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Thermodynamic Properties of Non-equilibrium Plasmas

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Handbook of Thermal Plasmas

Abstract

This chapter is devoted to the analysis of thermodynamic properties of thermal plasmas under nonequilibrium conditions. In the course of the development of thermal plasma technology, the assumption of local thermodynamic equilibrium (LTE) in the hot regions of the plasma has been generally accepted. However, over the past years there has been increasing evidence that the existence of LTE in thermal plasmas is rather the exception than the rule. Therefore, it is important to quantify the effects of deviations from LTE in order to provide guidance for computer simulation of flow, temperature, and particle concentrations in plasma reactors. This can only be achieved through a fundamental understanding of the basic phenomena involved and their influence on the plasma properties. The presentation of this chapter is divided into two main sections. The first section deals with two-temperature plasmas, calculation of the partition function and of the plasma composition, and their influence on the corresponding thermodynamic properties. The second section deals with deviations from local chemical equilibrium introducing the concepts of steady-state kinetic calculations, state-to-state approach, and pseudo-equilibrium calculations. Examples are given mostly for argon and nitrogen plasmas at atmospheric and higher pressures. These are complemented by other gaseous systems including argon–hydrogen, or nitrogen–oxygen, and CO2 mixtures.

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Abbreviations

DC:

Direct Current

LCE:

Local chemical equilibrium

LTE:

Local thermodynamic equilibrium

NIST:

National Institute of Standards and Technology

NLCE:

Non-local chemical equilibrium

NLTE:

Non-local thermodynamic equilibrium

RF:

Radio Frequency

References

  • André P (1995) Partition functions and concentrations in plasmas out of thermal equilibrium. IEEE Trans Plasma Sci 23(3):453–458

    Article  Google Scholar 

  • André P, Abbaoui M, Lefort A, Parizet MJ (1996) Numerical method and composition in multi-temperature plasmas: application to an Ar-H2 mixture. Plasma Chem Plasma Process 16(3):379–398

    Article  Google Scholar 

  • André P, Abbaoui M, Bessege R, Lefort A (1997) Comparison between Gibbs free energy minimization and mass action law for a multitemperature plasma with application to nitrogen. Plasma Chem Plasma Process 17(2):207–217

    Article  Google Scholar 

  • André P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (1999) In: Fauchais P, Amouroux J (eds) Plasma concentrations out of equilibrium: N2 (kinetic method and mass action law), Ar–CCl4 and Ar–H2CCl4 (mass action law). The Annals of the New York Academy of Sciences, New York, pp 85–94

    Google Scholar 

  • André P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (2001) A new modified pseudoequilibrium calculation to determine the composition of hydrogen and nitrogen plasmas at atmospheric pressure. Plasma Chem Plasma Process 21(1):83–105

    Article  Google Scholar 

  • Aubreton J, Elchinger MF, Fauchais P (1998) New method to calculate thermodynamic and transport properties of a multi-temperature plasma: application to N2 plasma. Plasma Chem Plasma Process 18(1):1–27

    Article  Google Scholar 

  • Aubreton J, Elchinger MF, Fauchais P, Rat V, André P (2004) Thermodynamic and transport properties of a ternary Ar–H2–He mixture out of equilibrium up to 30,000K at atmospheric pressure. J Phys D Appl Phys 37:2232–2246

    Article  Google Scholar 

  • Aubreton J, Elchinger MF, Andre P (2013) Influence of partition function and interaction potential on transport properties of thermal plasmas. Plasma Chem Plasma Process 33:367–399

    Article  Google Scholar 

  • Baeva M, Kozakov R, Gorchakov S, Uhrlandt D (2012) Two-temperature chemically non-equilibrium modeling of transferred arcs. Plasma Sources Sci Technol 21:055027, 13 pp

    Article  Google Scholar 

  • Boselli M, Colombo V, Ghedini E, Gherardi M, Sanibondi P (2013) Two-temperature modeling and optical emission spectroscopy of a constant current plasma arc welding process. J Phys D Appl Phys 46(22):224009

