Skip to main content

Local Equilibrium of the Gibbs Surface for the Two-Phase Binary Mixture

  • Chapter
  • First Online:
Multicomponent Interfacial Transport

Part of the book series: Springer Theses ((Springer Theses))

  • 729 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    \(\widehat{p}_{\parallel}(x)\) gives the surface tension for the dividing surface \(x.\) This can be expanded in the curvatures with the coefficient \(x\widehat{p}_{\parallel}(x)-\widehat{x\,p_{\parallel}}(x)\) for the linear term. Zero of this expression defines the position of the surface of tension \(x^{\gamma}.\)

  2. 2.

    Note, that for some quantities this definition differs from the one, used in [10]. We will come back to this point later.

  3. 3.

    Note, that the scale on Fig. 5.3. is different from the one on Fig. 5.2.

References

  1. Rowlinson JS, Widom B (1982) Molecular theory of capillarity. Clarendon Press, Oxford

    Google Scholar 

  2. Williard Gibbs J (1993) The scientific papers of J. Williard Gibbs. Ox Bow Press

    Google Scholar 

  3. Bakker G (1928) Kapillaritat und Oberflachenspannung, volume 6 of Handbuch der Experimentalphysik. Akad. Verlag, Leipzig

    Google Scholar 

  4. Guggenheim EA (1967) Thermodynamics, 5th edn. North-Holland, Amsterdam

    Google Scholar 

  5. Defay R, Prigogine I (1966) Surface tension and adsorption. Treatise on thermodynamics: based on the methods of Gibbs and De Donder. Longmans, London

    Google Scholar 

  6. Kjelstrup S, Bedeaux D (2008) Non-equilibrium thermodynamics of heterogeneous systems. Series on advances in statistical mechanics, vol 16. World Scientific, Singapore

    Google Scholar 

  7. Bedeaux D (1986) Nonequilibrium thermodynamics and statistical physics of surfaces. Adv Chem Phys 64:47–109

    Article  CAS  Google Scholar 

  8. Bedeaux D, Albano AM, Mazur P (1976) Boundary conditions and non-equilibrium thermodynamics. Phys A 82:438–462

    Google Scholar 

  9. Albano AM, Bedeaux D (1987) Non equilibrium electro thermodynamics of polarizable multicomponent fluids with an interface. Phys A 147:407–435

    Article  Google Scholar 

  10. Johannessen E, Bedeaux D (2003) The nonequilibrium van der Waals square gradient model. (II). Local equilibrium of the Gibbs surface. Phys A 330:354

    Article  Google Scholar 

  11. Røsjorde A, Fossmo DW, Bedeaux D, Kjelstrup S, Hafskjold B (2000) Non-equilibrium molecular dynamics simulations of steady-state heat and mass transport in condensation I: Local equilibrium. J Colloid Interface Sci 232:178–185

    Article  Google Scholar 

  12. Simon J-M, Kjelstrup S, Bedeaux D, Hafskjold B (2004) Thermal flux through a surface of n-octane. A non-equilibrium molecular dynamics study. J Phys Chem B 108:7186–7195

    Article  CAS  Google Scholar 

  13. Ge J, Kjelstrup S, Bedeaux D, Simon JM, Rousseau B (2007) Coefficients for evaporation of a system with a lennard–jones long range spline potential. Phys Rev E 75:061604–061610

    Google Scholar 

  14. Hafskjold B, Kjelstrup S (1996) Molecular interpretation of coupled heat and mass transport across a vapour/liquid interface. In: Proceedings of the ECOS Conference, pp 1–8

    Google Scholar 

  15. Kjelstrup S, Hafskjold B (1996) Nonequilibrium molecular dynamics simulations of steady-state heat and mass transport in distillation. Ind Eng Chem Res 35:4203–4213

    Article  CAS  Google Scholar 

  16. Olivier M-L (2002) Development of a non-equilibrium mass and heat transfer computation in multiphase hydrocarbon system. Ph.D. thesis, Norwegian University of Science and Technology, Department of Refrigeration and Air Conditioning, Trondheim, Norway. ISBN 82-471-5527-3, ISSN 0809-103X

    Google Scholar 

  17. Olivier M-L, Rollier J-D, Kjelstrup S (2002) Equilibrium properties and surface transfer coefficients from molecular dynamics simulations of two- component fluids. Colloids Surf A: Physicochem Eng Aspects 210:199–222

    Article  CAS  Google Scholar 

  18. Glavatskiy KS, Bedeaux D (2009) Numerical solution of the nonequilibrium square-gradient model and verification of local equilibrium for the Gibbs surface in a two-phase binary mixture. Phys Rev E 79:031608

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kirill Glavatskiy .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Glavatskiy, K. (2011). Local Equilibrium of the Gibbs Surface for the Two-Phase Binary Mixture. In: Multicomponent Interfacial Transport. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15266-5_5

Download citation

Publish with us

Policies and ethics