Research Article  Open Access
SeungKyo Oh, "Modified LennardJones Potentials with a Reduced TemperatureCorrection Parameter for Calculating Thermodynamic and Transport Properties: Noble Gases and Their Mixtures (He, Ne, Ar, Kr, and Xe)", Journal of Thermodynamics, vol. 2013, Article ID 828620, 29 pages, 2013. https://doi.org/10.1155/2013/828620
Modified LennardJones Potentials with a Reduced TemperatureCorrection Parameter for Calculating Thermodynamic and Transport Properties: Noble Gases and Their Mixtures (He, Ne, Ar, Kr, and Xe)
Abstract
The threeparameter LennardJones potential function is proposed to calculate thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their mixtures at low density. Empirical modification is made by introducing a reduced temperaturecorrection parameter to the LennardJones potential function for this purpose. Potential parameters (, , and ) are determined individually for each species when the second virial coefficient and viscosity data are fitted together within the experimental uncertainties. Calculated thermodynamic and transport properties are compared with experimental data by using a single set of parameters. The present study yields parameter sets that have more physical significance than those of second virial coefficient methods and is more discriminative than the existing transport property methods in most cases of pure gases and of gas mixtures. In particular, the proposed model is proved with better results than those of the twoparameter LennardJones potential, Kihara Potential with group contribution concepts, and other existing methods.
1. Introduction
Accurate representation of thermodynamic and transport properties is essential to process engineers to design and optimize equipment and chemical processes. Second virial coefficient is an important quantity which is useful in calculating vessel size from volumetric data, heating requirements from calorimetric data, and stage requirements from phase equilibrium data. Transport properties such as viscosity, thermal conductivity, and diffusion coefficient are critically important parameters in many engineering applications: for the determination of pipeline, heatexchanger and separation equipment size, mass transfer efficiency of reservoir of oils, and the power required to pump fluid [1].
The intermolecular forces are of great importance to scientists in a wide field of disciplines as information of these interactions provides the progress of collisions between molecules and determines the bulk properties of substances. Approximation of thermodynamic and transport properties from statistical mechanics requires a realistic intermolecular potential [2]. The theoretical basis in statistical mechanics for the virial equation is one of its attractions. The viral equation truncated after the second term is a popular tool to calculate accurate thermodynamic properties at low or moderate densities. A number of investigators have emphasized the determination of second virial coefficient through experiments and correlations. When ChapmanEnskog gas kinetic theory [3] allows the prediction of transport properties, the potential energy of molecular interactions is known as a function of intermolecular separation and orientation. A description of the spherically symmetric potential as a function of intermolecular separation, averaged over all molecular orientations, suffices to calculate dilute gas viscosities, thermal conductivities, and diffusion coefficients of monoatomic gases.
A realistic intermolecular potential allows the calculation of thermodynamic and transport properties. A lot of studies have focused on individual properties like second virial coefficient or viscosity for the determination of intermolecular potential parameters [2]. Potential parameters of any given model that give the best fit for thermodynamic and transport properties (e.g., second virial coefficient, viscosity, thermal conductivity, and diffusion coefficient) are generally different. Therefore, for a simple model such as LennardJones potential, there is one specific set of potential parameters suitable for each property, producing significantly different results [4].
Several investigators [2, 5–7] have used statistical mechanics and kinetic theory of gases to represent thermodynamic and transport properties with a single set of molecular parameters, namely, those appearing in an intermolecular potential function. The LennardJones potential has been widely used for the representation of thermodynamic and transport properties of normal fluids. In one particularly interesting study of Tee et al. [6], a single set of molecular parameters was evaluated from the LennardJones potential for each species; in this procedure, viscosity data for each substance was fitted first by leastsquares analysis, second virial coefficient was fitted next, and the data on second virial coefficient and viscosity were statistically analyzed simultaneously to develop corresponding states correlations with a single set of potential parameters for each substance. They concluded that when second virial coefficient and viscosity data were fitted together, their sets of molecular parameters give the best overall fit to the data for each species and tend to be least affected by experimental errors; beside that their results are quite comparable to those determined individually from viscosity. Potential parameters obtained in this manner were proved to be successful in predicting second virial coefficients and dilute gas viscosities for molecules ranging in shape from spherical to chains as long as nheptane with good result. Hence, the LennardJones potential is still attractive for its simplicity and capability of predicting noble gas properties if its weak point is compensated for and its accuracy is improved.
The objective of this study is to represent thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their binary mixtures at low density using a single set of modified LennardJones potential parameters. For this purpose, a temperaturecorrection parameter was introduced to the reduced temperature in the LennardJones potential function. A set of potential parameters was determined when the second virial coefficient and viscosity data are fitted simultaneously within their experimental errors, separately for each noble gas; parameters obtained in this manner were used in all subsequent calculations of properties such as thermal conductivity and diffusion coefficient, in which data were not supplied to parameter estimations, and in mixture property computations. Validity of the modified LennardJones potential with a reduced temperaturecorrection parameter was tested with good results in comparison with other existing methods.
2. Theory
In this paper, special focus was placed on the LennardJones intermolecular potential for the computations of noble gas properties, even though more accurate potentials exist. A form of this potential was first established by LennardJones [8] and is a mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. The most common expression of the LennardJones potential has the form where is the intermolecular potential energy as a function of the separation distance between a pair of molecules, is the depth of the potential well in Joule, and is the finite distance in angstrom Ǻ at which the interparticle potential becomes zero.
These potential parameters can be fitted by leastsquares analysis and lead to provide accurate calculations of dilute gas thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases, as summarized below.
2.1. Second Virial Coefficient
From statistical mechanics, the relations between second virial coefficient and intermolecular potential functions were theoretically derived; in particular, explicit expression of the second virial coefficient for the LennardJones potential was rigorously derived by Hirschfelder et al. [4] for a computational use: in which is the Avogadro’s constant 6.022·10^{23} mol^{−1}, is the reduced (dimensionless) temperature , and is the Boltzmann constant 1.3806488·10^{−23} JK^{−1}. However, Kojima [9] observed that it is quite effective for calculating virial coefficients from the Stockmayer intermolecular potential model with an aid of introducing a reduced temperaturecorrection parameter of as instead of using temperature . This temperaturecorrection parameter was also proved in developing a new virial equation of state by Ichikura et al. [10].
In the present study, our observations on the accurate approximation not only of thermodynamic property (second virial coefficient), but also of transport properties (viscosities, thermal conductivities, and diffusion coefficients) in the dilute gaseous phase of noble gases were made by introducing temperaturecorrection parameter to the reduced temperature shown in the LennardJones (126) potential function:
Then the second virial coefficient can be calculated from (2) and (3) when three potential parameters of the modified LennardJones potential are fitted together to second virial coefficient and viscosity data separately for each substance.
For interaction of different molecular species, the combining rules are used for the molecular distance, energy, and reduced temperaturecorrection parameter for mixture computations:
For spherical molecules, these equations are of high accuracy for the prediction of second crossvirial coefficient required in (2) and other mixture properties discussed later.
