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Thermophysical Properties of High Temperature Reacting Mixtures of Carbon and Water in the Range 400–30,000 K and 0.1–10 atm. Part 2: Transport Coefficients

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Abstract

The present contribution is continuation of Part 1: Equilibrium composition and thermodynamic properties. This paper is devoted to the calculation of transport properties of mixtures of water and carbon at high temperature. The transport properties, including electron diffusion coefficient, viscosity, thermal conductivity, and electrical conductivity are obtained by using the Chapman–Enskog method expanded to the third-order approximation (second-order for viscosity), taking only elastic processes into account. The calculations, which assume local thermodynamic equilibrium, are performed for atmospheric pressure plasmas in the temperature range from 400 to 30,000 K for pressures of 0. 10, 1.0, 3.0, 5.0 and 10.0 atm. with the results obtained are compared to those of previously published studies, and the reasons for discrepancies are analyzed. The results provide reliable reference data for simulation of plasmas in mixtures of carbon and water.

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References

  1. Wang WZ, Murphy AB, Rong MZ, Yan JD, Spencer JW, Fang MTC (2011) Thermophysical properties of high-temperature reacting mixtures of carbon and water in the range 400–30,000 K and 0.1–10 atm. Part 1: equilibrium composition and thermodynamic properties. Plasma Chem Plasma Process. doi:10.1007/s11090-011-9327-y

  2. Aubreton J, Elchinger MF, Hacala A, Michon U (2009) Transport coefficients of typical biomass equimolar CO–H2 plasma. J Phys D Appl Phys 42:095206

    Article  ADS  Google Scholar 

  3. Tanaka Y, Yamachi N, Matsumoto S, Kaneko S, Okabe S, Shibuya M (2008) Thermodynamic and transport properties of CO2, CO2–O2, and CO2–H2 mixtures at temperatures of 300 to 30,000 K and pressures of 0.1 to 10 MPa. Electr Eng. Japan 163:18–29

    Article  Google Scholar 

  4. Hirschfelder JO, Curtis CF, Bird RB (1964) Molecular theory of gases and liquids, 2nd edn. Wiley, New York

    Google Scholar 

  5. Chapman S, Cowling TG (1970) The mathematical theory of non-uniform gases, 3rd edn. Cambridge University Press, Cambridge

    Google Scholar 

  6. Ferziger JH, Kaper HG (1972) Mathematical theory of transport processes in gases. North-Holland, Amsterdam

    Google Scholar 

  7. Wang WZ, Rong MZ, Murphy AB, Wu Y, Spencer JW, Yan JD, Fang MTC (2011) Thermophysical properties of carbon–argon and carbon–helium plasmas. J Phys D Appl Phys 44:355207

    Article  Google Scholar 

  8. Rat V, André P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (2002) Transport coefficients including diffusion in a two-temperature argon plasma. J Phys D Appl Phys 35:981–991

    Article  ADS  Google Scholar 

  9. Devoto RS (1973) Transport coefficients of ionized argon. Phys Fluids 16:616–623

    Article  ADS  Google Scholar 

  10. Devoto RS (1967) Third approximation to the viscosity of multicomponent mixtures. Phys Fluids 10:2704–2706

    Article  ADS  Google Scholar 

  11. Butler JN, Brokaw RS (1957) Thermal conductivity of gas mixtures in chemical equilibrium. J Chem Phys 26:1636–1643

    Article  ADS  Google Scholar 

  12. Meador WE, Stanton LD (1965) Electrical and thermal properties of plasmas. Phys Fluids 8:1694–1703

    Article  ADS  Google Scholar 

  13. Monchick L, Yun KS, Mason EA (1963) Formal kinetic theory of transport phenomena in. polyatomic gas mixtures. J Chem Phys 39:654–669

    Article  ADS  Google Scholar 

  14. Hirschfelder JO (1957) Heat conductivity in polyatomic or electronically excited gases. Chem Phys 26:282–285

    ADS  Google Scholar 

  15. Hirschfelder JO (1957) In: Proceedings of 6th international symposium on Combustion. Reinhold, New York, p 351

  16. Sourd B, Aubreton J, Elchinger MF, Labrot M, Michon U (2006) High temperatures transport coefficients in e/C/H/N/O mixture. J Phys D Appl Phys 39:1105–1119

