Abstract
The previously proposed model is used to determine the values of the self-diffusion coefficient of He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO2, NH3, and CH4 in the liquid and dense gaseous states, which were compared with the experimental data obtained at a pressure of ≈200 MPa and a temperature of ≈500 K. The calculations are carried out with the use of the equation of state of these substances in the form of a modified van der Waals model. The self-diffusion model was generalized for the case of mutual diffusion in binary mixtures, which is based on the modified model of the van der Waals state equation for mixtures. The modeled coefficient of mutual diffusion for a great number of binary mixtures of the above-mentioned individual substances is determined, and the results are compared with the known data. Without special calibration for the experiment, the model correctly predicts the relationship of the self-diffusion and mutual diffusion coefficients (with their variation by several orders of magnitude in the case where the density changes from gaseous to liquid) with both pressure and temperature. For most substances considered in the paper, the maximum deviations of calculations from the experiment do not exceed 30–50%.
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References
J. O. Hirschfelder, C. F. Curtiss, R. B. Bird, et al., Molecular Theory of Gases and Liquids (Wiley, 1954).
R. C. Reid and T. K. Sherwood, The Properties of Gases and Liquids: Their Estimation and Correlation (McGraw-Hill, 1966).
A. B. Medvedev, “Transport Coefficients in the Van der Waals Modified Model,” Teplofiz. Vysok. Temp. 33 (2), 227–235 (1995).
A. B. Medvedev, “State Equation Model with Account for Evaporation, Ionization, and Melting,” Vopr. Atomn. Nauki Tekh., Ser. Teoret. Prikl. Fiz. 1, 12–19 (1992).
A. B. Medvedev, “Modification of the van der Waals Model for Dense States of Matter,” in High-Pressure Shock Compression of Solids VII. Shock Waves and Extreme States of Matter, Ed. by V. E. Fortov, L. V. Al’tshuler, R. F. Trunin, and A. I. Funtikov (Springer-Veriag, New York, 2004).
A. B. Medvedev, “Equation of State and Transport Coefficients of Argon, Based on a Modified Van der Waals Model up to Pressures of 100 GPa,” Fiz. Goreniya Vzryva 46 (4), 116–126 (2010) [Combust., Expl., Shock Waves 46 (4), 472–481 (2010)].
A. B. Medvedev and R. F. Trunin, “Shock Compression of Porous Metals and Silicates,” Usp. Fiz. Nauk 182 (8), 829–846 (2012).
J. H. Dymond, “Corrected Enskog Theory and the Transport Coefficients of Liquids,” J. Chem. Phys. 60 (3), 969–973 (1974).
H. Sigurgeeirsson and D. M. Heyes, “Transport Coefficients of Hard Sphere Fluids,” Molec. Phys. 101 (3), 469–482 (2003).
R. J. Speedy, “Diffusion in Hard Sphere Fluid,” Molec. Phys. 62 (2), 509–515 (1987).
J. J. Van Loef, “The Corrected Enskog Theory and the Transport Properties of Molecular Liquids,” Physica. A 87, 258–272 (1977).
J. J. Van Loef, “The Corrected Enskog Theory Applied to the Transport Properties of Liquid Hydrogen and Deuterium,” Physica, B+C 90, 272–274 (1977).
Z. N. Gerek and J. R. Elliott, “Self-Diffusivity Estimation by Molecular Dynamics,” Ind. Eng. Chem. Res. 49 (7), 3411–3423 (2010).
D. Chandler, “Rough Hard Sphere Theory of the Self- Diffusion Constant for Molecular Liquids,” J. Chem. Phys. 62 (4), 1358–1362 (1975).
T. Grob, J. Buchhauser, and H.-D. Ludemann, “Self- Diffusion in Fluid Carbon Dioxide at High Pressures,” J. Chem. Phys. 109 (11), 4518–4522 (1998).
V. P.Kopyshev, A. B. Medvedev, and V. V. Khrustalev, “ Equation of State of Explosion Products on the Basis of a Modified Van der Waals Model,” Fiz. Goreniya Vzryva 42 (1), 87–99 (2006) [Combust., Expl., Shock Waves 42 (1), 76–87 (2006)].
V. P. Kopyshev, A. B. Medvedev, and A. V. Skobeev, “Calculation of Detonation Characteristics of Condensed Explosives with the use of a Modified van der Waals Model,” in 65 Years of VNIIEF, Physics and Equipment of High-Density Energies, Ed. by R. I. Il’kaev et al. (VNIIEF, Sarov, 2011).
