A molecular simulation study of shear and bulk viscosity and thermal conductivity of simple real fluids
aa r X i v : . [ phy s i c s . c h e m - ph ] J un A molecular simulation study of shear and bulkviscosity and thermal conductivity of simple real fluids
G.A. Fern´andez, J. Vrabec ∗ , and H. HasseInstitute of Thermodynamics and Thermal Process Engineering,University of Stuttgart, D-70550 Stuttgart, GermanyTotal number of pages: 31Number of tables: 2Number of figures: 7 ∗ To whom correspondence should be addressed, tel.: +49-711/685-6107, fax: +49-711/685-7657, email: [email protected] BSTRACT
Shear and bulk viscosity and thermal conductivity for argon, krypton, xenon,and methane and the binary mixtures argon+krypton and argon+methanewere determined by equilibrium molecular dynamics with the Green-Kubomethod. The fluids were modeled by spherical Lennard-Jones pair-potentialswith parameters adjusted to experimental vapor liquid-equilibria data alone.Good agreement between the predictions from simulation and experimentaldata is found for shear viscosity and thermal conductivity of the pure fluids andbinary mixtures. The simulation results for the bulk viscosity show only pooragreement with experimental data for most fluids, despite good agreementwith other simulations data from the literature. This indicates that presentlyavailable experimental data for the bulk viscosity, a property which is difficultto measure, are inaccurate.
KEYWORDS:
Viscosity; Thermal conductivity; Green-Kubo; Lennard-Jones;Molecular Dynamics; Molecular Simulation.2 . Introduction
Transport properties play an important role in many technical and naturalprocesses. With the rapid increase of available computing power, molecularsimulation in combination with molecular modeling is becoming an interestingoption for describing transport properties in regions where experimental dataare not available or difficult to obtain. The calculation of transport coefficientsby molecular simulation can be achieved by non-equilibrium molecular dynam-ics (NEMD) or equilibrium molecular dynamics (EMD). In NEMD, transportcoefficients are calculated as the ratio of a flux to an appropriate driving force,extrapolating to the limit of zero driving force [1]. In EMD transport coeffi-cients are often calculated by the Green-Kubo formalism [2,3]. The choicebetween EMD and NEMD is largely a matter of taste and inclination, see e.g.[4,5,6]. There are numerous contributions in the literature in which both meth-ods were applied for the calculation of shear viscosity [4,7,8,10,11,12], bulkviscosity [13,14,15], and thermal conductivity [7,10,11,16,17] with comparableperformance. To our knowledge the most comprehensive study on transportcoefficients of the spherical Lennard-Jones fluid is reported in [18,19]. Despiteof the large number of publications on simulation of transport properties withthe spherical Lennard-Jones potential, not much effort seems to have beenspent on a comparison of simulation results with experimental data of realfluids. Exceptions are the works of Michels et al. [20] and Heyes et al. [10,11].Michels et al. [20] compared the self-diffusion coefficient to the Chapman-Enskog theory and experimental data for krypton and methane at high den-sities, but thermodynamic properties were not considered. Heyes et al. [10,11]simulated both transport and thermodynamic properties of argon+krypton,argon+methane, and methane+nitrogen, but properties of pure fluids were3ot considered. In other cases [21,22] more complex molecules like ethylene,carbon dioxide, phenol, alkanes, or carbon tetrachloride were modeled by thespherical Lennard-Jones potential, which surely is an oversimplification. Simu-lation data on transport properties were compared there to experimental data,but not the thermodynamic properties.The interest here lies in the quantitative evaluation of the performance ofLennard-Jones models [23], which have been optimized for the accurate pre-diction of thermodynamic properties, in the description of transport proper-ties. In this work EMD is used to carry out a comprehensive comparison, ofshear and bulk viscosity and thermal conductivity of pure fluids and binarymixtures of noble gases and methane. The molecular models are taken from[23]. These models were adjusted only to vapor-liquid equilibria and yield ac-curate descriptions of static thermodynamic properties over a wide range oftemperatures and densities. Furthermore, they were recently applied for theprediction of diffusion coefficients of pure and binary mixtures of simple fluidsover a wide range of temperatures and densities with good results [24].4 . Theoretical background
Transport coefficients are associated to irreversible processes, however, it ispossible to describe irreversible processes in terms of reversible microscopicfluctuations, through the fluctuation dissipation theory [25]. In that theory,it is shown that transport coefficients can be calculated as integrals of time-correlation functions of appropriate quantities [2,3]. There are different meth-ods to relate transport coefficients to time-correlation functions; a good reviewcan be found in [26].
