Shock Waves

, Volume 28, Issue 2, pp 141–151 | Cite as

Non-equilibrium theory employing enthalpy-based equation of state for binary solid and porous mixtures

Original Article

Abstract

A generalized enthalpy-based equation of state, which includes thermal electron excitations and non-equilibrium thermal energies, is formulated for binary solid and porous mixtures. Our approach gives rise to an extra contribution to mixture volume, in addition to those corresponding to average mixture parameters. This excess term involves the difference of thermal enthalpies of the two components, which depend on their individual temperatures. We propose to use the Hugoniot of the components to compute non-equilibrium temperatures in the mixture. These are then compared with the average temperature obtained from the mixture Hugoniot, thereby giving an estimate of non-equilibrium effects. The Birch–Murnaghan model for the zero-temperature isotherm and a linear thermal model are then used for applying the method to several mixtures, including one porous case. Comparison with experimental data on the pressure–volume Hugoniot and shock speed versus particle speed shows good agreement.

Keywords

Equation of state Hugoniot Mixture theory Grüneisen parameter Enthalpy parameter 

Notes

Acknowledgements

The authors thank the reviewers and editor of Shock Waves for critical reviews and suggestions to improve the presentation of the paper.

References

  1. 1.
    Trunin, R.F.: Shock Compression of Condensed Materials. Cambridge University Press, Cambridge (1998)CrossRefGoogle Scholar
  2. 2.
    Davison, L.: Fundamentals of Shock Wave Propagation in Solids. Springer, Berlin (2008)MATHGoogle Scholar
  3. 3.
    Zeldovich, Y.B., Raizer, Y.P.: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Vol -II. Academic, New York (1967)Google Scholar
  4. 4.
    Kapila, A.K., Menikoff, R., Bdzil, J.B., Son, S.F., Stewart, D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations. Phys. Fluids 13, 3002–3024 (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Duvall, G.E., Taylor, S.M.: Shock parameters in a two component mixture. J. Compos. Mater. 5(2), 130–139 (1971)CrossRefGoogle Scholar
  6. 6.
    Krueger, B.R., Vreeland, T.: A Hugoniot theory for solid and powder mixtures. J. Appl. Phys. 69(2), 710–716 (1991)CrossRefGoogle Scholar
  7. 7.
    Gavrilyuk, S.L., Saurel, R.: Rankine–Hugoniot relations for shocks in heterogeneous mixtures. J. Fluid Mech. 575(1), 495–507 (2007)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Dremin, A.N., Karpukhin, I.A.: Method of determination of shock adiabat of the dispersed substances. Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki 1(3), 184–188 (1960). (in Russian)Google Scholar
  9. 9.
    Alekseev, YuF, Al’tshuler, L.V., Krupnikova, V.P.: Shock compression of two-component paraffin–tungsten mixtures. J. Appl. Mech. Tech. Phys. 12(4), 624–627 (1971)CrossRefGoogle Scholar
  10. 10.
    Saurel, R., Le Metayer, O., Massoni, J., Gavrilyuk, S.: Shock jump relations for multiphase mixtures with stiff mechanical relaxation. Shock Waves 16(3), 209–232 (2007)CrossRefMATHGoogle Scholar
  11. 11.
    McQueen, R.G., Marsh, S.P., Taylor, J.W., Fritz, J.N., Carter, W.J.: The Equation of State of Solids from Shock Wave Studies. In: Kinslow, R. (ed.) High Velocity Impact Phenomena, pp. 293–417. Academic, New York (1970)Google Scholar
  12. 12.