    Article  ADS  Google Scholar 

  17. Aubreton J, Elchinger MF, Vinson JM (2009) Transport coefficients in water plasma: part I: equilibrium plasma. Plasma Chem Plasma Process 29:149–171

    Article  Google Scholar 

  18. André P, Aubreton J, Clain S (2010) Transport coefficients in thermal plasma. Applications to mars and titan atmospheres. Eur Phys J D 57:227–234

    Article  ADS  Google Scholar 

  19. Paul P, Warnatz J (1998) In: A re-evaluation of the means used to calculate transport properties of reacting flows 27th symposium (international) on Combustion. The Combustion Institute, pp 495–504

  20. Capitelli M, Cappelletti D, Colonna G, Gorse C, Laricchiuta A, Liuti G, Longo S, Pirani F (2007) On the possibility of using model potentials for collision integral calculations of interest for planetary atmospheres. Chem Phys 338:62–68

    Article  ADS  Google Scholar 

  21. Laricchiuta A, Colonna G, Bruno D, Celiberto R, Gorse C, Pirani F, Capitelli M (2007) Classical transport collision integrals for a Lennard–Jones like phenomenological model potential. Chem Phys Lett 445:133–139

    Article  ADS  Google Scholar 

  22. Andrea L, Federico P (2008) A comparison of interatomic potentials for rare gas nanoaggregates. J Mol Struct (Theochem) 857:22–29

    Google Scholar 

  23. Laricchiuta A, Bruno D, Capitelli M, Catalfamo C, Celiberto R, Colonna G, Diomede P, Giordano D, Gorse C, Longo S, Pagano D, Pirani F (2009) High temperature Mars atmosphere. Part I: transport cross section. Eur Phys J D 54:607–612

    Article  ADS  Google Scholar 

  24. Catalfamo C, Bruno D, Colonna G, Laricchiuta A, Capitelli M (2009) High temperature Mars atmosphere. Part II: transport properties. Eur Phys J D 54:613–621

    Article  ADS  Google Scholar 

  25. Miller TM, Bederson B (1977) Atomic and molecular polarizabilities—a review of recent advances. Adv At Mol Phys 13:1–55

    Article  Google Scholar 

  26. Woon DE, Herbst E (2009) Computed dipole moments and dipole polarizabilies for neutral astromolecules. APJS 185:273–288

    Article  ADS  Google Scholar 

  27. Olney TN, Cann NM, Cooper G, Brion CE (1997) Absolute scale determination for photoabsorption spectra and the calculation of molecular properties using dipole sum-rules. J Chem Phys 223:59–98

    Google Scholar 

  28. Lide DR (ed) (1994) CRC handbook of chemistry and physics, 7th edn. CRC, Boca Raton

    Google Scholar 

  29. Bose TK, Cole RH (1970) Dielectric and pressure virial coefficients of imperfect gases. II. CO2-argon mixtures. J Chem Phys 52:140–147

    Article  ADS  Google Scholar 

  30. Du S, Francisco JS, Schenter GK, Iordanov TD, Garrett BC, Dupuis M, Li J (2006) The OH radical-H2O molecular interaction potential. J Chem Phys 124:22438

    Article  Google Scholar 

  31. Cybulski SM, Haley TP (2004) New approximations for calculating dispersion coefficients. J Chem Phys 121:7711–7716

    Article  ADS  Google Scholar 

  32. Applequist J, Carl JR, Fung KK (1972) An atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc 94:2952–2960

    Article  Google Scholar 

  33. Stout JM, Dykstra CE (1994) Static dipole polarizabilities of organic molecules. Ab initio calculations and a predictive model. J Am Chem Soc 117:5127–5132

    Article  Google Scholar 

  34. (2004) In: Johnson III RD (ed) NIST Computational Chemistry Comparison and Benchmark Database, NIST standard reference database number 101, Release 10th edn