The shear viscosity η s , as defined in Newton’s ”law” of viscosity, describes theresistance of a fluid to shear forces. It refers to the resistance of an infinitesimalvolume element to shear at constant volume [27]. The shear viscosity can alsobe related to momentum transport under the influence of velocity gradients.From a microscopic point of view, the shear viscosity can be calculated byintegration of the time-autocorrelation function of the off diagonal elementsof the stress tensor J xyp [28,29] η s = 1 V k B T Z ∞ d t D J xyp ( t ) · J xyp (0) E , (1)where V is the volume, k B is the Boltzmann constant, T the temperature, and < ... > denotes the ensemble average. The statistics of the ensemble averagein Eq. (1) can be improved using all three independent off diagonal elementsof the stress tensor J xyp , J xzp and J yzp . For a pure fluid, the component J xyp ofthe microscopic stress tensor J p is given by5 xyp = N X i =1 m i v xi v yi − N X i =1 N X j>i r xij ∂u ( r ij ) ∂r yij . (2)Here i and j are the indices of the particles and the upper indices x and y denote the vector components of the particle velocities v i . Eqs. (1) and (2)can be applied directly to mixtures.On the other hand, the bulk viscosity η b refers to the resistance to dilatationof an infinitesimal volume element at constant shape [27]. The bulk viscosityin polyatomic molecules, is related to a characteristic time required for thetransfer of energy from the translational to the internal degrees of freedom[30]. Moreover, the bulk viscosity plays an important role to describe ultrasonicwave absorption and dispersion [31]. From a microscopic point of view, thebulk viscosity can be calculated by integration of the time-autocorrelationfunction of the diagonal elements of the stress tensor and an additional termthat involves the product of pressure p and volume V that does not occurin the shear viscosity, cf. Eq.(1). In the N V E ensemble the bulk viscosity isgiven by [28,29] η b = 1 V k B T Z ∞ d t D ( J xxp ( t ) − pV ( t )) · ( J xxp (0) − pV (0)) E . (3)The component J xxp of the microscopic stress tensor J p is given by J xxp = N X i =1 m i v xi v xi − N X i =1 N X j>i r xij ∂u ( r ij ) ∂r xij . (4)The statistics of the ensemble average in Eq. (4) can be improved using allthree independent diagonal elements of the stress tensor J xxp , J yyp , J zzp , andtheir permutations. In the case of mixtures Eqs. (3) and (4) can be directly6pplied. This equation is used in many simulation studies on the bulk viscositye.g. [10,11,13,15]. The thermal conductivity λ , as defined in Fourier’s ”law” of heat conduction,characterizes the capability of a substance for molecular transport of energydriven by temperature gradients. It can be calculated by integration of thetime-autocorrelation function of the elements of the microscopic heat flow J xq ,and is given by [28,29] λ = 1 V k B T Z ∞ d t D J xq ( t ) · J xq (0) E . (5)Here, the heat flow J q for a pure fluid is given by J q = 12 N X i =1 m i v i v i − N X i =1 N X j>i h r ij : ∂u ( r ij ) ∂ r ij − I · u ( r ij ) i · v i , (6)where v i is the velocity vector of particle i and r ij is the distance vectorbetween particles i and j . The term in squared parenthesis denotes the dif-ference between a dyadic product and the unitary tensor I multiplied by theintramolecular potential energy u ( r ij ). This description of the heat flow is notsufficient for binary and multi-component mixtures. In mixtures both diffusionand energy transport occur coupled [32], so that energy can be transported ona molecular level by diffusion or by heat transport. In a binary mixture withthe components α and β the heat flow is given by [16,28]7 q = 12 β X k = α N k X i =1 m ki ( v ki ) v ki − β X k = α β X l = α N k X i =1 N l X j>i h r klij : ∂u ( r klij ) ∂ r klij − I · u ( r klij ) i · v ki − β X k = α h k N k X i =1 v ki , (7)where h k denotes the partial molar enthalpy of component k . The computationof the heat flow in a binary mixture can, in principle, be accomplished in onesimulation, however, here two separate simulations were preferred. One N pT simulation was performed for the computation of the partial molar enthalpies,corresponding to the enthalpic part of the energy flow, and another
N V E simulation for the calculation of the autocorrelation function of the heat flow.
