A new combining rule for fluid mixtures

2009 ◽  
Vol 74 (2) ◽  
pp. 363-391 ◽  
Author(s):  
José Alfredo González-Calderón ◽  
Fernando del Río

We present evidence for the regular behaviour of the Boyle temperature TB in gaseous binary mixtures of small molecules with negligible multipolar moments. We use this regularity to construct a new combining rule for the prediction of the cross interaction u12(r) in those mixtures. The combining rule gives TB of the cross interaction as the harmonic mean of the Boyle temperatures of the pure components. The validity of this harmonic rule is based on experimental data of 28 binary mixtures, whose TB have been obtained from experimental data of the cross virial coefficient B12(T). In determining TB we make use of non-conformal potentials that have been proven to represent very accurately the effective interactions of the molecules investigated. The new combining rule is used to give interaction parameters of several dozens of binary mixtures involving noble gases (Ne, Ar, Kr and Xe), diatomic molecules (N2, O2 and CO) and n-alkanes (from methane to n-octane). These interaction parameters lead to a prediction of cross virial coefficients B12(T) within experimental error. Electrostatic interactions, originating in permanent dipolar, quadrupolar, octupolar and hexadecapolar moments and exemplified by molecules of HCl, CO2, CF4 and SF6, depart from the regular non-polar behaviour.

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
Author(s):  
Ivan Cibulka ◽  
Lubomír Hnědkovský ◽  
Květoslav Růžička

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.


The second virial coefficients of some binary mixtures of organic vapours have been measured at temperatures between 50 and 120° C. Mixtures of n -hexane with chloroform and of n -hexane with diethyl ether show a linear variation of second virial coefficient with composition. This is shown to be in accordance with prediction from the principle of corresponding states. Mixtures of chloroform with diethyl ether show a linear variation at 120° C, but pronounced curvature at lower temperatures. This is interpreted quantitatively as being due to association by hydrogen bonding with an energy of 6020 cal/mole.


1993 ◽  
Vol 48 (3) ◽  
pp. 505-513
Author(s):  
Uwe Hohm

Abstract A reasonable heuristic extrapolation of a theory given by Buckingham is used to estimate the frequency-and temperature-dependence of the second refractivity virial coefficient. The calculations are carried out for the atoms He, Ne, Ar, Kr, Xe and the small molecules H2 , N2 , O2 , HCl, CO2 , N2O, NH3 , CH4 , C2H4 , and SF6 . In some cases the frequency-dependence of BR (ω, T) is compared with experimental values, showing sometimes considerable deviations between experiment and the heuristic approach used in this work.


2021 ◽  
Author(s):  
Seyedeh Hoda Mozaffari

Thermodiffusion phenomenon in fluid mixtures has been investigated by several scientists in theoretical as well as experimental fields for decades. Nevertheless, due to shortcomings of both methods, interest in searching for alternative approaches to shed some light on molecular scale of the phenomenon has spurred. The objective of this thesis is to develop an accurate molecular dynamics (MD) algorithm that can predict thermodiffusive separation in binary and ternary fluid mixtures. More importantly, the proposed algorithm should be computationally efficient in order to be suitable for integration into multi-scale computational models to simulate thermodiffusion in a large system such as an oil reservoir. In developing such an effective and efficient computational tool, this thesis introduces a modified heat exchange algorithms, wherein, a new mechanism is introduced to rescale velocities which curbs the energy loss in the system and at the same time minimizes the computational time. The performance of the new algorithm in studying Soret effect for binary and ternary mixtures has been compared with other non-equilibrium molecular dynamics (NEMD) models including regular heat exchange algorithm (HEX) and reverse non-equilibrium molecular dynamics (RNEMD). Different types of binary mixtures were studied including one equimolar mixture of argon (Ar)-krypton (Kr) above its triple point, non-equimolar normal alkane mixtures of hexane (nC6)-decane (nC10) as well as hexane (nC6)-dodecane (nC12) for six compositions, three non-equimolar mixtures of pentane (nC5) decane (nC10) at atmospheric temperature and pressure. Additionally, the new algorithm was validated for different ternary mixtures including ternary normal alkanes methane (nC1)-butane (nC4)- dodecane (nC12) for three compositions, and one composition of different types of alkane mixture of 1,2,3,4-tetrahydronaphthalene (THN)-dodecane (nC12)-sobutylbenzene (IBB). The new algorithm demonstrates a significant improvement in reducing the energy loss by nearly 32%. Additionally, the new algorithm is about 7-9% more computationally efficient than the regular HEX for medium and large systems. In terms of direction of thermodiffusive segregations in binary mixtures, in agreement with the experimental data, the new algorithm shows that the heavier component moves towards the cold region whereas the lighter component accumulates near the hot zone. Additionally, the strength of segregation process diminishes as the concentration of heavy component in the mixture increases. The new algorithm improved the prediction of thermodiffusion factor in binary mixtures by 24% in binary mixtures. With respect to the ternary mixtures, similarly to binary mixtures the heaviest and lightest component in the mixture move towards, cold and hot zones, respectively. While the intermediate component shows the least tendency to segregate. In terms of the strength of Soret effect, the new algorithm is about 17% more accurate than the regular HEX algorithm with respect to experimental data.