  35. Barker JA, Fock W, Smith F (1964) Calculation of gas transport properties and the Interaction of argon atoms. Phys Fluids 7:897–903

    Article  ADS  MATH  Google Scholar 

  36. Murphy AB, Arundell CJ (1994) Transport coefficients of argon, nitrogen, oxygen, argon–nitrogen, and argon–oxygen plasmas. Plasma Chem Plasma Process 14:451–490

    Article  Google Scholar 

  37. Thakkar A, Das AK (2001) Anisotropic polarizabilities and hyperpolarizabilities of second-period cations. J Mol Str (Theochem) 547:233

    Article  Google Scholar 

  38. Shevelko VP, Vinogradov AV (1979) Static dipole polarizability of atoms and ions in the Thomas-Fermi Model. Phys Scr 19:275–282

    Article  ADS  Google Scholar 

  39. Alagia M, Brunetti BG, Candori P, Falcinelli S, Teixidor MM, Pirani F, Richter R, Stranges S, Vecchiocattivi F (2004) Low-lying electronic states of HBr2+. J Chem Phys 120:6985–6991

    Article  ADS  Google Scholar 

  40. Magnasco V, Ottonelli M (1999) Dipole polarizability pseudospectra and C6 dispersion coefficients for H2 +–H2 +. J Mol Struct Theochem 469:31–40

    Article  Google Scholar 

  41. Gorfinkiel JD, Tennyson J (2004) Electron–H3 + collisions at intermediate energies. J Phys B: At Mol Opt Phys 37:L343

    Article  Google Scholar 

  42. Pluta T, Sadlej AJ, Bartlett R (1988) Polarizability of OH. Chem Phys Lett 143:91–96

    Article  ADS  Google Scholar 

  43. McDaniel EW, Mason EA (1973) The mobility and diffusion of ions in gases. John Wiley, New York

    Google Scholar 

  44. Maroulis G (1988) Electrical properties for HCO+ and NNH+ from fourthorder Moller-Plesset pertubation theory. Z Naturforsch 43:419–429

    Google Scholar 

  45. Chipot C, Dehez F, Angyan J, Millot C, Orozco M, Luque FJ (2001) Alternative approaches for the calculation of induction energies: Characterization, effectiveness, and pitfalls. J Phys Chem A 105:11505–11514

    Article  Google Scholar 

  46. Bruno D, Catalfamo C, Capitelli M, Colonna G, Pascale ODE, Diomede P, Gorse C, Laricchiuta A, Longo S, Giordano D, Pirani F (2010) Transport properties of high-temperature Jupiter atmosphere components. Phys Plasmas 17:112315

    Article  ADS  Google Scholar 

  47. Krstic PS, Schultz DR (1999) Elastic scattering and charge transfer in slow collisions: isotopes of H and H+ colliding with isotopes of H and with He. J Phys B: At Mol Opt Phys 32:3485–3509

    Article  ADS  Google Scholar 

  48. Yevseyev AV, Radtsig AA, Smirnov BM (1982) The asymptotic theory of resonance charge exchange between diatomics. J Phys B: At Mol Phys 15:4437–4452

    Article  ADS  Google Scholar 

  49. Huels MA, Champion RL, Doverspike LD, Wang YC (1990) Charge transfer and electron detachment for collisions of H- and D- with H. Phys Rev A 41:4809–4815

    Article  ADS  Google Scholar 

  50. Copeland FBM, Crothers DSF (1997) Cross sections for resonant charge transfer between atoms and their positive ions atomic data. Nucl Data Tables 65:273–288

    Article  ADS  Google Scholar 

  51. Roche AE, Goodyear CC (1971) Electron transfer in collisions of low-energy negative oxygen ions with O2. J Phys D Appl Phys 4:1513–1519