In this work, noble gases and methane are considered. These molecules ex-hibit rather simple intermolecular interaction so that the description of themolecular interactions by the Lennard-Jones 12-6 (LJ) potential is sufficientand physically meaningful for many technically relevant applications [33]. TheLJ potential u is defined by u ( r ij ) = 4 ǫ σr ij ! − σr ij ! , (8)where σ is the LJ size parameter, ǫ the LJ energy parameter and r ij the in-termolecular distance between particles i and j . The parameters σ and ǫ aretaken from [23] and given in Table 1. They were adjusted to experimentalpure substance vapor-liquid equilibrium data alone. For modeling mixtures,parameters for the unlike interactions are needed. Following previous work ofour group [24,34,35], they are given by a modified Lorentz-Berthelot combi-nation rule with 8 = ( σ + σ )2 , (9)and ǫ = ξ · √ ǫ ǫ , (10)where ξ is an adjustable binary interaction parameter. This parameter allowsan accurate description of the binary mixture data and was determined inprevious work by an adjustment to one experimental bubble point [34,35]. Thebinary interaction parameters used in the present work are listed in Table 2. The molecular simulations were performed in a cubic box of volume V con-taining N =500 or N =864 particles modeled by the LJ potential. The cut-offradius was set to r c = 5 σ , however, for very high densities where V is small, r c was set to half of the box length, standard techniques for periodic boundaryconditions and long-range corrections were used [36]. The simulations werestarted with the particles in a face-centered-cubic lattice with randomly as-signed velocities, the total momentum of the system was set to zero and New-ton’s equations of motion were solved with a Gear predictor-corrector of fifthorder [37]. The time step for this algorithm was set to ∆ t · q ǫ /m /σ = 0 . N V E ensemble, using equa-tions (1), (3), (5) and (7). The relative fluctuations in the total energy inthe
N V E ensemble were less than 10 − for the longest run. The simulationswere initiated in a N V T ensemble until equilibrium at the desired density andtemperature was reached. Between 100 000 and 200 000 time steps were usedfor the equilibration depending on the state point. Once the equilibrium isreached, the thermostat was turned off and then the
N V E ensemble invokedto calculate the transport coefficients by averaging the appropriate autocorre-9ation function. The length of the production period depended on density andtemperature of the state point. At least 3 000 independent autocorrelationfunctions were used in the calculation of each coefficient of viscosity and 4 000in the calculation of each coefficient of thermal conductivity. In theory as Eqs.(1), (3) and 5 show, the value of the transport coefficient are determined byan infinite time integral. In fact, however, the integral is evaluated based onthe length of the simulation. Therefore, the integration must be stopped atsome finite time, ensuring that the contribution of the long-time tail [38] issmall. Figure 1 shows the behavior of the different autocorrelation functionsand their integrals given by Eqs. (1), (3) and (5) for the most dense statepoints of argon for each transport property. As can be seen, all autocorrela-tion functions decay after 2 ps to less than 1 % of their normalized value.Later they oscillate around zero. To consider the effect of the long time tail,the calculation of the autocorrelations functions was extended to 5.4 ps forthermal conductivity and shear viscosity and to 6.5 ps for bulk viscosity. Thiswas done because this autocorrelation function exhibits the largest fluctuationaround zero attributable to long time correlation. The statistical uncertaintyof the transport coefficients and thermodynamic properties were estimatedusing the Fincham’s method [39]. For the calculation of the thermal conduc-tivity of mixtures it is necessary to include the partial molar enthalpies. Forthat purpose, Widom’s test particle insertion [41] was taken using 2 000 testparticles after each time step, 100 000 time steps for reaching equilibrium and300 000 for production. Our codes to calculate shear and bulk viscosity andthermal conductivity were successfully tested with the simulation results ofShoen et al. for viscosity [12], Heyes [14] for bulk viscosity and Vogelsang etal. [16] for thermal conductivity. 10 . Results and Discussion