2.2. Viscosity
Transport properties (viscosity, thermal conductivity, and diffusion coefficient) at low density can be calculated by using ChapmanEnskog kinetic theory [3], which has been applied rigorously to monatomic gases in a number of studies [11]. The dilute gas viscosity can be well presented by the ChapmanEnskog approximation derived from the kinetic theory: where is the molecular weight (gram mol^{−1}), is the absolute temperature in Kelvin, and the viscosity is in micropoise . For mixture viscosity calculations, the formula proposed by Hirschfelder et al. [4] was used in this study, in which the interaction quantity must be determined to employ this method in advance: in which and are the molecular weights of the components 1 and 2, respectively, and is the modified reduced temperature for mixture calculations, . The composition dependence of viscosity on the binary gas mixture is defined as follows: where is the mixture viscosity, and , , and are the mole fractions, the molecular weights, and the viscosities at the mixture temperature of the pure components . And the quantities and are the collision integrals for viscosity and diffusion coefficient, respectively, and are defined as a function of the reduced temperature which depends on the intermolecular potential selected. Neufeld et al. [12] proposed analytical approximations to transport collision integrals for the LennardJones potential in the range , being convenient for easy computer application:
2.3. Thermal Conductivity
Since the ChapmanEnskog gas kinetic theory uses a common basis for the evaluation of viscosity and thermal conductivity, the statistical expression for the thermal conductivity involves the same collision integral as does the viscosity. For a pure monoatomic gas at low density, which has no rotational or vibrational degrees of freedom, thermal conductivity was calculated through a rigorous analysis by Brokaw [13]: where the thermal conductivity is microwatts per meter per degree Kelvin in mW m^{−1} K^{−1} and is the universal gas constant 83.14 cm^{3} bar mol^{−1} k^{−1}. Thus, the thermal conductivity of the noble gas can be calculated from the estimated potential parameters or from experimental viscosity data which are generally available for the molecule. In the present work, pure viscosity value obtained from (7) was used for the calculation of thermal conductivity of pure substance. It thus implies that a check on the thermal conductivity serves as a crosscheck between the viscosity and thermal conductivity data and not necessarily as a check on the potential function chosen [14].
Various prediction methods for estimating mixture thermal conductivity have appeared, one of which is essentially empirical and it is reduced to some form of the Wassiljewa equation [15]: where is the mixture thermal conductivity and is a combinational factor. This factor is empirically expressed by Mason and Saxena [16] as where are the thermal conductivities of pure component determined from (16), which are sufficient to predict mixture thermal conductivity when its measurements are not available in the literature.
2.4. Diffusion Coefficient
The ChapmanEnskog expression for binary diffusion coefficient of dilute gas is presented by Hirschfelder et al. [4]: where is in cm^{2} sec^{−1} and is in bar. And is the collision integral for diffusion coefficient of nonpolar LennardJones potential given by (15). When molecules 1 and 2 are identical, (19) becomes expression for the selfdiffusion coefficient:
3. Results and Discussion
3.1. Pure Noble Gases
As a part of systematic program of our researches, modified LennardJones potential function with a reduced temperaturecorrection parameter was applied to noble gases (He, Ne, Ar, Kr, and Xe) for the computation of thermodynamic (second virial coefficient) and transport properties (viscosity, thermal conductivity, and selfdiffusion coefficient) at low density.
Using (2), (3), and (7), three potential parameters were evaluated from the simultaneous regression of second virial coefficient and viscosity data separately for each species. For instance, three parameter values for helium gas were determined from second virial coefficient and viscosity data of pure helium gas. Potential parameters of other noble gases were evaluated in an analogous manner.
A critical review of the literature on second virial coefficient was achieved by Dymond et al. [17]. They provided the recommended values of virial coefficients for each compound fitted to a smoothing function of temperature by the leastsquares criterion. This smoothing function for second virial coefficient is the polynomial of reciprocal temperature with usually three terms. In particular, two different smoothing correlations of helium were given in the temperature ranges between 1.59 K and 35.1 K and between 35.1 K and 1473.15 K. We have used their comprehensive compilation of the second virial coefficient data as our data source. And pure viscosity data required for the potential parameter determinations were all taken from Stephan and Lucas [18], even though other recommended or various sets of data exist. Nonlinear leastsquares parameter estimation subroutine based on the LevenbergMarquardt algorithm supplied by IMSL STAT/library [19] was used in this data regression, in which each data point was weighted by its estimated experimental uncertainty taken from the corresponding Refs. A set of potential parameters individually for each substance can then be estimated when the following objective function is minimized: in which is the observed uncertainty of second virial coefficient in cm^{3} mol^{−1} and is of dimensionless fractional uncertainty of viscosity in %. It is noted that the first term is designated for second virial coefficient and the second for viscosity.
Table 1 summarizes determined parameter values of modified LennardJones potential of noble gases (He, Ne, Ar, Kr, and Xe). In Table 2, resulting deviations between observed and regressed second virial coefficient data are given on an RMSD (rootmeansquare deviation) basis in cm^{3} mol^{−1}, which is defined by

 
Two different smoothing functions were used in the temperature ranges between 1.59 K and 35.1 K, and between 35.1 K and 1473.15 K. 
Comparisons of the proposed method with other existing methods are shown in Table 2 along with their data sources and observed temperature ranges. The average RMSD between a total of observed and calculated 735 second virial coefficient data of five noble gases by the present method was 3.33 cm^{3} mol^{−1}, indicating that the proposed method compares very well with the Dymond’s correlations [17] 3.29 cm^{3} mol^{−1} and yields more accurate results than other existing methods: original twoparameter LennardJones potential [4] 6.79 cm^{3} mol^{−1}, Kihara potential with group contribution concept [20] 5.99 cm^{3} mol^{−1}, and the corresponding states method of Tsonopoulos [21] 18.6 cm^{3} mol^{−1}. A comparison of the measured and calculated second virial coefficients from Dymond et al. [17] for pure noble gases (He, Ne, Ar, Kr, and Xe) is presented in Figures 1, 2, 3, 4, and 5, in order. Also included in Table 2 are prediction results from other second virial coefficient data of helium and xenon available in the literature, showing similar results.
In Table 3, deviations of regression results between observed and calculated viscosity data are presented on an RMSD_{r} (rootmeansquare deviation, relative) basis in %, which is defined by
 
Number of data points for each noble gas. Total number of data points for all noble gases. 
The average RMSD_{r} value between a total of observed and regressed 117 viscosity data for five noble gases was found to be 1.90%, indicating that the present work is quite comparable to the Refprop Database correlations [22] 1.78% and is in better agreement with experimental data than any other existing methods: original LennardJones potential 6.60%, Kihara potential with group contribution concept 5.74%, the corresponding states method of Lucas [23] 2.25%, and the Simsci Database correlations [24] 2.08%. Comparisons of the measured and calculated viscosities for pure noble gases (He, Ne, Ar, Kr, and Xe) are presented in Figures 6, 7, 8, 9, and 10, in order. Using the same set of potential parameters, other 2597 viscosity data available in the literature other than Stephan and Lucas [18] were reproduced with an overall average RMSD_{r} 3.09% for all noble gases, noting that these results are more accurate than other existing investigations; original LennardJones potential 5.06%, Kihara potential with group contribution method 6.92%, Lucas method 3.15%, Simsci correlations 3.31%, and Refprop correlations 9.19%.
It is mentioned here that for each dilute noble gas at 0.1 MPa pressure, the Refprop Database provides selected viscosity data valid in specific temperature ranges, for example, 4–2219 K for helium, 27–1037 K for neon, 87–2992 K for argon, 119–1124 K for krypton, and 164–1100 K for xenon. In this work, their recommended viscosity data were fitted separately for each substance by leastsquares analysis to obtain smoothing functions, usually reciprocal temperature expressions of third order, which were used to represent viscosity data at the same temperature as those of experimental data for the reasonable comparisons. Prediction results from the Refprop correlations are observed to be not in reliable agreement with measured viscosity data, especially near upper and lower limits of temperature ranges specified previously, as shown in Table 3. The Simsci Database [24] provides the smoothing viscosity function with four coefficients valid in specific temperature ranges: 20–2000 K for helium, 30–3272 K for neon, 83–3273 K for argon, 100–1500 K for krypton, and 100–1600 K for xenon.