    Article  ADS  Google Scholar 

  52. Rutherford JA, Vroom DA (1974) The reaction of atomic oxygen with several atmospheric ions. J Chem Phys 61:2514–2519

    Article  ADS  Google Scholar 

  53. Rapp D, Francis WE (1962) Charge-exchange between gaseous ions and atoms. J Chem Phys 37:2631–2645

    Article  ADS  Google Scholar 

  54. Brunger MJ, Buckman BSJ (2002) Electron-molecule scattering cross-sections. I. Experimental techniques and data for diatomic molecules. Phys Rep 357:215–458

    Article  ADS  Google Scholar 

  55. England JP, Elford MT, Crompton RW (1988) A study of the vibrational excitation of H2 by measurements of the drift velocity of electrons in H2–Ne mixtures. J Phys 4:573–586

    Google Scholar 

  56. Muse J, Silva H, Lopes MCA, Khakoo MA (2008) Low energy elastic scattering of electrons from H2 and N2. J Phys B: At Mol Opt Phys 41:095203

    Article  ADS  Google Scholar 

  57. Shyn TW, Sharp WE (1981) Angular distributions of electrons elastically scattered from H2. Phys Rev A 24:1734–1740

    Article  ADS  Google Scholar 

  58. Itikawa Y (1974) Momentum-transfer cross sections for electron collisions with atoms and molecules. Atom Data Nucl Data Tables 14:1–10

    Article  ADS  Google Scholar 

  59. Bray I, Konovalov DA, McCarthy IE (1991) Coupled-channel optical calculation of electron-hydrogen scattering: elastic scattering from 0.5 to 30 eV. Phys Rev A 43:5878–5885

    Article  ADS  Google Scholar 

  60. Gupta GP, Mathur KC (1980) Differential cross sections for the elastic scattering of electrons by hydrogen atoms at intermediate energies. J Phys B 13:1719

    Article  ADS  Google Scholar 

  61. Itikawa Y (2009) Cross sections for electron collisions with oxygen molecules. J Phys Chem Ref Data 38:1–20

    Article  ADS  Google Scholar 

  62. Sullivan JP, Gibson JC, Gulley RG, Buckman SJ (1995) Low energy electron scattering from O2. J Phys B 28:4319–4328

    Article  ADS  Google Scholar 

  63. Linert I, King GC, Zubek M (2004) Measurements of differential cross sections for elastic electron scattering in the backward direction by molecular oxygen. J Phys B 37:468–491

    Article  Google Scholar 

  64. Machado LE, Ribeiro EMS, Lee MT, Fujimoto MM, Brescansin LM (1999) Cross sections and polarization fractions for elastic e–O2 collisions. Phys Rev A 60:1199–1205

    Article  ADS  Google Scholar 

  65. Tabata T, Shirai T, Sataka M, Kubo HA (2006) Analytic cross sections for electron impact collisions with nitrogen molecules. Atom Data Nucl Data Tables 92:375–406

    Article  ADS  Google Scholar 

  66. Thomas LD, Nesbet RK (1975) Addendum: low energy electron scattering by atomic oxygen. Phys Rev A 12:1729–1730

    Article  ADS  Google Scholar 

  67. Blaha M, Davis J (1975) Elastic scattering of electrons by oxygen and nitrogen at intermediate energies. Phys Rev A 12:2319–2324

    Article  ADS  Google Scholar 

  68. Itikawa Y, Ichimura A (1990) Cross sections for collisions of electrons and photons with atomic oxygen. J Phys Chem Ref Data 19:637–651

    Article  ADS  Google Scholar 

  69. Sobrinho AMC (2004) Elastic and absorption cross sections for electron–hydroxyl radical collisions. Phys Rev A 70:032717

    Article  ADS  Google Scholar 

  70. Chen X, Morgan LA (1997) Low-energy electron scattering from the X 2Σ state of the OH molecule. J Phys B 30:3709–3717

    Article  ADS  Google Scholar 

  71. Khakoo MA, Silva H, Muse J, Lopes MCA, Winstead C, McKoy V (2008) Electron scattering from H2O: elastic scattering. Phys Rev A 78:052710

    Article  ADS  Google Scholar 

  72. Faure A, Gorfinkiel JD, Tennyson J (2004) Low-energy electron collisions with water: elastic and rotationally inelastic scattering. J Phys B: At Mol Opt Phys 37:801–807