In this section the prediction of shear and bulk viscosity and thermal conduc-tivity are compared pointwise with experimental data. For the shear viscositythe correlation of Rowley et al. [8,9], which is based on molecular simulationresults, was also used.Figure 2 shows the results for the shear viscosity of argon, krypton, xenonand methane in comparison with experimental data. The data are reported atdifferent temperatures and were taken from Vargaftik [42] for the noble gasesand from Evers et al . [43] for methane. Overall, very good agreement betweensimulation and experimental data is found. The lowest relative deviations arefound for argon and krypton with a few percent at lower densities. Also theresults of shear viscosity of xenon and methane show very good agreement atlow density, however, as the density increases, the deviations from the exper-imental data reach up to about 15% for xenon and about 20% for methane.It can be observed that the simulations for krypton, xenon and methane tendto underestimate the experimental viscosities as the density increases. Thisunderestimation is larger in the results given by Rowley’s correlation for theshear viscosity.Figure 3 shows the results for the shear viscosity of the binary mixtures ar-gon+krypton and argon+methane for two temperatures, the experimentaldata were taken from Mikhailenko et al . [44,45]. Good agreement between sim-ulation and experimental data is found. For the mixture argon+krypton thetypical deviations are about 10% and the highest deviations occur for krypton-rich state points. The predictions for the mixture argon+methane show a bet-ter agreement with the experimental data than those for argon+krypton. Typ-11cal deviations of the mixture argon+methane are about 10% at 100 K and 6%at 120 K, simulations performed at one intermediate temperature ( T =110 K)confirm that better agreement between simulation and experiments is foundas the temperature increases. The comparison of the present simulations withprevious simulations of Heyes [10,11], shows a comparable agreement for themixture argon+krypton, however, in the mixture argon+methane the presentsimulations show better agreement than those of Heyes, specially in methane-rich state points, c.f. Fig. 3.Figure 4 shows the results for the bulk viscosity of argon, krypton, xenonand methane in comparison with experimental data. The experimental dataare reported at different temperatures and were taken from Cowan et al .,Malbrunotet et al ., Cowan et al . and Singer [46,47,48,49], respectively. Theagreement is poor. Neither the density dependence nor the absolute value of η b predicted by molecular simulation agrees with the experimental data. Thebest results for η b are achieved at the low temperatures and high densities forkrypton. In this case the typical error is about 13%, even here the densitydependence in not predicted correctly. For the other fluids, the predictions arelower than the experimental data by about 50%. Likewise, the experimentaldata of bulk viscosity show a stronger dependence on the density than thesimulations. It must be pointed out here, however, that the method to measurethe bulk viscosity by means of acoustic absorption of sound waves, involvesconsiderable error [50]. Among the quoted experimental data, the kryptondata are claimed to be the most accurate with an error band of about 25%,for the remainder error bands of up to 40% can be assumed. In the light of thefact that these simple molecular models describe both the thermal and caloricproperties accurately [51] as well as the transport properties self-diffusion [24],12hear viscosity and thermal conductivity (see below), it can be argued thatthe deviations founded