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Hydrodynamic Analysis of Sound Wave Propagation in a Reactive Mixture Confined Between Two Parallel Plates

  • Denize Kalempa
  • Adriano W. Silva
  • Ana Jacinta Soares
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 258)

Abstract

The aim of this work is to study the problem of sound wave propagation through a binary mixture undergoing a reversible chemical reaction of type A \(+\) A \(\rightleftharpoons \) B \(+\) B, when the mixture is confined between two flat, infinite and parallel plates. One plate is stationary, whereas the other oscillates harmonically in time and constitutes an emanating source of sound waves that propagate in the mixture. The boundary conditions imposed in our problem correspond to assume that the plates are impenetrable and that the mixture chemically react at the surface plates, reaching the chemical equilibrium instantaneously. The reactive mixture is described by the Navier-Stokes equations derived from the Boltzmann equation in a chemical regime for which the chemical reaction is in its final stage. Explicit expressions for transport coefficients and chemically production rates are supplemented by the kinetic theory. Starting from this setting, we study the dynamics of the sound waves in the reactive mixture in the low frequency regime and investigate the influence of the chemical reaction on the properties of interest in the considered problem. We then compute the amplitude and phase profiles of the relevant macroscopic quantities, showing how they vary in the reactive flow between the plates in dependence on several factors, as the chemical activation energy, concentration of products and reactants, as well as oscillation speed parameter.

Keywords

Sound propagation Chemically reactive mixtures Kinetic theory Navier-Stokes equations 

Notes

Acknowledgements

The paper is partially supported by CMAT-University of Minho, through the FCT research Project UID/MAT/00013/2013.

References

  1. 1.
    Sharipov, F., Marques Jr., W., Kremer, G.M.: Free molecular sound propagation. J. Acoust. Soc. Am. 112, 395–401 (2002)CrossRefGoogle Scholar
  2. 2.
    Hadjiconstantinou, N.G.: Sound wave propagation in transition-regime micro- and nanochannels. Phys. Fluids 14, 802–809 (2002)CrossRefGoogle Scholar
  3. 3.
    Marques Jr., W., Alves, G.M., Kremer, G.M.: Light scattering and sound propagation in a chemically reacting binary gas mixture. Phys. A 323, 401–412 (2003)CrossRefGoogle Scholar
  4. 4.
    Hansen, J.S., Lemarchand, A.: Mixing of nanofluids: molecular dynamics simulations and modelling. Mol. Simul. 32, 419–426 (2007)CrossRefGoogle Scholar
  5. 5.
    Kalempa, D., Sharipov, F.: Sound propagation through a rarefied gas confined between source and receptor at arbitrary Knudsen number and sound frequency. Phys. Fluids 21(103601), 1–14 (2009)zbMATHGoogle Scholar
  6. 6.
    Groppi, M., Desvillettes, L., Aoki, K.: Kinetic theory analysis of a binary mixture reacting on a surface. Eur. Phys. J. B 70, 117–126 (2009)CrossRefGoogle Scholar
  7. 7.
    Greenspan, M.: Propagation of sound in five monatomic gases. J. Acoust. Soc. Am. 28, 644–648 (1956)CrossRefGoogle Scholar
  8. 8.
    Sharipov, F.: Data on the velocity slip and temperature jump on a gas-solid interface. J. Phys. Chem. Ref. Data 40(023101), 1–28 (2011)Google Scholar
  9. 9.
    Desvillettes, L., Lorenzani, S.: Sound wave resonances in micro-electro-mechanical systems devices vibrating at high frequencies according to the kinetic theory of gases. Phys. Fluids 24(092001), 1–24 (2014)Google Scholar
  10. 10.
    Bisi, M., Lorenzani, S.: High-frequency sound wave propagation in binary gas mixtures flowing through microchannels. Phys. Fluids 28(052003), 1–21 (2016)Google Scholar
  11. 11.
    Kalempa, D., Sharipov, F.: Sound propagation through a binary mixture of rarefied gases at arbitrary sound frequency. Eur. J. Mech. B/Fluids 57, 50–63 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sharipov, F., Kalempa, D.: Velocity slip and temperature jump coefficients for gaseous mixtures. IV. Temperature jump coefficient. Int. J. Heat Mass Transf. 48, 1076–1083 (2005)CrossRefGoogle Scholar
  13. 13.
    Sharipov, F., Kalempa, D.: Numerical modeling of the sound propagation through a rarefied gas in a semi-infinite space on the basis of linearized kinetic equation. J. Acoust. Soc. Am. 124, 1993–2001 (2008)CrossRefGoogle Scholar
  14. 14.
    Marques Jr., W., Kremer, G.M., Soares, A.J.: Influence of reaction heat on time dependent processes in a chemically reacting binary mixture. In: Proceedings of 28th International Symposium on Rarefied Gas Dynamics 2012. AIP Conference, vol. 1501, pp. 137–144 (2012)Google Scholar
  15. 15.
    Ramos, M.P., Ribeiro, C., Soares, A.J.: Modelling and analysis of time dependent processes in a chemically reactive mixture. Continuum Mech. Thermodyn. 30, 127–144 (2018)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Garcia-Colin, L.S., de la Selva, S.M.Y.: On the propagation of sound in chemically reacting fluids. Physica 75, 37–56 (1974)CrossRefGoogle Scholar
  17. 17.
    Barton, J.P.: Sound propagation within a chemically reacting ideal gas. J. Acoust. Soc. Am. 81, 233–237 (1987)CrossRefGoogle Scholar
  18. 18.
    Haque, M.Z., Barton, J.P.: A theoretical tool to predict the effects of chemical kinetics on sound propagation within high temperature hydrocarbon combustion products. In: ASME Proceedings of International Gas Turbine Aeroengine Congress and Exhibition, vol. 2, Paper No. 99-GT-276, pp. 1–6 (1999)Google Scholar
  19. 19.
    Kremer, G.M.: An Introduction to the Boltzmann Equation and Transport Processes in Gases. Springer, Berlin (2010)CrossRefGoogle Scholar
  20. 20.
    Sharipov, F.: Rarefied Gas Dynamics: Fundamentals for Research and Practice. Wiley-VCH (2015)Google Scholar
  21. 21.
    Radtke, G.A., Hadjiconstantinou, N.G., Takata, S., Aoki, K.: On the second-order temperature jump coefficient of a dilute gas. J. Fluid Mech. 707, 331–341 (2012)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Struchtrup, H., Weiss, W.: Temperature jump and velocity slip in the moment method. Continuum Mech. Thermodyn. 12, 1–18 (2000)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Struchtrup, H.: Maxwell boundary condition and velocity dependent accommodation coefficient. Phys. Fluids 25(112001), 1–12 (2013)Google Scholar
  24. 24.
    Alves, G.M., Kremer, G.M.: Effect of chemical reactions on the transport coefficients of binary mixtures. J. Chem Phys. 117, 2205–2215 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Denize Kalempa
    • 1
  • Adriano W. Silva
    • 2
  • Ana Jacinta Soares
    • 3
  1. 1.Departamento de Ciências Básicas e AmbientaisEscola de Engenharia de Lorena, Universidade de São PauloLorenaBrazil
  2. 2.Instituto Federal de Educação, Ciência e Tecnologia do ParanáCuritibaBrazil
  3. 3.CMAT, Universidade do MinhoBragaPortugal

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