The next stage of this work is to calculate other properties such as thermal conductivity and selfdiffusion coefficient, not used for parameter determinations, using the same set of potential parameters determined earlier. As shown in Table 4, the overall average RMSD_{r} value of 3.59% between a total of 3352 experimental and calculated thermal conductivities obtained by the proposed model is somewhat less reliable to the Simsci correlations 2.78%, but compares very well with the original LennardJones potential 9.28% and the Refprop correlations 4.93%.
 
Number of data points for each noble gas. Total number of data points for all noble gases. 
Like the case of viscosities, the Refprop Database [22] provides dilute gas thermal conductivity data at 0.1 MPa suitable in specific temperature ranges: 4–1100 K for helium, 27–1039 K for neon, 87–2968 K for argon, 119–1100 K for krypton, and 164–1101 K for xenon. The procedure to produce thermal conductivity data is the same as that of viscosity. The Simsci Database also provides the same type of soothing thermal conductivity function, (24), in specific temperature ranges: 30–2000 K for helium, 30–3272 K for neon, 90–3273 K for argon, 120–2000 K for krypton, and 165–1500 K for xenon. Comparisons of the measured and calculated thermal conductivities for pure noble gases (He, Ne, Ar, Kr, and Xe) are depicted in Figures 11, 12, 13, 14, and 15, in order. As shown in Figures 14 and 15, Refprop Database shows considerably larger discrepancies between measured and calculated thermal conductivities for krypton and xenon than other methods particularly at hightemperature region, at which recommended data is not reliable, as specified by them.
A total of 237 selfdiffusion coefficient data were next tested. As shown in Table 5, the overall average RMSD_{r} value of 5.03% from all noble gases was obtained by this work, in which the result is in better agreement with experimental data than those of the original LennardJones potential 8.73% and of the Fuller method [25] 10.7%. It is indicated that for the helium and neon gas, the proposed method is less accurate than the original LennardJones potential. Comparisons of the measured and calculated selfdiffusion coefficients for noble gases (He, Ne, Ar, Kr, and Xe) are depicted in Figures 16, 17, 18, 19, and 20, in order.
 
Number of data points for each noble gas. Total number of data points for all noble gases. 
3.2. Noble Gas Mixtures
The same set of potential parameters estimated from pure gas information was applied to predict mixture properties such as second crossvirial coefficient, mixture viscosity, mixture thermal conductivity, and binary diffusion coefficient with no additional parameters.
Table 6 shows that for the second crossvirial coefficient calculations, a total of 489 data of noble gas mixtures taken from the critical compilation of Dymond et al. [17] and from the Kestin et al. [26] were fitted to be overall average RMSD value of 5.73 cm^{3} mol^{−1}, while the 6.25 cm^{3} mol^{−1} value was obtained by the smoothing functions of Dymond et al. in the same fashion as used in the pure gas calculations. And the 45.0 and 9.28 cm^{3} mol^{−1} RMSD values were found by the original LennardJones potential and the corresponding states method of Tsonopoulos, respectively. A comparison of measured and calculated second crossvirial coefficients of Ar + Kr mixture is shown in Figure 21.
 
Number of data points for each gas mixture. Total number of data points for all gas mixtures. 
Prediction results of noble gas mixture viscosities are presented in Table 7. A total of 2918 viscosity data points for all noble gas mixtures were calculated in this paper, indicating that the present study is in better agreement between experimental and calculated data than other methods on a criterion: 2.93% by the present model, 10.6% by the original LennardJones potential, and 4.05% by the Lucas method. However, it is noted that for krypton and xenon mixture, this work is less reliable to the Lucas method. Figure 22 shows the comparison of measured and calculated viscosities of He + Ne mixture.
 
Number of data points for each gas mixture.Total number of data points for all gas mixtures. 
Given in Table 8 are the resulting values between a total of 2092 measured and predicted mixture thermal conductivity data. Based on the overall average value of all noble gas mixtures, 7.65% of the present study is in slightly worse agreement between measured and predicted mixture thermal conductivities than 6.50% of the Wassiljewa equation [15] with the combinational factor of Mason and Saxena [16] and is more feasible to 10.8% of the original LennardJones potential. A comparison of measured and calculated thermal conductivities of Ne + Kr mixture is shown in Figure 23.
 
Number of data points for each mixture. Total number of data points for all gas mixture mixtures. ^{ a}Wassiljewa equation [15] with the combinational factor of Mason and Saxena [16]. 
Included in Table 9 are the resulting values between a total of 1240 measured and predicted binary diffusion coefficient data for noble gas mixtures, in which 4.98 of the present study is in quite better agreement between measured and predicted binary diffusion coefficients than 7.95 of the original LennardJones potential and 6.24 of the Fuller method. A comparison of measured and calculated binary diffusion coefficients for He + Ne mixture is shown in Figure 24.
 
Number of data points for each mixture. **Total number of data points for all gas mixtures. 
4. Conclusions
The threeparameter LennardJones potential function has been empirically modified by introducing a temperaturecorrection parameter to the reduced temperature for the calculation of the thermodynamic property (second virial coefficient) and dilute transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their binary mixtures. Separately for each species, a single set of three potential parameters is estimated when the second virial coefficient and viscosity data are regressed together within the experimental errors. Obtained potential parameters are used to reproduce second virial coefficient and viscosity data and in all following predictions of other properties like thermal conductivity and diffusion coefficient. Noble gas mixture properties are calculated with the same set of parameters as well.
For the second virial coefficient calculations of pure noble gases, the threeparameter LennardJones potential proposed in this paper is quite comparable to Dymond’s correlations and produces more accurate results than the original twoparameter LennardJones potential, the Kihara potential with group contribution concept, and the Tsonopoulos correlations. For the viscosity calculations, the proposed model agrees better with the observed and calculated data than the original LennardJones potential, the Kihara potential with group contribution method, the Lucas method, the Simsci Database, and the Refprop Database. Agreement between experimental and calculated thermal conductivities obtained by the proposed model is somewhat less accurate than the Simsci Database, but compares very well with the original LennardJones potential and with the Refprop Database. Calculation of selfdiffusion coefficients shows that this work is in better agreement with experimental data than those of the original LennardJones potential and of the Fuller method, and that for helium gas and for neon gas results of the proposed method is less accurate than the original LennardJones potential.
For mixture property predictions, the same set of potential parameters is applied with no additional parameters. Second crossvirial coefficient data calculated by the present study is less feasible to those of Dymond’s correlations and is in better agreement with the observed data than the original LennardJones potential and the corresponding states method of Tsonopoulos. The present study is in better agreement between experimental mixture viscosity data than the original LennardJones potential and the Lucas method, except for the mixture of kr + Xe. The present study is in somewhat worse agreement between measured and calculated mixture thermal conductivities than the Wassiljewa equation with the combinational factor of Mason and Saxena and is more accurate than the original LennardJones potential. However, thermal conductivity of the He + Ne and Kr + Xe mixtures was reproduced better with the Wassiljewa equation than with the proposed method. The present study is in appreciably better agreement between the observed and calculated binary diffusion coefficients of noble gases mixtures than the original LennardJones potential and the Fuller method.
In this work, the empirical approach of adding a temperaturecorrection parameter to the reduced temperature in the LennardJones potential function has been tested with good success for the calculations of thermodynamic and transport property of noble gases and their binary mixtures in dilute gas region. Application of this approach to other substances such as polyatomic, polar gases will be tested in the near future.