for the bulk viscosity are due to experimental error.Figure 5 shows the results for bulk viscosity of the binary mixtures argon+krypton and argon+methane. The agreement is again poor. Neither the com-position dependence nor the absolute value of η b predicted by molecular simu-lation agrees with the experimental data. The best results for η b are achievedat the lowest temperature for the mixture argon+krypton. In this case, a dis-crepancy of about 50% is found. In agreement with the results for pure fluids,it is found that the predictions are much too low in comparison to experimen-tal data. Previous work on these mixtures by Heynes et al . [10,11] confirmslower values from simulation, c.f. Fig. 5.Figure 6 shows the results for the thermal conductivity of argon, krypton,xenon and methane in comparison with experimental data. The data are re-ported at different temperatures along the bubble line and were taken fromVargaftik et al . [42]. Overall, very good agreement between simulation and ex-perimental data is present. The lowest relative deviations are found for argonand xenon, typical values are 4% for argon and 7% for xenon. The deviationsfor krypton and methane reach up to about 20%, no tendency is observed inthese deviations. The good agreement for methane is especially remarkable,considering that the molecular model is very simplified and does not considerthe contribution of rotation or internal degrees of freedom [52,53,54].Figure 7 shows the results for the thermal conductivity of the binary mixturesargon+krypton and argon+methane for two temperatures, the experimentaldata were taken from Mikhailenko et al . [44,45]. In general good agreementbetween simulation and experimental data is found. Due to the error intro-13uced by the partial molar enthalpy, the statistical uncertainty of the thermalconductivity was estimated as 5%. For the mixture argon+krypton the typicaldeviations are about 5% at 120 K, and about 7% at 140 K. For most of thesimulated state points, these deviations lie within the uncertainty bars. For themixture argon+methane a better agreement is found than for the mixture ar-gon+krypton. Over the whole composition range, simulation and experimentfor argon+methane agree within the statistical uncertainties. The comparisonof the present simulations with previous simulations of Heynes [10,11] showsgood agreement, c.f. Fig. 7. 14 . Conclusion In the present work, the Green-Kubo formalism was used to calculate transportproperties for pure and binary mixtures of four noble gases and methane. Themolecular interactions of the fluids were modeled by the spherical Lennard-Jones pair potential with parameters adjusted to vapor-liquid equilibrium only.A comprehensive comparison with available experimental data shows goodagreement for pure fluids and binary mixtures for shear viscosity and thermalconductivity. On the other hand, for the bulk viscosity, with the exceptionof pure krypton, considerable systematic deviations between simulations andexperiment occur. This disagreement hints towards highly inaccurate mea-surements. The present results support the finding that the spherical LJ 12-6potential is an adequate description for the regarded noble gases and alsomethane, in spite of the simplicity of the used model. Likewise the modifiedLorentz-Berthelot combination rules with one binary interaction parameterare an adequate description of the molecular binary unlike interaction. It isworthwhile to extend the study to more complex fluids.15 ist of Symbols E Energy h k partial molar enthalpy of component ki particle counting index j particle counting index J xyp xy stress tensor element J xq x heat flow element k B Boltzmann constant k species counting index M molar mass m molecular mass N number of particles r intermolecular distance r c cut-off radius t time T temperature u pair potential energy v velocity V volume x cartesian coordinate y cartesian coordinate z cartesian coordinate 16 reek Symbols α component β component∆ t integration time step ǫ Lennard-Jones energy parameter η s shear viscosity η v bulk viscosity λ thermal conductivity ξ adjustable binary interaction parameter σ Lennard-Jones size parameter