    Article  Google Scholar 

  • Capitelli M, Giordano D, Colonna G (2008) The role of Debye-Hückel electronic energy levels on the thermodynamic properties of hydrogen plasmas including isentropic coefficients. Phys Plasmas 15:082115

    Article  Google Scholar 

  • Capitelli M, Armenise I, Bruno D, Cacciatore M, Celiberto R, Colonna G, De Pascale O, Diomede P, Esposito F, Gorse C, Hassouni K, Laricchiuta A, Longo S, Pagano D, Pietanza D, Rutigliano M (2007) Non-equilibrium plasma kinetics: a state-to-state approach. Plasma Sources Sci Technol 16:S30–S44

    Article  Google Scholar 

  • Capitelli M, Armenise I, Bisceglie E, Bruno D, Celiberto R, Colonna G, D’Ammando G, De Pascale O, Esposito F, Gorse C, Laporta V, Laricchiuta A (2012) Thermodynamics, transport and kinetics of equilibrium and non-equilibrium plasmas: a state-to-state approach. Plasma Chem Plasma Process 32:427–450

    Article  Google Scholar 

  • Chen X, Han P (1999) On the thermodynamic derivation of the Saha equation modified to a two-temperature plasma. J Phys D Appl Phys 32:1711–1718

    Article  Google Scholar 

  • Chen DM, Hsu KC, Pfender E (1981) Two-temperature modeling of an arc plasma reactor. Plasma Chem Plasma Process 1:295–314

    Article  Google Scholar 

  • Cliteur GJ, Suzuki K, Tanaka Y, Sakuta T, Matsubara T, Yokomizu Y, Matsumura T (1999) On the determination of the multi-temperature SF6 plasma composition. J Phys D Appl Phys 32:1851–1856

    Article  Google Scholar 

  • Colombo V, Ghedini E, Sanibondi P (2009) Two-temperature thermodynamic and transport properties of argon–hydrogen and nitrogen–hydrogen plasmas. J Phys D Appl Phys 42:055213

    Article  Google Scholar 

  • Colombo V, Ghedini E, Sanibondi P (2011) Two-temperature thermodynamic and transport properties of carbon–oxygen plasmas. Plasma Sources Sci Technol 20:035003

    Article  Google Scholar 

  • Fauchais P, Coudert JF, Vardelle M (1989) In: Flamm D, Aucellio F (eds) Plasma diagnostics, vol 1. Academic, New York, pp 349–446

    Chapter  Google Scholar 

  • Ghorui S, Heberlein JVR, Pfender E (2007) Thermodynamic and transport properties of two-temperature oxygen plasmas. Plasma Chem Plasma Process 27:267–291

    Article  Google Scholar 

  • Ghorui S, Heberlein JVR, Pfender E (2008) Thermodynamic and transport properties of two-temperature nitrogen-oxygen. Plasma Chem Plasma Process 28:553–582

    Article  Google Scholar 

  • Gleizes A, Chervy B, Gonzalez JJ (1999) Calculation of a two-temperature plasma composition: bases and application to SF6. J Phys D Appl Phys 32:2060–2067

    Article  Google Scholar 

  • Gordon MH, Kruger CH (1993) Temperature and density measurements in a recombining argon plasma with diluent. Plasma Chem Plasma Process 13:365–378

    Article  Google Scholar 

  • Herzberg G (1959) Spectra of diatomic molecules. D. van Nostrand Company, New York

    Google Scholar 

  • Hsu KC, Pfender E. Calculation of thermodynamic and transport properties of a two-temperature argon plasma. In: Proceedings of the fifth international symposium on plasma chemistry, vol. 1144. Heriot- Watt University Edinburgh, Scotland

    Google Scholar 

  • Park J, Heberlein J, Pfender E, Candler G, Chang CH (2008) Two-dimensional numerical modeling of direct- current electric arcs in nonequilibrium. Plasma Chem Plasma Process 28:213–231