Nomenclature
:  Combinational factor in (18) 
:  Defined by (13), 
:  Second virial coefficient (cm^{3} mol^{−1}) 
:  Diffusion coefficient (cm^{2} sec^{−1}) 
:  Boltzmann constant, 1.3806488·10^{−23} (JK^{−1}) 
:  Molecular weight (gram mol^{−1}) 
:  Avogadro constant, 6.022·10^{23} (mol^{−1}) 
:  Pressure (bar) 
:  Distance between molecular centers of molecules 1 and 2 (Ǻ) 
:  Rootmeansquare deviation (cm^{3} mol^{−1}) 
:  Percent relative rootmeansquare deviation, relative (%) 
:  Absolute temperature (K) 
:  Reduced temperature, 
:  Intermolecular potential function 
:  Mole fraction in the gas phase 
:  Defined by (10) 
:  Defined by (11) 
:  Defined by (12). 
:  Depth of the potential well [J] 
:  Viscosity () 
:  Thermal conductivity (mW m^{−1} K^{−1}) 
:  Collision diameter (Ǻ) 
:  Reduced temperaturecorrection parameter 
:  Collision integral for diffusion coefficient 
:  Collision integral for viscosity. 
Acknowledgment
This paper was supported by the Konyang University Research Fund, in 20122013.
References
 T. H. Chung, M. Ajlan, L. L. Lee, and K. E. Starling, “Generalized multiparameter correlation for nonpolar and polar fluid transport properties,” Industrial & Engineering Chemistry Research, vol. 27, no. 4, pp. 671–679, 1988. View at: Publisher Site  Google Scholar
 J. P. O'Connell and J. M. Prausnitz, “Advances in thermophysical properties at extreme temperatures and pressures,” in Proceedings of the 3rd Symposium of Thermophysical Properties, ASME, New York, NY, USA, 1965. View at: Google Scholar
 S. Chapman and T. G. Cowling, The Mathematical Theory of NonUniform Gases, Cambridge University Press, New York, NY, USA, 3rd edition, 1970.
 J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, NY, USA, 1954.
 J. H. Dymond and B. J. Alder, “Pair potential for Argon,” The Journal of Chemical Physics, vol. 51, no. 50, pp. 309–320, 1969. View at: Google Scholar
 L. S. Tee, S. Gotoh, and W. E. Stewart, “Molecular parameters for normal fluids. LennardJones 126 Potential,” Industrial and Engineering Chemistry Fundamentals, vol. 5, no. 3, pp. 356–363, 1966. View at: Publisher Site  Google Scholar
 L. S. Tee, S. Gotoh, and W. E. Stewart, “molecular parameters for normal fluids. kihara potential with spherical core,” Industrial and Engineering Chemistry Fundamentals, vol. 5, no. 3, pp. 363–367, 1966. View at: Publisher Site  Google Scholar
 J. E. LennardJones, “On the determination of molecular fields. II. from the equation of state of a gas,” Proceedings of the Royal Society A, vol. 106, no. 738, pp. 463–477, 1924. View at: Publisher Site  Google Scholar
 T. Kojima, A Study on measurement for speed of sound in R125, R143a, and the mixture and precise determination of thermodynamic properties base on intermolecular potential model [M.S. thesis], Keio University, Yokohama, Japan, 2001.
 K. Ichikura, Y. Kano, and H. Sato, “Importance of third virial coefficients for representing the gaseous phase based on measuring PVTproperties of 1,1,1Trifluoroethane (R143a),” International Journal of Thermophysics, vol. 27, pp. 23–38, 2006. View at: Publisher Site  Google Scholar
 B. E. Poling, J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and Liquids, McGraw Hill, New York, NY, USA, 5th edition, 2004.
 P. D. Neufeld, A. R. Janzen, and R. A. Aziz, “Empirical equations to calculate 16 of the transport collision integrals ${\mathrm{\Omega}}^{\left(l,s\right)}$* for the lennardjones (126) potential,” The Journal of Chemical Physics, vol. 57, no. 3, pp. 1100–1102, 1972. View at: Google Scholar
 R. Brokaw, “Predicting transport properties of dilute gases,” Industrial & Engineering Chemistry Process Design and Development, vol. 8, no. 2, pp. 240–253, 1969. View at: Publisher Site  Google Scholar
 H. J. M. Hanley and M. Klein, “Application of the m68 potential to simple gases,” The Journal of Physical Chemistry, vol. 76, no. 12, pp. 1743–1751, 1972. View at: Publisher Site  Google Scholar
 A. Wassiljewa, “Wärmeleitung in Gasgemischen,” Physikalische Zeitschrift, vol. 5, p. 737, 1904. View at: Google Scholar
 E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Physics of Fluids, vol. 1, no. 5, pp. 361–369, 1958. View at: Google Scholar
 J. H. Dymond, K. N. Marsh, R. C. Wilhoit, and K. C. Wong, Virial Coefficients of Pure Gases and Mixtures, vol. 4 of LandoltBörnstein: Numerical Data and Functional Relationships in Science and Technology, part 21A&B, Springer, Hidelberg, Germany, 2002.
 K. Stephan and K. Lucas, Viscosity of Dense Fluids, Plenum Press, New York, NY, USA, 1979.
 IMSL, IMSL STAT/LIBRARY: Regression, IMSL, Houston, Tex, USA, 1994.
 S.K. Oh, “An extension of the group contribution method for estimating thermodynamic and transport properties. Part III. Noble gases,” Korean Journal of Chemical Engineering, vol. 22, no. 6, pp. 949–959, 2005. View at: Publisher Site  Google Scholar
 C. Tsonopoulos, “Empirical correlation of second virial coefficients,” AIChE Journal, vol. 20, no. 2, pp. 263–272, 1974. View at: Google Scholar
 E. W. Lemmon, M. L. Huber, and M. O. McLinden, “NIST standard reference database 23,” Reference Fluid Thermodynamic and Transport Properties (REFPROP), version 9.0, National Institute of Standards and Technology, 2010. View at: Google Scholar
 K. Lucas, Phase Equilibria and Fluid Properties in the Chemical Industry, Dechema, Frankfurt, Germany, 1980.
 Simsci Database, Pro/II with Provision Software, http://iom.invensys.com/EN/Pages/SimSciEsscor_ProcessEngSuite_PROII.aspx.
 E. N. Fuller, P. D. Schettler, and J. C. Giddings, “new method for prediction of binary gasphase diffusion coefficients,” Industrial & Engineering Chemistry Research, vol. 58, no. 5, pp. 18–27, 1966. View at: Publisher Site  Google Scholar
 J. Kestin, K. Knierim, E. A. Mason, B. Najafi, S. T. Ro, and M. Waldman, “equilibrium and transport properties of the noble gases and their mixtures at low density,” Journal of Physical and Chemical Reference Data, vol. 13, no. 1, 75 pages, 1984. View at: Publisher Site  Google Scholar
 A. Arteconi, G. Di Nicola, G. Santori, and R. Stryjek, “Second virial coefficients for dimethyl ether,” Journal of Chemical & Engineering Data, vol. 54, no. 6, pp. 1840–1843, 2009. View at: Publisher Site  Google Scholar
 A. A. Richcardo and M. N. da Ponte, “Second virial coefficients of mixtures of Xenon and lower hydrocarbons. 1. Experimental apparatus and results for Xe + C_{2}H_{6},” The Journal of Physical Chemistry, vol. 100, no. 48, pp. 18839–18843, 1996. View at: Publisher Site  Google Scholar