Vectorial and tensorial quantities I unitary matrix J p stress tensor J q heat flow vector r ij distance vector v i velocity of particle i eferences [1] D.J. Evans, G.P. Morris, Statistical Mechanics of Nonequilibrium Liquids,Academic Press, London 1990.[2] M.S. Green, J. Chem. Phys. 22(1954)398-413.[3] R. Kubo, J. Phys. Soc. Jpn. 12(1957)570-586.[4] B.L. Holian, D.J. Evans, J. Chem. Phys. 78(1983)5147-5150.[5] J.J. Erpenbeck, Phys. Rev. A. 35(1987)218-232.[6] S.T. Cui, P.T. Cummings, and H.D. Cochran, Mol. Phys. 93(1998)117-121.[7] M.F. Pas, and B. Zwolinski, Mol. Phys. 73(1991)483-494.[8] R.L. Rowley, M.M. Paiter, Int. J. Thermophys. 18(1997)1109-1121.[9] R.L. Rowley, personal comunication. There exist two erros in the cited referenceof Rowley et al., it should read: b =1067.97, w =-2.2065, also the subscript inequation (10) should read j instead i .[10] D.M. Heyes, S.R. Preston, Phys. Chem. Liq. 23(1991)123-149.[11] D.M. Heyes, J. Chem. Phys. 96(1992)2217-2227.[12] M. Schoen, C. Hoheisel, Mol. Phys. 56(1985)653-672.[13] P. Borgelt, C. Hoheisel, and G. Stell, Phys. Rev. A 42(1990)789-794.[14] D.M. Heyes, J. Chem. Soc. Faraday Trans. II 80(1984)1363-1394.[15] W.G. Hoover, D.J. Evans, R.B. Hickman, W.T. Ashurst, and B. Moran, Phys.Rev. A 22(1980)1690-1697.[16] R. Vogelsang, C. Hoheisel, and G. Ciccoti J. Chem. Phys. 35(1987)3487-3491.[17] R. Vogelsang, C. Hoheisel, Phys. Rev. A 35(1987)3487-3491.[18] K. Meier, A. Laesecke, and S. Kabelac, Int. J. Thermophys. 18(1997)161-173.[19] K. Meier, PhD Thesis, Computer Simulation and Interpretation of theTransport Coefficients of the Lennard-Jones Model Fluid, Shaker Publishers,Aachen, 2002.[20] J.P.J. Michels, N.J. Trappeniers, Physica A 90(1978)179-195.[21] L.A.F. Coelho, J.V. de Oliveira, F.W. Tavares, and M.A. Matthews, Fluid PhaseEquilibria 194(2002)1131-1140.[22] J.M. Stoker, and R.L. Rowley, J. Chem. Phys. 91(1989)3670-3676.[23] J. Vrabec, J. Stoll, and H. Hasse, J. Phys. Chem. B. 48(2001)12126-12133.
24] G.A. Fernandez, J. Vrabec, and H. Hasse, Int. J. Thermophys. 25(2004)175-186.[25] R. Kubo, Rpts. Progr. Phys., 29(1966)255-284.[26] R. Zwanzig, Ann. Rev. Phys. Chem. 12(1965)67-102.[27] A.F.M. Baron, The dynamic liquid state, Longman, London, 1974.[28] K.E. Gubbins, in K. Singer (Ed.), Statistical Mechanics vol. 1, The ChemicalSociety, Burlington House, London, 1972, pp 194-253.[29] W.A. Steele, in H.J.M. Hanley (Ed.), Transport Phenomena in Fluids, MarcelDekker, New York and London, 1969, pp 209-312.[30] J.O. Hirschfelder, C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases andLiquids, John Wiley & Sons Inc., Ney York, 1954.[31] S.M. Karim, Rev. Mod. Phys. 24(1952)108-116.[32] S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics, Dover, New York,1984.[33] I.R. McDonald, K. Singer, Mol. Phys. 23(1972)29-40.[34] J. Vrabec, J. Stoll, and H. Hasse, Molecular models of unlike interaction inmixtures, Int. J. Thermophys, to be submited (2004).[35] J. Stoll, J. Vrabec, and H. Hasse. AIChE. J. 49(2003)2187-2198.[36] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press,Oxford, 1987.[37] J.M. Haile, Molecular Dynamics Simulation, John Wiley & Sons Inc., New York,1997.[38] B.J. Alder, and T.E. Wainwright, Phys. Rev. A 1(1970)18-21.[39] D. Fincham, N. Quirke, and D.J. Tildesley, J. Chem. Phys. 84(1986)4535-4546.[40] H.C. Andersen, J. Chem. Phys. 72(1980)2384-2393.[41] P. Sindzingre, G. Ciccoti, C. Massobrio, and D. Frenkel, Chem. Phys. Lett.136(1987)35-41.[42] N.B. Vargaftik, Y.K. Vinogradov, and V.S. Yargin, Handbook of PhysicalProperties of Liquids and Gases, Begell house, inc., New York, 1996.[43] C. Evers, H.W. L¨osch, and W. Wagner, Int. J. Thermophys. 23(2002)1411-1439.[44] S.A. Mikhailenko, V.G. Dudar, V.N. Derkach, and V.N. Zozulya, Sov. J. Low.Temp. Phys. 3(1977)331-336.[45] S.A. Mikhailenko, V.G. Dudar, and V.N. Derkach, Sov. J. Low. Temp. Phys.4(1978)205-212.[46] J.A. Cowan, R.N. Ball, Can. J. Phys. 50(1972)1881-1886.