    Article  ADS  Google Scholar 

  73. Katase A, Ishibashi K, Matsumoto Y, Sakae T, Maezono S, Murakami E, Watanabe K, Maki H (1986) Elastic scattering of electrons by water molecules over the range 100–1000 eV. J Phys B: At Mol Phys 19:2715–2734

    Article  ADS  Google Scholar 

  74. Itikawa Y (2005) Cross sections for electron collisions with water molecules. J Phys Chem Ref Data 34:1–22

    Article  ADS  Google Scholar 

  75. Gibson JC, Green MA, Trantham KW, Buckman SJ, Teubner PJO, Brunger MJ (1998) Elastic electron scattering from CO2. J Phys B: At Mol Opt Phys 32:213–233

    Article  ADS  Google Scholar 

  76. Iga I, Homem MGP, Mazon KT, Lee MT (1999) Elastic and total cross sections for electron–carbon dioxide collisions in the intermediate energy range. J Phys B: At Mol Opt Phys 32:4373–4388

    Article  ADS  Google Scholar 

  77. Itikawa Y (2002) Cross sections for electron collisions with carbon dioxide. J Phys Chem Ref Data 31:749–767

    Article  ADS  Google Scholar 

  78. Gibson JC, Morganz LA, Gulleyx RJ, Brungerk MJ, Bundschuy CT, Buckmany SJ (1996) Low energy electron scattering from CO: absolute cross section measurements and R-matrix calculations. J Phys B: At Mol Opt Phys 29:3197–3214

    Article  ADS  Google Scholar 

  79. Allan M (2010) Electron collisions with CO: elastic and vibrational excitation cross sections. Phys Rev A 81:042706

    Article  ADS  Google Scholar 

  80. Lee MT, Iga I, Brescansin LM, Machado LE, Machado FBC (2002) Theoretical studies on electron-carbon monoxide collisions in the low and intermediate energy range. J Mol Struct (Theochem) 585:181–187

    Article  Google Scholar 

  81. Land JE (1978) Electron scattering cross sections for momentum transfer and inelastic excitation in carbon monoxide. J App Phys 49:5716–5721

    Article  ADS  Google Scholar 

  82. Lee MT, Iga I, Machado LE, Brescansin LM (2000) Model absorption potential for electron-molecule scattering in the intermediate-energy range. Phys Rev A 62:062710

    Article  ADS  Google Scholar 

  83. Cho H, Park YS, Castro EAY, De Souza GLC, Iga I, Machado LE, Brescansin LM, Lee MT (2008) A comparative experimental–theoretical study on elastic electron scattering by methane. J Phys B: At Mol Opt Phys 41:045203

    Article  ADS  Google Scholar 

  84. Bundschuy CT, Gibsony JC, Gulleyz RJ, Brungerx MJ, Buckmany SJ, Sannak N, Gianturco FA (1997) Low-energy electron scattering from methane. J Phys B: At Mol Opt Phys 30:2239–2259

    Article  ADS  Google Scholar 

  85. Sohn W, Kochem KH, Scheuerlein KM, Jung K, Ehrhardt H (1986) Elastic electron scattering from CH4, for collision energies between 0.2 and 5 eV. J Phys B: At Mol Phys 19:3625–3632

    Article  ADS  Google Scholar 

  86. Nakamura Y (2010) Electron swarm parameters in pure C2H2 and in C2H2–Ar mixtures and electron collision cross sections for the C2H2 molecule. J Phys D Appl Phys 43:365201

    Article  Google Scholar 

  87. Khakoot MA, Jayawee T, Wangs S, Trajmarg S (1999) Differential electron scattering from acetylene-elastic scattering and vibrational excitation. J Phys B: At Mol Opt Phys 26:4845–4860

    Article  ADS  Google Scholar 

  88. Kochem KH, Sohn W, Jung K, Ehrhardt H, Changt ES (1985) Direct and resonant vibrational excitation of C2H2 by electron impact from 0 to 3.6 eV. J Phys B: At Mol Opt Phys 18:1253–1266