 D. R. Lide, CRC Handbook of Chemistry and Physics, CRC Press, New York, NY, USA, 90th edition, 2010.
 J. Kestin and J. Yata, “Viscosity and diffusion coefficient of six binary mixtures,” The Journal of Chemical Physics, vol. 49, no. 11, pp. 4780–4791, 1968. View at: Google Scholar
 A. S. Kalelkar and J. Kestin, “Viscosity of HeAr and HeKr binary gaseous mixtures in the temperature range 25–720°C,” The Journal of Chemical Physics, vol. 52, no. 8, pp. 4248–4261, 1970. View at: Google Scholar
 J. Kestin, E. Paykoç, and J. V. Sengers, “On the density expansion for viscosity in gases,” Physica, vol. 54, no. 1, pp. 1–19, 1971. View at: Google Scholar
 J. Kestin, S. T. Ro, and Ber. Bunsenges, “The viscosity of nine binary and two ternary mixtures of gases at low density,” Berichte der Bunsengesellschaft für Physikalische Chemie, vol. 20, no. 1, pp. 20–24, 1974. View at: Publisher Site  Google Scholar
 J. Kestin, S. T. Ro, and W. A. Wakeham, “Viscosity of the binary gaseous mixture Heliumnitrogen,” The Journal of Chemical Physics, vol. 56, no. 8, pp. 4032–4036, 1972. View at: Google Scholar
 J. Kestin, S. T. Ro, and W. A. Wakeham, “Viscosity of the noble gases in the temperature range 25–700°C,” Journal of Chemical Physics, vol. 56, no. 8, 6 pages, 1972. View at: Publisher Site  Google Scholar
 J. Kestin, S. T. Ro, and W. A. Wakeham, “Viscosity of the binary gaseous mixtures He–Ne and Ne–N_{2} in the Temperature Range 25–700°C,” Journal of Chemical Physics, vol. 56, no. 12, 6 pages, 1972. View at: Publisher Site  Google Scholar
 J. Kestin, H. E. Kalifa, S. T. Ro, and W. A. Wakeham, “The viscosity and diffusion coefficients of eighteen binary gaseous systems,” Physica A, vol. 88, no. 2, pp. 242–260, 1977. View at: Publisher Site  Google Scholar
 J. Kestin, H. E. Khalifa, and W. A. Wakeham, “The viscosity and diffusion coefficients of the binary mixtures of Xenon with the other noble gases,” Physica A, vol. 90, no. 2, pp. 215–228, 1978. View at: Google Scholar
 J. Kestin and W. A. Wakeham, “The viscosity and diffusion coefficient of binary mixtures of nitrous oxide with He, Ne and CO,” Berichte der Bunsengesellschaft für Physikalische Chemie, vol. 87, no. 4, pp. 309–311, 1983. View at: Publisher Site  Google Scholar
 M. Trauntz and K. F. Kipphan, “Die Reibung, Wärmeleitung und diffusion in gasmischungen. IV. Die reibung binärer und ternärer edelgasgemische,” Annalen der Physik, vol. 394, no. 6, p. 743, 1929. View at: Google Scholar
 M. Trauntz and R. Zink, “Die Reibung, Wärmeleitung und diffusion in gasmischungen XII. Gasreibung bei höheren temperaturen,” Annalen der Physik, vol. 399, no. 4, p. 427, 1930. View at: Google Scholar
 M. Trauntz and H. Zimmermann, “Die Reibung, Wärmeleitung und diffusion von gasmischungen XXX. Die innere reibung bei tiefen temperaturen von wasserstoff, helium und neon und binären gemischen davon bis 90,0° abs. herab,” Annalen der Physik, vol. 414, no. 2, p. 189, 1935. View at: Google Scholar
 J. Kestin and W. Leidenfrost, “The viscosity of Helium,” Physica, vol. 25, no. 1–6, pp. 537–555, 1959. View at: Google Scholar
 K. Kestin and W. Leidenfrost, Thermal and Transport Properties of Gases and Liquids, McGrawHill, New York, NY, USA, 1959.
 E. Thornton, “Viscosity and thermal conductivity of binary gas mixtures: XenonKrypton, XenonArgon, XenonNeon and XenonHelium,” Proceedings of the Physical Society, vol. 76, no. 1, p. 104, 1960. View at: Publisher Site  Google Scholar
 E. Thornton, “Viscosity and thermal conductivity of binary gas mixtures: KryptonArgon, KryptonNeon, and KryptonHelium,” Proceedings of the Physical Society, vol. 77, no. 6, p. 1166, 1961. View at: Publisher Site  Google Scholar
 E. Thornton and W. A. D. Baker, “Viscosity and thermal conductivity of binary gas mixtures: ArgonNeon, ArgonHelium, and NeonHelium,” Proceedings of the Physical Society, vol. 80, no. 5, p. 1171, 1962. View at: Publisher Site  Google Scholar
 H. Iwasaki and J. Kestin, “The viscosity of ArgonHelium mixtures,” Physica, vol. 29, no. 12, pp. 1345–1372, 1963. View at: Publisher Site  Google Scholar
 A. B. Rakshit and C. S. Roy, “Viscosity and polarnonpolar interactions in mixtures of inert gases with ammonia,” Physica, vol. 78, no. 1, pp. 153–164, 1974. View at: Google Scholar
 A. O. Rietveld, A. Van Itterbeek, and G. J. Van Den Berg, “Measurements on the viscosity of mixtures of Helium and Argon,” Physica, vol. 19, no. 112, pp. 517–524, 1953. View at: Google Scholar
 A. O. Rietveld, A. Van Itterbeek, and C. A. Velds, “Viscosity of binary mixtures of hydrogen isotopes and mixtures of He and Ne,” Physica, vol. 25, no. 1–6, pp. 205–216, 1959. View at: Google Scholar
 A. E. Schuil, “A note on the viscosity of gases and molecular mean free path,” Philosophical Magazine Series 7, vol. 28, no. 191, p. 679, 1939. View at: Publisher Site  Google Scholar
 J. Kestin and A. Nagashima, “Viscosity of NeonHelium and NeonArgon mixtures at 20° and 30°C,” The Journal of Chemical Physics, vol. 40, no. 12, pp. 3648–3654, 1964. View at: Google Scholar
 J. Kestin, Y. Kobayashi, and R. T. Wood, “The viscosity of four binary, gaseous mixtures at 20° and 30°C,” Physica, vol. 32, no. 6, pp. 1065–1089, 1966. View at: Google Scholar
 H. Landolt and R. Börnstein, LandoltBörnstein Physikalischchemische Tabellen, Springer, Berlin, Germany, 1923.
 N. B. Vargaftik, Tables on the Thermophysical Properties of Liquids and Gases, Hemisphere, Washington, DC, USA, 2nd edition, 1975.
 K. Stephan and T. Heckenberger, Thermal Conductivity and Viscosity Data of Fluid Mixtures, vol. 10 of Chemistry Data Series, Dechema, Frankfurt, Germany, 1988.
 E. Bich, J. Millat, and E. Vogel, “The viscosity and thermal conductivity of pure monatomic gases from their normal boiling point up to 5000 K in the limit of zero density and at 0.101325 MPa,” Journal of Physical and Chemical Reference Data, vol. 19, no. 6, article 1289, 17 pages, 1990. View at: Publisher Site  Google Scholar
 W. A. Wakeham, A. Nagashima, and J. V. Sengers, Measurement of the Transport Properties of Fluids, IUPAC Chemical Data Series no. 37, Blackwell Scientific, London, UK, 1991.
 A. Bejan and A. D. Kraus, Heat Transfer Handbook, chapter 2, John Wiley & Sons, New York, NY, USA, 2003.
 G. C. Maitland and E. B. Smith, “Critical reassessment of viscosities of 11 common gases,” Journal of Chemical & Engineering Data, vol. 17, no. 2, pp. 150–156, 1972. View at: Publisher Site  Google Scholar
 G. F. C. Rogers and Y. R. Mayhew, Thermodynamic and Transport Properties of Fluids, Basil Blackwell, Oxford, UK, 3rd edition, 1981.