2021 ◽  
Author(s):  
Seyedeh Hoda Mozaffari

Thermodiffusion phenomenon in fluid mixtures has been investigated by several scientists in theoretical as well as experimental fields for decades. Nevertheless, due to shortcomings of both methods, interest in searching for alternative approaches to shed some light on molecular scale of the phenomenon has spurred. The objective of this thesis is to develop an accurate molecular dynamics (MD) algorithm that can predict thermodiffusive separation in binary and ternary fluid mixtures. More importantly, the proposed algorithm should be computationally efficient in order to be suitable for integration into multi-scale computational models to simulate thermodiffusion in a large system such as an oil reservoir. In developing such an effective and efficient computational tool, this thesis introduces a modified heat exchange algorithms, wherein, a new mechanism is introduced to rescale velocities which curbs the energy loss in the system and at the same time minimizes the computational time. The performance of the new algorithm in studying Soret effect for binary and ternary mixtures has been compared with other non-equilibrium molecular dynamics (NEMD) models including regular heat exchange algorithm (HEX) and reverse non-equilibrium molecular dynamics (RNEMD). Different types of binary mixtures were studied including one equimolar mixture of argon (Ar)-krypton (Kr) above its triple point, non-equimolar normal alkane mixtures of hexane (nC6)-decane (nC10) as well as hexane (nC6)-dodecane (nC12) for six compositions, three non-equimolar mixtures of pentane (nC5) decane (nC10) at atmospheric temperature and pressure. Additionally, the new algorithm was validated for different ternary mixtures including ternary normal alkanes methane (nC1)-butane (nC4)- dodecane (nC12) for three compositions, and one composition of different types of alkane mixture of 1,2,3,4-tetrahydronaphthalene (THN)-dodecane (nC12)-sobutylbenzene (IBB). The new algorithm demonstrates a significant improvement in reducing the energy loss by nearly 32%. Additionally, the new algorithm is about 7-9% more computationally efficient than the regular HEX for medium and large systems. In terms of direction of thermodiffusive segregations in binary mixtures, in agreement with the experimental data, the new algorithm shows that the heavier component moves towards the cold region whereas the lighter component accumulates near the hot zone. Additionally, the strength of segregation process diminishes as the concentration of heavy component in the mixture increases. The new algorithm improved the prediction of thermodiffusion factor in binary mixtures by 24% in binary mixtures. With respect to the ternary mixtures, similarly to binary mixtures the heaviest and lightest component in the mixture move towards, cold and hot zones, respectively. While the intermediate component shows the least tendency to segregate. In terms of the strength of Soret effect, the new algorithm is about 17% more accurate than the regular HEX algorithm with respect to experimental data.