    Article  Google Scholar 

  • Potapov AV (1966) High Temp 4:48

    Google Scholar 

  • Rat V, André P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (2001) A modified pseudo-equilibrium model competing with kinetic models to determine the composition of a two-temperature SF6 atmosphere plasma. J Phys D Appl Phys 34:2191–2204

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Rat V, André P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (2002b) Two-temperature transport coefficients in argon–hydrogen plasmas – II: inelastic processes and influence of composition. Plasma Chem Plasma Process 22(4):475–493

    Article  Google Scholar 

  • Rat V, André P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (2002c) Two-temperature transport coefficients in argon–hydrogen plasmas – I: elastic processes and collision integrals. Plasma Chem Plasma Process 22(4):453–474

    Article  Google Scholar 

  • Rat V, Murphy AB, Aubreton J, Elchinger MF, Fauchais P (2008) Treatment of non-equilibrium phenom- ena in thermal plasma flows. J Phys D Appl Phys 41:183001, 28 pp

    Article  Google Scholar 

  • Richley E, Tuma DT (1982) On the determination of particle concentrations in multitemperature plasmas. J Appl Phys 53:8537–8542

    Article  Google Scholar 

  • Sourd B, Aubreton J, Elchinger MF, Labrot M, Michon U (2006) High temperature transport coefficients in e/C/H/N/O mixtures. J Phys D Appl Phys 39:1105

    Article  Google Scholar 

  • Tanaka Y (2004) Two-temperature chemically non-equilibrium modelling of high-power Ar–N2 inductively coupled plasmas at atmospheric pressure. J Phys D Appl Phys 37:1190–1205

    Article  Google Scholar 

  • Tanaka Y, Sakuta T (2002) Chemically non-equilibrium modelling of N2 thermal ICP at atmospheric pressure using reaction kinetics. J Phys D Appl Phys 35:468–476

    Article  Google Scholar 

  • Tanaka Y, Yokomizu Y (1997) Particle composition of high-pressure SF6 plasma with electron temperature greater than gas temperature. IEEE Trans Plasma Sci 25(5):991–995

    Article  Google Scholar 

  • Trelles JP, Heberlein JVR, Pfender E (2007) Non-equilibrium modeling of arc plasma torches. J Phys D Appl Phys 40:5937–5952

    Article  Google Scholar 

  • Trelles JP, Chazelas C, Vardelle A, Heberlein JVR (2009) Arc plasma torch modeling. J Therm Spray Technol 18(5–6):728–752

    Article  Google Scholar 

  • van de Sanden MCM, Schram PPJM, Peeters AG, van der Mullen JAM, Kroesen GMW (1989) Thermodynamic generalization of the Saha equation for a two-temperature plasma. Phys Rev A 40:5273–5276

    Article  Google Scholar 

  • Wang H-X, Sun W-P, Sun S-R, Murphy AB, Ju Y (2014) Two-temperature chemical-nonequilibrium modelling of a high-velocity argon plasma flow in a low-power arcjet thruster. Plasma Chem Plasma Process 34:559–577

    Article  Google Scholar 

  • Ye R, Murphy AB, Ishigaki T (2007) Numerical modeling of an Ar–H2 radio-frequency plasma reactor under thermal and chemical nonequilibrium conditions. Plasma Chem Plasma Process 27(2007):189–204

    Article  Google Scholar 

  • Yu L, Pierrot L, Laux CO, Kruger CH (2001) Effects of vibrational nonequilibrium on the chemistry of two-temperature nitrogen plasmas. Plasma Chem Plasma Process 21(4):483–503

    Article  Google Scholar 

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Correspondence to Maher I. Boulos .

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Boulos, M.I., Fauchais, P.L., Pfender, E. (2023). Thermodynamic Properties of Non-equilibrium Plasmas. In: Boulos, M.I., Fauchais, P.L., Pfender, E. (eds) Handbook of Thermal Plasmas. Springer, Cham. https://doi.org/10.1007/978-3-030-84936-8_9

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