 IAEA, Thermophysical Properties of Materials for Nuuclear Engineering: A Tutorial and Collection of Data, IAEA, Vienna, 2008.
 J. Kestin, W. Wakeham, and K. Watanabe, “Viscosity, thermal conductivity, and diffusion coefficient of ArNe and ArKr gaseous mixtures in the temperature range 25–700°C,” The Journal of Chemical Physics, vol. 53, no. 10, pp. 3773–3780, 1970. View at: Google Scholar
 J. Kestin, S. T. Ro, and W. A. Wakeham, “Viscosity of the binary gaseous mixture Neon–Krypton,” Journal of Chemical Physics, vol. 56, no. 8, article 4086, 6 pages, 1972. View at: Publisher Site  Google Scholar
 A. O. Rankine, “On the variation with temperature of the viscosities of the gases of the Argon group,” Zeitschrift für Physik, vol. 11, p. 497, pp. 745–762, 1910. View at: Google Scholar
 A. G. Clarke and E. B. Smith, “Lowtemperature viscosities of argon, krypton, and xenon,” The Journal of Chemical Physics, vol. 48, no. 9, pp. 3988–3991, 1968. View at: Google Scholar
 R. A. Dawe and E. B. Smith, “Viscosities of the inert gases at high temperatures,” The Journal of Chemical Physics, vol. 52, no. 2, pp. 693–703, 1970. View at: Google Scholar
 R. S. Edwards, “The effect of temperature on the viscosity of Neon,” Proceedings of the Royal Society A, vol. 119, no. 783, pp. 578–590, 1928. View at: Publisher Site  Google Scholar
 A. van Itterbeek and O. van Paemel, “Viscosity of liquid deuterium,” Physica, vol. 7, no. 3, p. 208, 1940. View at: Google Scholar
 R. Wobser and F. Müller, “Die innere reibung von gasen und dämpfen und ihre messung im Höpplerviskosimeter,” KolloidBeihefte, vol. 52, no. 67, pp. 165–276, 1941. View at: Publisher Site  Google Scholar
 H. Johnston and E. R. Grilly, “Viscosities of carbon monoxide, Helium, Neon, and Argon between 80° and 300°K. coefficients of viscosity,” The Journal of Physical Chemistry, vol. 46, no. 8, pp. 948–963, 1942. View at: Publisher Site  Google Scholar
 J. Kestin and W. Leidenfrost, “An absolute determination of the viscosity of eleven gases over a range of pressures,” Physica, vol. 25, no. 712, pp. 1033–1062, 1959. View at: Google Scholar
 G. P. Flynn, R. V. Hanks, N. A. Lemaire, and J. F. Ross, “Viscosity of Nitrogen, Helium, Neon, and Argon from −78.5° to 100°C below 200 Atmospheres,” Journal of Chemical Physics, vol. 38, no. 1, article 154, 9 pages, 1963. View at: Publisher Site  Google Scholar
 J. Kestin and J. H. Whitelaw, “A relative determination of the viscosity of several gases by the oscillating disk method,” Physica, vol. 29, no. 4, pp. 335–356, 1963. View at: Publisher Site  Google Scholar
 N. J. Trappeniers, A. Botzen, H. R. Van Den Berg, and J. Van Oosten, “The viscosity of Neon between 25°C and 75°C at pressures up to 1800 atmospheres. Corresponding states for the viscosity of the noble gases up to high densities,” Physica, vol. 30, no. 5, pp. 985–996, 1964. View at: Google Scholar
 A. O. Rietveld and A. van Itterbeek, “Measurements on the viscosity of NeA mixtures between 300 and 70°K,” Physica, vol. 22, no. 612, pp. 785–790, 1956. View at: Google Scholar
 M. Trautz and H. E. Binkele, “Die Reibung, Wärmeleitung und diffusion in gasmischungen. VIII. die reibung des H_{2}, He, Ne, Ar und ihrer binären gemische,” Annalen der Physik, vol. 397, no. 5, pp. 561–580, 1930. View at: Publisher Site  Google Scholar
 B. A. Younglove and H. J. M. Hanley, “The viscosity and thermal conductivity coefficients of gaseous and liquid Argon,” Journal of Physical and Chemical Reference Data, vol. 5, no. 4, article 1323, 15 pages, 1986. View at: Publisher Site  Google Scholar
 I. A. Barr, G. P. Matthews, E. B. Smith, and A. R. Tindell, “Intermolecular forces and the gaseous viscosities of ArgonXenon mixtures,” Journal of Physical Chemistry, vol. 85, no. 22, pp. 3342–3347, 1981. View at: Google Scholar
 J. M. Hellemans, J. Kestin, and S. T. Ro, “Viscosity of the binary gaseous mixtures of nitrogen with Argon and Krypton,” The Journal of Chemical Physics, vol. 57, no. 9, pp. 4038–4042, 1972. View at: Google Scholar
 J. Kestin and S. T. Ro, “The viscosity and diffusion coefficients of binary mixtures of nitrous Oxide with Ar, N_{2}, and CO_{2},” Berichte der Bunsengesellschaft für Physikalische Chemie, vol. 86, no. 10, pp. 948–950, 1982. View at: Google Scholar
 J. Kestin and W. A. Wakaham, “The viscosity of three polar gases,” Berichte der Bunsengesellschaft für Physikalische Chemie, vol. 83, no. 6, pp. 573–576, 1979. View at: Publisher Site  Google Scholar
 A. van Itterbeek and O. van Paemel, “Measurements on the viscosity of Argon gas at room temperature and between 9° and 55°K,” Physica, vol. 5, no. 10, pp. 1009–1012, 1938. View at: Google Scholar
 P. Gray and A. O. S. Maczek, “The thermal conductivities, viscositites, and diffusion coefficients of mixtures, containing two polar gases,” in Proceedings of the 4th Symposium on Thermophysical Properties, pp. 380–391, ASME, New York, NY, USA, 1968. View at: Google Scholar
 C. F. Bonilla, S. J. Wang, and H. Weiner, “The viscosity of steam, heavywater vapor, and Argon at atmospheric pressure up to high temperatures,” Transactions of the American Society of Mechanical Engineers, vol. 78, pp. 1285–1289. View at: Google Scholar
 H. Iwasaki, J. Kestin, and A. Nagashima, “Viscosity of Argonammonia mixtures,” The Journal of Chemical Physics, vol. 40, no. 10, pp. 2988–2995, 1964. View at: Google Scholar
 J. Hilsenrath, Tables of Thermal Properties of Gases, vol. 564 of National Bureau of Standards Circular, US Government Printing Office, Washington, DC, USA, 1955.
