Entropy production in a fluid-solid system far from thermodynamic equilibrium

  • Bong Jae Chung
  • Blas Ortega
  • Ashwin VaidyaEmail author
Regular Article
Part of the following topical collections:
  1. Non-equilibrium processes in multicomponent and multiphase media


The terminal orientation of a rigid body in a moving fluid is an example of a dissipative system, out of thermodynamic equilibrium and therefore a perfect testing ground for the validity of the maximum entropy production principle (MaxEP). Thus far, dynamical equations alone have been employed in studying the equilibrium states in fluid-solid interactions, but these are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In our past work, we have shown that the MaxEP is a reliable tool to help predict orientational equilibrium states of highly symmetric bodies such as cylinders, spheroids and toroidal bodies. The MaxEP correctly helps choose the stable equilibrium in these cases when the system is slightly out of thermodynamic equilibrium. In the current paper, we expand our analysis to examine i) bodies with fewer symmetries than previously reported, for instance, a half-ellipse and ii) when the system is far from thermodynamic equilibrium. Using two-dimensional numerical studies at Reynolds numbers ranging between 0 and 14, we examine the validity of the MaxEP. Our analysis of flow past a half-ellipse shows that overall the MaxEP is a good predictor of the equilibrium states but, in the special case of the half-ellipse with aspect ratio much greater than unity, the MaxEP is replaced by the Min-MaxEP, at higher Reynolds numbers when inertial effects come into play. Experiments in sedimentation tanks and with hinged bodies in a flow tank confirm these calculations.

Graphical abstract


Topical issue: Non-equilibrium processes in multicomponent and multiphase media 


  1. 1.
    Lars Onsager, Phys. Rev. 37, 405 (1931)CrossRefGoogle Scholar
  2. 2.
    Lars Onsager, Phys. Rev. 38, 2265 (1931)CrossRefGoogle Scholar
  3. 3.
    Ilya Prigogine, Introduction to Thermodynamics of Irreversible Processes, 3rd edition (Interscience, New York, 1967) p. 1Google Scholar
  4. 4.
    Hans Ziegler, An Introduction to Thermomechanics, Vol. 21 (Elsevier, 2012)Google Scholar
  5. 5.
    L.M. Martyushev, V.D. Seleznev, Phys. Rep. 426, 1 (2006)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Adrian Bejan, Sylvie Lorente, Phys. Life Rev. 8, 209 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    L.G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)ADSCrossRefGoogle Scholar
  8. 8.
    Yaoqi Joe Liu, Daniel D. Joseph, J. Fluid Mech. 255, 565 (1993)ADSCrossRefGoogle Scholar
  9. 9.
    Giovanni P. Galdi, Handb. Math. Fluid Dyn. 1, 653 (2002)CrossRefGoogle Scholar
  10. 10.
    Roberto Camassa, Vortex induced oscillations of cylinders at low and intermediate Reynolds numbers, in Advances in Mathematical Fluid Mechanics (Springer, Berlin Heidelberg, 2010) pp. 135--145Google Scholar
  11. 11.
    B. Chung et al., Arch. Appl. Mech. 86, 627 (2016)ADSCrossRefGoogle Scholar
  12. 12.
    R.E. Khayat, R.G. Cox, J. Fluid Mech. 209, 435 (1989)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Bong Jae Chung, Ashwin Vaidya, Physica D: Nonlinear Phenom. 237, 2945 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    Bong Jae Chung, Kirk McDermid, Ashwin Vaidya, Eur. Phys. J. B 87, 20 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    Bong Jae Chung, Ashwin Vaidya, Appl. Math. Comput. 218, 3451 (2011)MathSciNetGoogle Scholar
  16. 16.
  17. 17.
    Ryan Allaire et al., Int. J. Non-Linear Mech. 69, 157 (2015)CrossRefGoogle Scholar
  18. 18.
    Bogdan Nita, Peter Nolan, Ashwin Vaidya, Comput. Appl. Math. 36, 1733 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    F. Candelier, B. Mehlig, J. Fluid Mech. 802, 174 (2016)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    J. Einarsson et al., Phys. Fluids 28, 013302 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Greg A. Voth, Alfredo Soldati, Annu. Rev. Fluid Mech. 49, 249 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    Ichiro Aoki, Ecol. Complex. 3, 56 (2006)CrossRefGoogle Scholar
  23. 23.
    Ashwin Vaidya, MaxEP and Stable Configurations in Fluid-Solid Interactions, in Beyond the Second Law (Springer Berlin, Heidelberg, 2014) pp. 257--276Google Scholar
  24. 24.
    M.M. Zdravkovich, J. Fluid Mech. 350, 377 (1997)Google Scholar
  25. 25.
    Alfred Hubler, Andrey Belkin, Alexey Bezryadin, Complexity 20, 8 (2015)CrossRefGoogle Scholar
  26. 26.
    Tehran J. Davis et al., Ecol. Psychol. 28, 23 (2016)CrossRefGoogle Scholar
  27. 27.
    Dilip Kondepudi, Bruce Kay, James Dixon, Phys. Rev. E 91, 050902 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of BioengineeringGeorge Mason UniversityFairfaxUSA
  2. 2.Department of Mathematical ScienceMontclair State UniversityMontclairUSA

Personalised recommendations