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Thermosolutal Marangoni effects on the inclined flow of a binary liquid with variable density. I. Linear stability analysis

J. P. Pascal*

S. J. D. D'Alessio†

  • Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada

  • Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

  • *jpascal@ryerson.ca
  • †sdalessio@uwaterloo.ca
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Phys. Rev. Fluids 1, 083603 – Published 30 December, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.083603

Abstract

We consider the stability of a binary liquid film flowing down a heated incline. A theoretical model is implemented which captures the Soret effect and the dependence of surface tension on both temperature and solutal concentration. The model also allows for variation in the density of the liquid mixture with thermal and solutal differences. A linear stability analysis is performed with asymptotic and numerical results being obtained. The coupling of the effect of a variable density with the thermosolutal-Marangoni instability and the Soret effect is investigated. Good agreement with previous results for the constant density case is found.

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Thermosolutal Marangoni effects on the inclined flow of a binary liquid with variable density. II. Nonlinear analysis and simulations

S. J. D. D'Alessio and J. P. Pascal
Phys. Rev. Fluids 1, 083604 (2016)

Article Text

References (26)

  1. P. L. Kapitza and S. P. Kapitza, Wave flow of thin layers of a viscous fluid, Part III: Experimental study of undulatory flow conditions, Zh. Eksperim. i Teor. Fiz. 19, 105 (1949).
  2. T. B. Benjamin, Wave formation in laminar flow down an inclined plane, J. Fluid Mech. 2, 554 (1957).
  3. C.-S. Yih, Stability of liquid flow down an inclined plane, Phys. Fluids 6, 321 (1963).
  4. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  5. S. Kalliadasis, C. Ruyer-Quil, B. Scheid, and M. G. Velarde, Falling Liquid Films (Springer, London, 2012).
  6. S. J. D. D'Alessio, J. P. Pascal, and H. A. Jasmine, Instability in gravity-driven flow over uneven surfaces, Phys. Fluids 21, 062105 (2009).
  7. C. Heining and N. Aksel, Bottom reconstruction in thin-film flow over topography: Steady solution and linear stability, Phys. Fluids 21, 083605 (2009).
  8. P. M. J. Trevelyan, B. Scheid, C. Ruyer-Quil, and S. Kalliadasis, Heated falling films, J. Fluid Mech. 592, 295 (2007).
  9. S. J. D. D'Alessio, J. P. Pascal, H. A. Jasmine, and K. A. Ogden, Film flow over heated wavy inclined surfaces, J. Fluid Mech. 665, 418 (2010).
  10. J. P. Pascal, Linear stability of fluid flow down a porous inclined plane, J. Phys. D 32, 417 (1999).
  11. T. B. Benjamin, Effects of surface contamination on wave formation in falling liquid films, Arch. Mech. Stosow. 16, 615 (1964).
  12. S. Whitaker, Effect of surface active agents on the stability of falling liquid films, Ind. Eng. Chem. Fundam. 3, 132 (1964).
  13. M. G. Blyth and C. Pozrikidis, Effect of surfactant on the stability of film flow down an inclined plane, J. Fluid Mech. 521, 241 (2004).
  14. A. Pereira, P. M. J. Trevelyan, U. Thiele, and S. Kalliadasis, Dynamics of a horizontal thin liquid film in the presence of reactive surfactants, Phys. Fluids 19, 112102 (2007).
  15. A. Pereira and S. Kalliadasis, Dynamics of a falling film with solutal Marangoni effect, Phys. Rev. E 78, 036312 (2008).
  16. G. Karapetsas and V. Bontozoglou, The primary instability of falling films in the presence of soluble surfactants, J. Fluid Mech. 729, 123 (2013).
  17. G. Karapetsas and V. Bontozoglou, The role of surfactants on the mechanism of long-wave instability in liquid film flows, J. Fluid Mech. 741, 139 (2014).
  18. J. K. Bhattacharjee, Marangoni convection in binary liquids, Phys. Rev. E 50, 1198 (1994).
  19. S. W. Joo, Marangoni instabilities in liquid mixtures with Soret effect, J. Fluid Mech. 293, 127 (1995).
  20. A. Podolny, A. Oron, and A. A. Nepomnyashchy, Long-wave Marangoni instability in a binary-liquid layer with deformable interface in the presence of Soret effect: Linear theory, Phys. Fluids 17, 104104 (2005).
  21. A. Podolny, A. Oron, and A. A. Nepomnyashchy, Linear and nonlinear theory of long-wave Marangoni instability with the Soret effect at finite Biot numbers, Phys. Fluids 18, 054104 (2006).
  22. A. Podolny, A. Oron, and A. A. Nepomnyashchy, Long-wave Marangoni instability in a binary liquid layer on a thick solid substrate, Phys. Rev. E 76, 026309 (2007).
  23. M. Morozov, A. Oron, and A. A. Nepomnyashchy, Nonlinear dynamics of long-wave Marangoni convection in a binary mixture with the Soret effect, Phys. Fluids 25, 052107 (2013).
  24. J. Hu, H. Ben Hadid, D. Henry, and A. Mojtabi, Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate, J. Fluid Mech. 599, 269 (2008).
  25. S. J. D. D'Alessio, C. J. M. P. Seth, and J. P. Pascal, The effects of variable fluid properties on thin film stability, Phys. Fluids 26, 122105 (2014).
  26. J. Hu, H. Ben Hadid, and D. Henry, Linear stability analysis of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect, Phys. Fluids 19, 034101 (2007).

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Phys. Rev. Fluids 1, 083603– Published 30 December, 2016
  • Received 7 July 2016

©2016 American Physical Society

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