 J. M. Hellemans, J. Kestin, and S. T. Ro, “The viscosity of oxygen and of some of its mixtures with other gases,” Physica, vol. 65, no. 2, pp. 362–375, 1973. View at: Google Scholar
 E. F. May, R. F. Berg, and M. R. Moldover, “Reference viscosities of H_{2}, CH_{4}, Ar, and Xe at low densities,” International Journal of Thermophysics, vol. 28, no. 4, pp. 1085–1110, 2007. View at: Publisher Site  Google Scholar
 V. Vasilesco, “Recherches expérimentales sur la viscosité des gaz aux températures élevées,” Annales de Physique, vol. 20, pp. 292–334, 1945. View at: Google Scholar
 H. J. M. Hanley, “the viscosity and thermal conductivity coefficients of dilute Argon, Krypton, and Xenon,” Journal of Physical and Chemical Reference Data, vol. 3, no. 3, article 619, 24 pages, 1973. View at: Publisher Site  Google Scholar
 H. J. M. Hanley, R. D. McCarty, and W. M. Haynes J, “The viscosity and thermal conductivity coefficients for dense gaseous and liquid Argon, Krypton, Xenon, Nitrogen, and Oxygen,” Journal of Physical and Chemical Reference Data, vol. 3, no. 4, article 979, 39 pages, 1974. View at: Publisher Site  Google Scholar
 X. Wang, J. Wu, and Z. Liu, “Viscosity of gaseous HFC245fa,” Journal of Chemical & Engineering Data, vol. 55, no. 1, pp. 496–499, 2010. View at: Publisher Site  Google Scholar
 R. Kiyama and T. Makita, “The viscosity of carbon dioxide, ammonia, acetylene, Argon and oxygen under high pressures,” Review of Physical Chemistry of Japan, vol. 22, pp. 49–58, 1952. View at: Google Scholar
 T. Makita, “The viscosity at pressures to 80o kg/cm^{2} up of Argon, nitrogen and air,” Review of Physical Chemistry of Japan, vol. 27, no. 1, pp. 16–21, 1957. View at: Google Scholar
 M. Hongo, “Viscosity of Argon and of Argonammonia mixtures under pressures,” The Review of Physical Chemistry of Japan, vol. 48, no. 2, pp. 63–71, 1979. View at: Google Scholar
 J. Kestin, H. E. Khalifa, and W. A. Wakeham, “The viscosity of gaseous mixtures containing Krypton,” The Journal of Chemical Physics, vol. 67, no. 9, pp. 4254–4259, 1977. View at: Google Scholar
 M. Trautz, “Die reibung, Wärmeleitung und diffusion in Gasmischungen XXI. Absoluter ηWirkungsquerschnitt, molekulartheoretische bedeutung der kritischen temperatur und berechung kritischer drucke aus η,” Annalen Der Physik, vol. 407, no. 2, p. 198, 1932. View at: Google Scholar
 J. M. Gandhi and S. C. Saxena, “Thermal conductivity of binary and ternary mixtures of Helium, Neon and Xenon,” Molecular Physics, vol. 12, no. 1, p. 57, 1967. View at: Publisher Site  Google Scholar
 S. C. Saxena, M. P. Saksena, R. S. Gambhir, and J. M. Gandhi, “The thermal conductivity of nonpolar polyatomic gas mixtures,” Physica, vol. 31, no. 3, pp. 333–341, 1965. View at: Google Scholar
 H. Ziebland, “commission on physicochemical measurements and standards,” Pure & Applied Chemistry, vol. 53, no. 10, pp. 1863–1877, 1981. View at: Publisher Site  Google Scholar
 R. W. Powell, C. Y. Ho, and P. E. Liley, “Thermal conductivity of seleted materials,” National Standard Reference Data Series NBS 8, US Department of Commerce, 1966. View at: Google Scholar
 S. C. Saxena, “Transport properties of gases and gaseous mixtures at high temperatures,” High Temperature Science, vol. 3, pp. 168–188, 1971. View at: Google Scholar
 S. C. Saxena, S. Mathur, and G. P. Gupta, “The thermal conductivity data of some binary gas mixtures involving nonpolar polyatomic gases,” Defence Science Journal, vol. 16, supplement, pp. 99–112, 1966. View at: Google Scholar
 N. B. Vargaftik, L. P. Filippon, A. A. Tarzimanov, and E. E. Totskii, Handbook of Thermal Conductivity of Liquids and Gaseous, CRC Press, Boca Raton, Fla, USA, 1994.
 W. Van Dael and H. Cauwenbergh, “Measurements of the thermal conductivity of gases. II. Data for binary mixtures of He, Ne and Ar,” Physica, vol. 40, no. 2, pp. 173–181, 1968. View at: Google Scholar
 W. G. Kannuluik and E. H. Carman, “The thermal conductivity of rare gases,” Proceedings of the Physical Society B, vol. 65, no. 9, p. 701, 1952. View at: Publisher Site  Google Scholar
 R. S. Gambhir and S. C. Saxena, “Thermal conductivity of binary and ternary mixtures of Krypton, Argon and Helium,” Molecular Physics, vol. 11, no. 3, pp. 233–241, 1966. View at: Publisher Site  Google Scholar
 E. A. Mason and H. Von Ubisch, “Thermal conductivities of rare gas mixtures,” Physics of Fluids, vol. 3, no. 3, pp. 355–361, 1960. View at: Google Scholar
 S. C. Saxena, “Thermal conductivity of binary and ternary mixtures of helium, argon and xenon,” Indian Journal of Physics, vol. 31, pp. 597–606, 1957. View at: Google Scholar
 H. von Ubisch, “The thermal conductivities of mixtures of rare gases at 29° and 520°,” Arkiv för Fysik, vol. 16, pp. 93–100, 1959. View at: Google Scholar
 S. Mathur, P. K. Tondon, and S. C. Saxena, “Thermal conductivity of binary, ternary and quaternary mixtures of rare gases,” Molecular Physics, vol. 12, no. 6, pp. 569–579, 1967. View at: Publisher Site  Google Scholar
 C. Y. Ho, R. W. Powell, and P. E. Liley J, “Thermal conductivity of the elements,” Journal of Physical and Chemical Reference Data, vol. 1, no. 2, article 279, 143 pages, 1972. View at: Publisher Site  Google Scholar
 B. N. Srivastava and S. C. Saxena, “Thermal conductivity of binary and ternary rare gas mixtures,” Proceedings of the Physical Society B, vol. 70, no. 4, p. 369, 1957. View at: Publisher Site  Google Scholar
 K. Schäfer, “Transport Phenomena in the temperature range up to 1100 degrees,” Dechema Monograph, vol. 32, pp. 61–73, 1959. View at: Google Scholar
 K. C. Hansen, L. H. Tsao, T. M. Aminabhavi, and C. L. Yaws, “Gaseous thermal conductivity of hydrogen chloride, hydrogen bromide, boron trichloride, and boron trifluoride in the temperature range from 55 to 380°C,” Journal of Chemical and Engineering Data, vol. 40, no. 1, pp. 18–20, 1995. View at: Google Scholar
 R. S. Gambhir and S. C. Saxena, “Thermal conductivity of the gas mixtures: ArD_{2}, KrD_{2} and ArKrD_{2},” Physica, vol. 32, no. 1112, pp. 2037–2043, 1966. View at: Google Scholar
 L. Sun and J. E. S. Venart, “Thermal conductivity, thermal diffusivity, and heat capacity of gaseous Argon and nitrogen,” International Journal of Thermophysics, vol. 26, no. 2, pp. 325–372, 2005. View at: Publisher Site  Google Scholar
 L. Sun, J. E. S. Venart, and R. C. Prasad, “The thermal conductivity, thermal diffusivity, and heat capacity of gaseous Argon,” International Journal of Thermophysics, vol. 23, pp. 357–389, 2002. View at: Publisher Site  Google Scholar
 C. J. Zwakhals and K. W. Reus, “Corrections to the Smoluchowski equation in the presence of hydrodynamic interactions,” Physica C, vol. 100, no. 2, pp. 251–265, 1980. View at: Publisher Site  Google Scholar