S. H. Chen, H. T. Davis, and D. F. Evans, “Tracer Diffusion in Polyatomic Liquids. III,” J. Chem. Phys. 77 (5), 2540–2544 (1982).
M. A.Matthews and A. Akgerman, “Hardsphere Theory for Correlation of Tracer Diffusion of Gases and Liquids in Alkanes,” J. Chem. Phys. 87 (4), 2285–2291 (1987).
K. Rah and B. C. Eu, “The Generic van derWaals Equation of State and Self-Diffusion Coefficients of Liquids,” J. Chem. Phys. 115 (6), 7967–7976 (2001).
K. Rah and B. C. Eu, “Generic van der Waals Equation of State and Theory of Diffusion Coefficients: Binary Mixtures of Simple Liquids,” J. Chem. Phys. 116 (18), 2634–2640 (2002).
M. H. Cohen and D. Turnbull, “Molecular Transport in Liquids and Glasses,” J. Chem. Phys. 31 (5), 1164–1169 (1959).
K. Rah and B. C. Eu, “Self-Diffusion Coefficient of Liquid Nitrogen,” Molec. Phys. 100 (20), 3281–3283 (2002).
R. V. Telesnin, Molecular Physics (Lan’, St.-Petersburg, 2009) [in Russian].
M. N. Kogan, Rarefied Gas Dynamics (Springer, 1969).
Thermophysical Properties of Fluid Systems, NIST Webbook, http://webbook.nist.gov/chemistry/fluid.
J. W. Leachman, R. T. Jacobsen, S. G. Penoncello, et al., “Fundamental Equations of State for Parahydrogen, Normal Hydrogen, and Orthohydrogen,” J. Phys. Chem. Ref. Data 38 (3), 721–747 (2009).
A. B. Medvedev, “State Equations of Liquid Hydrogen and Deuterium to 1 TPa and 20 000 K,” in Extreme States of Matter. Detonation. Shock Waves, IX Khariton’s Topical Scientific Readings, March 12–16, 2007, Ed. by A. L. Mikhailov (VNIIEF, Sarov, 2011).
R. F. Trunin, G. V. Boriskov, A. I. Bykov, et al., “Shock Compression of Liquid Nitrogen at a Pressure of 320 GPa,” Pis’ma Zh. Eksp. Teoret. Fiz. 88 (3), 220–223 (2008) [JETP Letters 88 (3), 189–191 (2008)].
D. E. O’Reilly and E. M. Peterson, “Self-Diffusion of Liquid Hydrogen and Deuterium,” J. Chem. Phys. 66 (3), 934–937 (1977).
K. Krynicki, E. J. Rahkamaa, and J. G. Powles, “The Properties of Liquid Nitrogen I. Self-Diffusion Coefficient,” Molec. Phys. 28 (3), 853–855 (1974).
J. Naghizadeh and S. A. Rice, “Kinetic Theory of Dense Fluids. X. Measurement and Interpretation of Self-Diffusion in Liquid Ar, Kr, Xe, and CH4,” J. Chem. Phys. 36 (10), 2710–2720 (1962).
J. V. Gaven, J. S. Waugh, and W. H. Stockmayer, “Self-Diffusion and Impurity-Controlled Proton Relaxation in Liquid Methane,” J. Chem. Phys. 38 (2), 287–290 (1963).
J. H. Rugheimer and P. S. Hubbard, “Nuclear Magnetic Relaxation and Diffusion in Liquid CH4, CF4, and Mixtures of CH4 and CF4 with Argon,” J. Chem. Phys. 39 (3), 552–564 (1963).
J. W. Corbett and J. H, Wang, “Self-Diffusion in Liquid Argon,” J. Chem. Phys. 25 (3), 422–425 (1956).
G. Cini-Castagnoli and F. P. Ricci, “Self-Diffusion in Liquid Argon,” J. Chem. Phys. 32 (1), 19–20 (1960).
P. Zandveld, C. D. Andriesse, J. D. Bregman, et al., “Temperature Dependence of the Atomic Self-Motion in Liquid Argon,” Physica 50, 511–523 (1970).
T. R. Mifflin and C. O. Bennett, “Self-Diffusion in Argon to 300 Atmospheres,” J. Chem. Phys. 29 (5), 975–978 (1958).
L. Durbin and R. Kobayashi, “Diffusion of Krypton- 85 in Dense Gases,” J. Chem. Phys. 37 (8), 1643–1654 (1962).
P. Carelli, A. De Santis, I. Modena, et al., “Self- Diffusion in Simple Dense Fluids,” Phys. Rev. A 13 (3), 1131–1139 (1976).