1982 ◽  
Vol 60 (9) ◽  
pp. 1223-1236
Author(s):  
C. Roth

Expressions for the two- and three-body effective interactions in the configurations l″ and l″l′ were obtained, and then specialized for the case of the odd configurations in the iron group with l having a value of 2 and l′ a value of 1.There are four independent effective interaction parameters for the configuration d″. For the configuration d″p it was shown that there are 2 independent parameters for the two-body effective interactions, and 11 independent parameters for the three-body effective interactions.The results are being utilized in general investigtions for the odd configurations (3d + 4s)″4p in the iron group, and subsequently for the odd configurations in the palladium and platinum groups.


1978 ◽  
Vol 33 (9) ◽  
pp. 1095-1096
Author(s):  
R. E. Caligaris ◽  
J . C. Grangel

Third virial coefficient for helium is calculated using the realistic Beck pair potential. The first quantum correction and the triple-dipole dispersion interaction are included. The results are compared with experimental data and with theoretical values obtained using the MDD-2 pair potential.


1967 ◽  
Vol 45 (4) ◽  
pp. 373-378 ◽  
Author(s):  
M. Orentlicher ◽  
J. M. Prausnitz

An approximation is suggested for calculating the third virial cross-coefficient Cijk from available generalized tables for pure-component third virial coefficients Ciii which are based on any one of several, spherically symmetric potential functions. A comparison of calculated results with the very limited experimental data now available indicates that the suggested approximation can reproduce the experimental results essentially within the probable (large) experimental uncertainty.


1971 ◽  
Vol 24 (12) ◽  
pp. 2449 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling

The Hamann-Lambert model for globular molecules using Lennard-Jones 12- 6 potential functions for the atomic interactions has been used to obtain second virial coefficients for CH4, CF4, SF6, SiF4, CMe4, SiMe4, and the mixtures CH4-CF4, CH4-SF6, CH4-CMe4, CH4-SiMe4, and CF4-SF6. Additive third virial coefficients have been computed where experimental data are available. Of the 18 parameter sets needed for the 12-6 interactions in the above molecules and their combinations ten were obtained by a least-squares fitting process using experimental values of second virial coefficients, five were obtained from combining rules, and the remaining three from sources independent of virial coefficient data. The computed values of the virial coefficients agree well with the experimental data although in the case of the third virial coefficients improved agreement would be obtained if some form of non-additivity could be allowed for.


Author(s):  
Л. Р. Маилян ◽  
С. А. Стельмах ◽  
Е. М. Щербань ◽  
М. П. Нажуев

Состояние проблемы. Железобетонные элементы изготавливаются, как правило, по трем основным технологиям - вибрированием, центрифугированием и виброцентрифугированием. Однако все основные расчетные зависимости для определения их несущей способности выведены, исходя из основного постулата - постоянства и равенства характеристик бетона по сечению, что реализуется лишь в вибрированных колоннах. Результаты. В рамках диаграммного подхода предложены итерационный, приближенный и упрощенный способы расчета несущей способности железобетонных вибрированных, центрифугированных и виброцентрифугированных колонн. Выводы. Расчет по диаграммному подходу показал существенно более подходящую сходимость с опытными данными, чем расчет по методике норм, а также дал лучшие результаты при использовании дифференциальных характеристик бетона, чем при использовании интегральных и, тем более, нормативных характеристик бетона. Statement of the problem. Reinforced concrete elements are typically manufactured according to three basic technologies - vibration, centrifugation and vibrocentrifugation. However, all the basic calculated dependencies for determining their bearing capacity were derived using the main postulate, i.e., the constancy and equality of the characteristics of concrete over the cross section, which is implemented only in vibrated columns. Results. Within the framework of the diagrammatic approach, iterative, approximate and simplified methods of calculating the bearing capacity of reinforced concrete vibrated, centrifuged and vibrocentrifuged columns are proposed. Conclusions. The calculation according to the diagrammatic approach showed a significantly better convergence with the experimental data than that using the method of norms, and also performs better when using differential characteristics of concrete than when employing integral and particularly standard characteristics of concrete.


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