    Batsanov, S.S.: Effects of Explosions on Materials: Modification and Synthesis Under High-Pressure Shock Compression. Springer, Berlin (1994)CrossRefGoogle Scholar
  13. 13.
    Petel, O.E., Jette, F.X.: Comparison of methods for calculating the shock hugoniot of mixtures. Shock Waves 20, 73–83 (2010)CrossRefMATHGoogle Scholar
  14. 14.
    Zhang, X.F., Qiao, L., Shi, A.S., Zhang, J., Guan, Z.W.: A cold energy mixture theory for the equation of state in solid and porous metal mixtures. J. Appl. Phys. 110(1), 013506-1–013506-10 (2011)Google Scholar
  15. 15.
    Zhang, X.F., Shi, A.S., Zhang, J., Qiao, L., He, Y., Guan, Z.W.: Thermochemical modeling of temperature controlled shock-induced chemical reactions in multifunctional energetic structural materials under shock compression. J. Appl. Phys. 111(12), 123501-1–123501-9 (2012)Google Scholar
  16. 16.
    Rice, M.H., Walsh, J.M.: Equation of state of water to 250 kilobars. J. Chem. Phys. 26, 824–830 (1957)Google Scholar
  17. 17.
    Wu, Q., Jing, F.: Thermodynamic equation of state and application to Hugoniot predictions for porous materials. J. Appl. Phys. 80(8), 4343–4349 (1996)CrossRefGoogle Scholar
  18. 18.
    Boshoff-Mostert, L., Viljoen, H.J.: Comparative study of analytical methods for Hugoniot curves of porous materials. J. Appl. Phys. 86(3), 1245–1254 (1999)CrossRefGoogle Scholar
  19. 19.
    Nayak, B., Menon, S.V.G.: Explicit accounting of electronic effects on the Hugoniot of porous materials. J. Appl. Phys. 119(12), 125901–125907 (2016)CrossRefGoogle Scholar
  20. 20.
    Kormer, S.B., Funtikov, A.I., Urlin, V.D., Kolesnikova, A.N.: Dynamic compression of porous metals and the equation of state with variable specific heat at high temperatures. Sov. Phys. JETP 15(3), 477–488 (1962)Google Scholar
  21. 21.
    Carroll, M.M., Holt, A.C.: Static and dynamic pore-collapse relations for ductile porous materials. J. Appl. Phys. 43(4), 1626–1636 (1972)CrossRefGoogle Scholar
  22. 22.
    Walsh, J.M., Christian, R.H.: Equation of state of metals from shock wave measurements. Phys. Rev. 97(6), 1544–1556 (1955)CrossRefGoogle Scholar
  23. 23.
    Marsh, S.P.: LASL Shock Hugoniot Data. University of California Press, California (1980)Google Scholar
  24. 24.
    Bushman, A.V., Lomonosov, I.V., Khishchenko, K. V.: Shock wave data base. (2004). http://teos.ficp.ac.ru/rusbank. Accessed 25 Mar 2017
  25. 25.
    Birch, F.: Elasticity and constitution of the Earth’s interior. J. Geophys. Res. 57(2), 227–286 (1952)CrossRefGoogle Scholar
  26. 26.
    Vinet, P., Smith, J.R., Ferrante, J., Rose, J.H.: Temperature effects on the universal equation of state of solids. Phys. Rev. B 35(4), 1945–1953 (1987)CrossRefGoogle Scholar
  27. 27.
    Vinet, P., Rose, J.H., Ferrante, J., Smith, J.R.: Universal features of the equation of state of solids. J. Phys. Condens. Matter 1(11), 1941–1963 (1989)CrossRefGoogle Scholar
  28. 28.
    Hama, J., Suito, K.: The search for a universal equation of state correct up to very high pressures. J. Phys. Condens. Matter 8(1), 67–81 (1996)CrossRefGoogle Scholar
  29. 29.
    Young, D.A., Corey, E.M.: A new global equation of state for hot, dense matter. J. Appl. Phys. 78(6), 3748–3755 (1995)CrossRefGoogle Scholar
  30. 30.
    Burakovsky, L., Preston, D.L.: Analytic model of the Grüneisen parameter for all densities. J. Phys. Chem. Solids 65(8–9), 1581–1587 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Bhabha Atomic Research CentreMumbaiIndia
  2. 2.MumbaiIndia

Personalised recommendations