P. Carelli, I. Modena, and F. P. Ricci, “Self-Diffusion in Krypton in Intermediate Density,” Phys. Rev. A 7 (1), 298–303 (1973).
P. W. E. Peereboom, H. Luigjes, and K. O. Prins, “An NMR Spin-Echo Study of Self-Diffusion in Xenon,” Physica. A 156, 260–276 (1989).
S. H. Chen, T. A. Postol, and K. Skold, “Study of Self- Diffusion in Dense Hydrogen Gas by Quasielastic Incoherent Neutron Scattering,” Phys. Rev. A 16 (5), 2112–2119 (1977).
L. Chen, T. Grob, H. Krienke, et al., “T, p-Dependence of the Self-Diffusion and Spin-Lattice Relaxation in Fluid Hydrogen and Deuterium,” Phys. Chem. Chem. Phys. 3, 2025–2030 (2001).
T. Grob, J. Buchhauser, W. E. Price, et al., “The p,T -Dependence of Self-Diffusion in Fluid Ammonia,” J. Molec. Liquids 73/74, 433–444 (1997).
K. R. Harris and N. J. Trappeniers, “The Density Dependence of the Self-Diffusion Coefficient of Liquid Methane,” Physica. A 104, 262–280 (1980).
A. Greiner-Schmid, S. Wappmann, M. Has, et al., “Self-Diffusion in the Compressed Fluid Lower Alkanes: Methane, Ethane, and Propane,” J. Chem. Phys. 94 (8), 5643–5649 (1991).
E. Fukushima, A. A. V. Gibson, and T. A. Scott, “Carbon-13 NMR of Carbon Monoxide. II. Molecular Diffusion and Spin-Rotation Interaction in Liquid CO,” J. Chem. Phys. 71 (4), 1531–1536 (1979).
G. Careri, J. Reuses, and J. M. Beenaccer, “The Diffusion Coefficient in Dilute H2–D2 and He3–He4 Liquid Mixtures,” Nuovo Cimento 13 (1), 148–153 (1959).
G. Cini-Castagnoli, “Diffusion of Kr and He in Liquid Hydrogen,” J. Chem. Phys. 35 (6), 1999–2001 (1961).
G. Cini-Castagnoli, A. Giardini-Cuidoni, and F. P. Ricci, “Diffusion of Neon, HT, and Deuterium in Liquid Hydrogen,” Phys. Rev. 123 (2), 404–406 (1961).
G. Cini-Castagnoli, G. Pizzella, and F. P. Ricci, “The Diffusion of Argon and Tritium in Liquid Nitrogen,” Nuovo Cimento 10 (2), 303–309 (1958).
G. Cini-Castagnoli and F. Dupre, “Diffusion Coefficient of 37A in Liquid N2,” Nuovo Cimento 13 (2), 464–465 (1959).
P. J. Dunlop and C. M. Bignell, “Tracer Diffusion of Kr 85 in Liquid Ar, N2, and O2,” J. Chem. Phys. 108 (17), 7301–7304 (1998).
G. Cini-Castagnoli and F. P. Ricci, “Diffusion of 37A, Kr, HT in Liquid Argon between (84–90) K,” Nuovo Cimento 15 (5), 795–805 (1960).
D. Yu. Gamburg et al., Hydrogen. Properties, Production, Storage, Transportation, and Use (Khimiya, Moscow, 1989) [in Russian].
M. De Paz, F. Tantalo, and G. Varni, “Diffusion Measurements in Dense Gases. The Systems He–Ar and He–Ne,” J. Chem. Phys. 61 (10), 3875–3880 (1974).
Z. Balenovic, M. N. Myers, and J. Calvin Giddings, “Binary Diffusion in Dense Gases to 1360 atm by the Chromatographic Peak-Broadening Method,” J. Chem. Phys. 52 (2), 915–922 (1970).
T. R. Marrero and E. A. Mason, “Gaseous Diffusion Coefficients,” J. Phys. Chem. Ref. Data 1 (1), 3–118 (1972).
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Original Russian Text © A.B. Medvedev.
Published in Fizika Goreniya i Vzryva, Vol. 53, No. 4, pp. 58–71, July–August, 2017.
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Medvedev, A.B. Estimating the self-diffusion and mutual diffusion coefficients of binary mixtures on the basis of a modified van der Waals model. Combust Explos Shock Waves 53, 420–432 (2017). https://doi.org/10.1134/S0010508217040062
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DOI: https://doi.org/10.1134/S0010508217040062