarded due to the high deviations found for methane. Finally, it is found that a new six-coefficient general correlation, including the radius of gyration as an input fluid parameter, leads to an OMAPD of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.78</mn><mo>%</mo></mrow></semantics></math></inline-formula> for the fluid set considered. The use of other fluid properties as an alternative to the radius of gyration is briefly discussed. |
| format | Article |
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| institution | OA Journals |
| issn | 1420-3049 |
| language | English |
| publishDate | 2024-11-01 |
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| spelling | doaj-art-bdf56ab2f38a499da7cb2ef9179bce5e2025-08-20T01:55:27ZengMDPI AGMolecules1420-30492024-11-012923564310.3390/molecules29235643A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-AlkanesIsidro Cachadiña0Ariel Hernández1Ángel Mulero2Departamento de Física Aplicada, Universidad de Extremadura, 06006 Badajoz, SpainDepartamento de Ingeniería Industrial, Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción 4090541, ChileDepartamento de Física Aplicada, Universidad de Extremadura, 06006 Badajoz, SpainThe Density Gradient Theory (DGT) permits obtaining the surface tension by using an equation of state and the so-called influence parameter. Different correlations of the influence parameter versus temperature have been proposed, with the two-coefficient ones from Zuo and Stenby (full temperature range) and Miqueu et al. (valid for the lower temperature range) being widely used. Recently, Cachadiña et al. applied the DGT with the Peng-Robinson Equation of State to esters. They proposed a new two-coefficient correlation that uses a universal exponent related to the critical exponent associated with the dependence of coexistence densities on temperature near the critical point. When applied to <i>n</i>-alkanes, it is shown that the Cachadiña et al. correlation must be modified to improve the lower temperature range behavior. The proposed modification results in a three-coefficient correlation that includes the triple point temperature as an input parameter and incorporates the Zuo and Stenby and Miqueu et al. correlations as particular cases. Firstly, the correlation coefficients for each of the 32 <i>n</i>-alkanes considered are obtained by fitting the selected values for the surface tension obtained from different databases, books, and papers. The results obtained are comparable to other specific correlations reported in the literature. The overall mean absolute percentage deviation (OMAPD) between the selected and calculated data is just <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.79</mn><mo>%</mo></mrow></semantics></math></inline-formula>. Secondly, a general correlation with three adjustable coefficients valid for all the <i>n</i>-alkanes is considered. Despite the OMAPD of 4.38% obtained, this correlation is discarded due to the high deviations found for methane. Finally, it is found that a new six-coefficient general correlation, including the radius of gyration as an input fluid parameter, leads to an OMAPD of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.78</mn><mo>%</mo></mrow></semantics></math></inline-formula> for the fluid set considered. The use of other fluid properties as an alternative to the radius of gyration is briefly discussed.https://www.mdpi.com/1420-3049/29/23/5643surface tensionPeng–Robinson equation of stateDensity Gradient Theoryinfluence parameter<i>n</i>-alkanes |
| spellingShingle | Isidro Cachadiña Ariel Hernández Ángel Mulero A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-Alkanes Molecules surface tension Peng–Robinson equation of state Density Gradient Theory influence parameter <i>n</i>-alkanes |
| title | A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-Alkanes |
| title_full | A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-Alkanes |
| title_fullStr | A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-Alkanes |
| title_full_unstemmed | A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-Alkanes |
| title_short | A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng–Robinson Equation of State for <i>n</i>-Alkanes |
| title_sort | new general correlation for the influence parameter in density gradient theory and peng robinson equation of state for i n i alkanes |
| topic | surface tension Peng–Robinson equation of state Density Gradient Theory influence parameter <i>n</i>-alkanes |
| url | https://www.mdpi.com/1420-3049/29/23/5643 |
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