    Article  ADS  Google Scholar 

  89. Iga I, Lee MT, Rawat P, Brescansin LM, Machado LE (2004) Elastic and total cross-sections for electron scattering by acetylene in the intermediate energy range. Eur Phys J D 31:45–51

    Article  ADS  Google Scholar 

  90. Lee MT, Machado LE, Brescansin LM, Iga I (2005) A theoretical study on elastic electron–CHx (x = 1, 2, 3, 4) collisions in the low-energy range. J Phys B: At Mol Opt Phys 38:3795–3804

    Article  ADS  Google Scholar 

  91. Castroa EAY, Souzab GLC, Brescansind LM, Machadoc LE, Dos Santosc AS, Lee MT (2010) Application of the scaled quasi-free scattering model absorption potential to electron scattering by CHx (x = 1, 2, 3,4). J Electron Spectros Relat Phenom 182:4–10

    Article  Google Scholar 

  92. Michelin SE, Oliveira HL, Kroin T, Soares LSS, Veiteinheimer E, Luz CAR, Lima MF, Fujimoto MM, Lee MT (2005) A comparative study for elastic electron collisions on the isoelectronic CNN, NCN, and CCO radicals. J Chem Phys 122:094309

    Article  ADS  Google Scholar 

  93. Andr′e P, Brunet L, Bussi`ere W, Caillard J, Lombard JM, Picard JP (2004) Transport coefficients of plasmas consisting of insulator vapours. Eur Phys J Appl Phys 25:169–182

    Article  ADS  Google Scholar 

  94. Fujimoto MM, Lee MT, Michelin SE (2004) Elastic cross sections for electron-ketenylidene (C2O) collisions. Phys Rev A 69:052706

    Article  ADS  Google Scholar 

  95. Spencer FE, Phelps AV (1976) Momentum transfer cross sections and conductivity integrals for gases of MHD interest. In: Proceedings of 15th symposium engineering aspects of MHD, University of Pennsylvania, Philadelphia, PA, p IX.9.1

  96. Kovitya P (1984) Thermodynamic and transport properties of ablated vapours of PTFE, alumina, perspex and PVC in the temperature range 5000–30000 K. IEEE Trans Plasma Sci 12:38–42

    Article  ADS  Google Scholar 

  97. Mason EA, Munn RJ (1967) Transport coefficients of ionized gases. Phys Fluids 10:1827–1832

    Article  ADS  Google Scholar 

  98. Devoto RS (1973) Transport properties of ionized gas. Phys Fluids 16:616–623

    Article  ADS  Google Scholar 

  99. Murphy AB (2000) Transport coefficients of hydrogen and argon–hydrogen plasmas. Plasma Chem Plasma Process 20:279–297

    Article  Google Scholar 

  100. Wright MJ, Hwang HH, Schwenke DW (2007) Recommended collision integrals for transport property computations part 2: Mars and Venus entries. AIAA J 45:281–288

    Article  ADS  Google Scholar 

  101. Krěnek P (2008) Thermophysical Properties of H2O–Ar Plasmas at Temperatures 400–50,000 K and Pressure 0.1 MPa. Plasma Chem Plasma Process 28:107–122

    Article  Google Scholar 

  102. Magin T, Sdegrze G, Sokolova I (2002) Thermodynamic and transport properties of Martian atmosphere for space entry application 33rd plasmadynamics and lasers conference. Hawaii, 20–23 May 2002

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Acknowledgments

This work was supported by the Chinese Government Scholarship program for postgraduates and the Dual Collaborative PhD Degree Program between Xi’an Jiaotong University and University of Liverpool.

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Wang, W., Yan, J.D., Rong, M. et al. Thermophysical Properties of High Temperature Reacting Mixtures of Carbon and Water in the Range 400–30,000 K and 0.1–10 atm. Part 2: Transport Coefficients. Plasma Chem Plasma Process 32, 495–518 (2012). https://doi.org/10.1007/s11090-012-9365-0

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