47] P. Malbrunot, A. Boyer, and E. Charles, Phys. Rev. A 27(1983)1523-1534.[48] J.A. Cowan, J.W. Leech, Can. J. Phys. 59(1981)1280-1288.[49] J.R. Singer, Can. J. Phys. 51(1969)4729-4733.[50] R.E. Graves, J. Thermophysics Heat Transf. 51(1969)4729-4733.[51] J. Vrabec, J. Stoll, and H. Hasse, J. Phys. Chem. B 105(2001)12126-12133.[52] D.J. Evans, S. Murad, Mol. Phys. 68(1989)1219-1223.[53] B.Y. Wang, P.T, Cummings, D.J. Evans, Mol. Phys. 75(1992)1345-1356.[54] T. Tokumasu, T. Ohara, and K. Kamijo, J. Chem. Phys. 118(2003)3677-3685.[55] B.E. Poling, J.M. Prausnitz, and J.P. O’Connell, The Properties of Gases andLiquids, 5th Edition, McGraw-Hill, New York, 2001. able 1Potential model parameters for the pure fluids used in this work [23] and molarmass [55]. Fluid σ / ˚A ( ǫ/k B ) / K M / g/molneon 2.8010 33.921 20.180argon 3.3952 116.79 39.948krypton 3.6274 162.58 83.8xenon 3.9011 227.55 131.29methane 3.7281 148.55 16.043 able 2Binary interaction parameters taken from [34].Mixture ξ argon + krypton 0.988argon + methane 0.964 ist of Figures T =90 K and ρ =34433 mol · m − ,middle: shear viscosity T =150.7 K and ρ =35046 mol · m − ,bottom: bulk viscosity T =100 K and ρ =32843 mol · m − . 252 Shear viscosity of argon, krypton, xenon and methanepredicted by molecular simulation (full symbols) compared toexperimental data (empty symbols) [42,43]. argon T =300 K N ; krypton T =230 K (cid:4) ; xenon T =270 K H ; methane T =100 K - 293.15 K (cid:7) ; correlation of Rowley et al. [8] − . 263 Shear viscosity of the mixtures argon+krypton (top) andargon+metane (bottom) predicted by molecular simulation(full symbols) compared to experimental data (empty symbols)[44,45]. The lines are a guide for the eye. 274 Bulk viscosity of argon, krypton, xenon and methanepredicted by molecular simulation (full symbols) compared toexperimental data (empty symbols) [46,47,48,49]. The linesare a guide for the eye. argon T =100 K - 145 K N ; krypton T =116 K - 130 K (cid:4) ; xenon T =165 K - 265 K H ; methane T =100 K - 293.15 K (cid:7) . 2823 Bulk viscosity of the mixtures argon+krypton (top) andargon+metane (botton) predicted by molecular simulation(full symbols) compared to experimental data (empty symbols)[44,45]. The lines are a guide for the eye. 296 Thermal conductivity of argon, krypton, xenon and methanepredicted by molecular simulation (full symbols) compared toexperimental data (empty symbols) [42]. The data correspondto bubble points reported at different temperatures. argon T =90 K - 140 K N ; krypton T =140 K - 184 K (cid:4) ; xenon T =170 K - 270 K H ; methane T =100 K - 180 K (cid:7) . 307 Thermal conductivity of the mixtures argon+krypton (top)and argon+metane (botton) predicted by molecular simulation(full symbols) compared to experimental data (empty symbols)[44,45]. The lines are a guide for the eye. 3124 ig. 1. ig. 2. ig. 3. ig. 4. ig. 5. ig. 6. ig. 7.ig. 7.