 W. Groth and E. Sußner, “Selbstdiffusionsmessungen III. Der selbstdiffusionskoeffizient des neon (selfdiffusion measurments III. The coefficient of self diffusion of neon),” Zeitschrift für Physikalische Chemie, vol. 193, pp. 296–300, 1944. View at: Google Scholar
 W. Groth and P. Harteck, “Die selbstdiffusion des Xenons und des Kryptons,” Zeitschrift für Elektrochemie, vol. 47, no. 2, pp. 167–172, 1941. View at: Publisher Site  Google Scholar
 M. P. Saksena and S. C. Saxena, “Viscosity of multicomponent gas mixtures,” Physica A, vol. 31, p. 18, 1965. View at: Google Scholar
 H. Iwasaki and J. Kestin, “The viscosity of ArgonHelium mixtures,” Physica, vol. 29, no. 12, pp. 1345–1372, 1963. View at: Publisher Site  Google Scholar
 D. J. Richardson, G. Mason, B. A. Buffham, K. Hellgardt, I. W. Cumming, and P. A. Russell, “Viscosity of binary mixtures of carbon monoxide and Helium,” Journal of Chemical and Engineering Data, vol. 53, no. 1, pp. 303–306, 2008. View at: Publisher Site  Google Scholar
 S. C. Saxena and T. K. S. Narayanan, “Multicomponent viscosities of gaseous mixtures at high temperatures,” Industrial & Engineering Chemistry Fundamentals, vol. 1, no. 3, pp. 191–195, 1962. View at: Publisher Site  Google Scholar
 J. W. Buddenberg and C. R. Wilke, “Calculation of gas mixture viscosities,” Industrial & Engineering Chemistry Research, vol. 41, no. 7, pp. 1345–1347, 1949. View at: Publisher Site  Google Scholar
 J. Wachsmuth, “Über die wärmeleitung von gemischen zwischen argon und helium,” Physikalische Zeitschrift, vol. 7, p. 235, 1908. View at: Google Scholar
 E. A. Mason and T. R. Marrero, “Gaseous diffusion coefficients,” Journal of Physical and Chemical Reference Data, vol. 1, no. 1, 116 pages, 1972. View at: Publisher Site  Google Scholar
 R. J. J. Van Heijningen, J. P. Harpe, and J. J. M. Beenakker, “Determination of the diffusion coefficients of binary mixtures of the noble gases as a function of temperature and concentration,” Physica, vol. 38, no. 1, pp. 1–34, 1968. View at: Google Scholar
 P. S. Arora, H. L. Robjohns, and P. J. Dunlop, “Use of accurate diffusion and second virial coefficients to determine (m, 6, 8) potential parameters for nine binary noble gas systems,” Physica A, vol. 95, no. 3, pp. 561–571, 1979. View at: Google Scholar
 M. Trautz and W. Muller, “Die reibung, wärmeleitung und diffusion in gasmischungen III. Die korrektion der bisher mit der verdampfungsmethode gemessenen diffusionskonstanten,” Annalen der Physik, vol. 414, no. 4, pp. 333–352, 1935. View at: Google Scholar
 J. N. Holsen and M. R. Strunk, “Binary diffusion coefficients in nonpolar gases,” Industrial and Engineering Chemistry Fundamentals, vol. 3, no. 2, pp. 143–146, 1964. View at: Publisher Site  Google Scholar
 S. L. Seager, L. R. Geertson, and J. C. Giddings, “Temperature dependence of gas and vapor diffusion coefficients,” Journal of Chemical & Engineering Data, vol. 8, no. 2, pp. 168–169, 1963. View at: Publisher Site  Google Scholar
 A. T. Hu and R. Kobayashi, “Measurements of gaseous diffusion coefficients for dilute and moderately dense gases by perturbation chromatography,” Journal of Chemical & Engineering Data, vol. 15, no. 2, pp. 326–335, 1970. View at: Publisher Site  Google Scholar
 A. P. Malinauskas, “Gaseous diffusion. The systems He–Ar, Ar–Xe, and He–Xe,” Journal of Chemical Physics, vol. 42, no. 1, article 157, 4 pages, 1965. View at: Publisher Site  Google Scholar
 R. A. Strehlow, “The temperature dependence of the mutual diffusion coefficient for four gaseous systems,” Journal of Chemical & Engineering Data, vol. 21, no. 12, article 2101, 6 pages, 1953. View at: Publisher Site  Google Scholar
 R. E. Walker and A. A. Westenberg , “Molecular diffusion studies in gases at high temperature. III. results and interpretation of the He—a system,” Journal of Chemical Physics, vol. 31, no. 519, 4 pages, 1959. View at: Publisher Site  Google Scholar
 J. C. Giddings and S. L. Seager, “Method for the rapid determination of diffusion coefficients. theory and application,” Industrial and Engineering Chemistry Fundamentals, vol. 1, no. 4, pp. 277–283, 1962. View at: Publisher Site  Google Scholar
 S. C. Sexena and E. A. Mason, “Thermal diffusion and the approach to the steady state in gases: II,” Molecular Physics, vol. 2, no. 4, p. 379, 1959. View at: Publisher Site  Google Scholar
 E. N. Fuller, P. D. Schettler, and J. C. Giddings, “New method for prediction of binary gasphase diffusion coefficients,” Industrial & Engineering Chemistry, vol. 58, no. 5, pp. 18–27, 1966. View at: Google Scholar
 M. Keil, L. Danielson, and P. J. Dunlop, “On obtaining interatomic potentials from multiproperty fits to experimental data,” Journal of Chemical Physics, vol. 84, no. 14, article 296, 14 pages, 1991. View at: Publisher Site  Google Scholar
 A. P. Malinauskas, “Gaseous Diffusion. The Systems He–Ar, Ar–Xe, and He–Xe,” Journal of Chemical Physics, vol. 42, no. 1, article 156, 4 pages, 1964. View at: Publisher Site  Google Scholar
 K. Schafer and K. Schuhman Z, “Zwischenmolekulare kräfte und temperaturabhängigkeit von diffusion und selbstdiffusion in Edelgasen,” Zeitschrift für Elektrochemie, vol. 61, no. 2, pp. 246–252, 1957. View at: Publisher Site  Google Scholar
 B. N. Srivastava and K. P. Srivastava, “Mutual diffusion of pairs of rare gases at different temperatures,” Journal of Chemical Physics, vol. 30, no. 984, article 984, 7 pages, 1959. View at: Publisher Site  Google Scholar
 W. Sutherland, “The viscosity of gases and molecular force,” Philosophical Magazine, vol. 36, pp. 507–631, 1893. View at: Publisher Site  Google Scholar
 W. Sutherland, “The attraction of unlike molecules.I. The diffusion of gases,” Philosophical Magazine, vol. 38, no. 230, pp. 1–19, 1894. View at: Publisher Site  Google Scholar
 V. P. S. Main and S. C. Saxena, “measurement of the concentration diffusion coefficient for NeAr, NeXe, NeH_{2}, XeH_{2}, H_{2}N_{2} and H_{2}O_{2} gas systems,” Applied Scientific Research, vol. 23, pp. 121–133, 1971. View at: Publisher Site  Google Scholar
 A. E. Humphreys and E. A. Mason, “Intermolecular forces: thermal diffusion and diffusion in Ar–Kr,” Physics of Fluids, vol. 13, no. 1, article 65, 6 pages, 1970. View at: Publisher Site  Google Scholar
 P. J. Dunlop and C. M. Bignell, “Diffusion and thermal diffusion in binary mixtures of methane with noble gases and of Argon with Krypton,” Physica A, vol. 145, no. 3, pp. 584–596, 1987. View at: Google Scholar
 L. Andrussow and T. F. Schatzki, “Diffusion coefficients of the systems Xe–Xe and A–Xe,” Journal of Chemical Physics, vol. 27, no. 5, article 1049, 6 pages, 1957. View at: Publisher Site  Google Scholar
 E. A. Mason and T. R. Marrero, “The diffusion of atoms and molecules,” Advances in Atomic and Molecular Physics, vol. 6, pp. 155–232, 1970. View at: Publisher Site  Google Scholar
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