Skip to main content
Log in

Flow of foam through a convergent channel

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

We study experimentally the flow of a foam confined as a bubble monolayer between two plates through a convergent channel. We quantify the velocity, the distribution and orientation of plastic events, and the elastic stress, using image analysis. We use two different soap solutions: a sodium dodecyl sulfate (SDS) solution, with a negligible wall friction between the bubbles and the confining plates, and a mixture containing a fatty acid, giving a large wall friction. We show that for SDS solutions, the velocity profile obeys a self-similar form which results from the superposition of plastic events, and the elastic deformation is uniform. For the other solution, the velocity field differs and the elastic deformation increases towards the exit of the channel. We discuss and quantify the role of wall friction on the velocity profile, the elastic deformation, and the rate of plastic events.

Graphical abstract

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. Cantat, S. Cohen-Addad, F. Elias, F. Graner, R. Höhler, O. Pitois, F. Rouyer, A. Saint-Jalmes, Foams, Structure and Dynamics, edited by S.J. Cox (Oxford University Press, 2013)

  2. G.K. Batchelor, J. Fluid Mech. 41, 545 (1970)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. C. Raufaste, B. Dollet, K. Mader, S. Santucci, R. Mokso, EPL 111, 38004 (2015)

    Article  ADS  Google Scholar 

  4. Y. Wang, K. Krishan, M. Dennin, Phys. Rev. E 73, 031401 (2006)

    Article  ADS  Google Scholar 

  5. G. Katgert, M.E. Möbius, M. van Hecke, Phys. Rev. Lett. 101, 058301 (2008)

    Article  ADS  Google Scholar 

  6. B. Dollet, A. Scagliarini, M. Sbragaglia, J. Fluid Mech. 766, 556 (2015)

    Article  ADS  Google Scholar 

  7. B. Dollet, M. Aubouy, F. Graner, Phys. Rev. Lett. 95, 168303 (2005)

    Article  ADS  Google Scholar 

  8. B. Dollet, M. Durth, F. Graner, Phys. Rev. E 73, 061404 (2006)

    Article  ADS  Google Scholar 

  9. B. Dollet, F. Graner, J. Fluid Mech. 585, 181 (2007)

    Article  MATH  ADS  Google Scholar 

  10. Y. Bertho, C. Becco, N. Vandewalle, Phys. Rev. E 73, 056309 (2006)

    Article  ADS  Google Scholar 

  11. B. Dollet, J. Rheol. 54, 741 (2010)

    Article  ADS  Google Scholar 

  12. T. Okuzono, K. Kawasaki, Phys. Rev. E 51, 1246 (1995)

    Article  ADS  Google Scholar 

  13. D.J. Durian, Phys. Rev. Lett. 75, 4780 (1995)

    Article  ADS  Google Scholar 

  14. I. Cantat, Soft Matter 7, 448 (2011)

    Article  ADS  Google Scholar 

  15. C. Raufaste, B. Dollet, S. Cox, Y. Jiang, F. Graner, Eur. Phys. J. E 23, 217 (2007)

    Article  Google Scholar 

  16. I.T. Davies, S.J. Cox, Colloids Surf. A 344, 8 (2009)

    Article  Google Scholar 

  17. I. Cheddadi, P. Saramito, B. Dollet, C. Raufaste, F. Graner, Eur. Phys. J. E 34, 1 (2011)

    Article  Google Scholar 

  18. F. Boulogne, S.J. Cox, Phys. Rev. E 83, 041404 (2011)

    Article  ADS  Google Scholar 

  19. S.A. Jones, B. Dollet, N. Slosse, Y. Jiang, S.J. Cox, F. Graner, Colloids Surf. A 382, 18 (2011)

    Article  Google Scholar 

  20. V.J. Langlois, J. Rheol. 58, 799 (2014)

    Article  ADS  Google Scholar 

  21. D.A. Reinelt, A.M. Kraynik, J. Fluid Mech. 311, 327 (1996)

    Article  MATH  ADS  Google Scholar 

  22. D.A. Reinelt, A.M. Kraynik, J. Rheol. 44, 453 (2000)

    Article  ADS  Google Scholar 

  23. N.D. Denkov, S. Tcholakova, K. Golemanov, K.P. Ananthapadmanabhan, A. Lips, Soft Matter 5, 3389 (2009)

    Article  ADS  Google Scholar 

  24. S. Arif, J.C. Tsai, S. Hilgenfeldt, EPL 92, 38001 (2010)

    Article  ADS  Google Scholar 

  25. S. Arif, J.C. Tsai, S. Hilgenfeldt, J. Rheol. 56, 485 (2012)

    Article  ADS  Google Scholar 

  26. I. Ben Salem, I. Cantat, B. Dollet, J. Fluid Mech. 714, 258 (2013)

    Article  MATH  ADS  Google Scholar 

  27. J.C. Earnshaw, A.H. Jaafar, Phys. Rev. E 49, 5408 (1994)

    Article  ADS  Google Scholar 

  28. D. Chen, K.W. Desmond, E.R. Weeks, Soft Matter 8, 10486 (2012)

    Article  ADS  Google Scholar 

  29. D. Chen, K.W. Desmond, E.R. Weeks, Phys. Rev. E 91, 062306 (2015)

    Article  ADS  Google Scholar 

  30. G.B. Jeffery, Philos. Mag. 29, 455 (1915)

    Article  MATH  Google Scholar 

  31. G. Hamel, Jahresber. Deutsch. Math.-Verein. 25, 34 (1916)

    MATH  Google Scholar 

  32. K. Pohlhausen, Z. Angew. Math. Mech. 1, 252 (1921)

    Article  MATH  Google Scholar 

  33. L. Landau, E. Lifshitz, Mécanique des fluides, 3ème édition (Mir, 1994)

  34. K. Golemanov, N.D. Denkov, S. Tcholakova, M. Vethamuthu, A. Lips, Langmuir 24, 9956 (2008)

    Article  Google Scholar 

  35. L. Bocquet, A. Colin, A. Ajdari, Phys. Rev. Lett. 103, 036001 (2009)

    Article  ADS  Google Scholar 

  36. D.J. Durian, D.A. Weitz, D.J. Pine, Science 252, 686 (1991)

    Article  ADS  Google Scholar 

  37. S.J. Cox, F. Graner, M.F. Vaz, Soft Matter 4, 1871 (2008)

    Article  ADS  Google Scholar 

  38. K.W. Desmond, E.R. Weeks, Phys. Rev. Lett. 115, 098302 (2015)

    Article  ADS  Google Scholar 

  39. B. Embley, P. Grassia, Colloids Surf. A 382, 8 (2011)

    Article  Google Scholar 

  40. P. Marmottant, F. Graner, Soft Matter 9, 9602 (2013)

    Article  Google Scholar 

  41. M. Durand, H.A. Stone, Phys. Rev. Lett. 97, 226101 (2006)

    Article  ADS  Google Scholar 

  42. A.L. Biance, S. Cohen-Addad, R. Höhler, Soft Matter 5, 4672 (2009)

    Article  ADS  Google Scholar 

  43. V. Mansard, A. Colin, P. Chaudhuri, L. Bocquet, Soft Matter 9, 7489 (2013)

    Article  ADS  Google Scholar 

  44. J.D. Barry, D. Weaire, S. Hutzler, Philos. Mag. Lett. 91, 432 (2011)

    Article  ADS  Google Scholar 

  45. A. Scagliarini, B. Dollet, M. Sbragaglia, Colloids Surf. A 473, 133 (2015)

    Article  Google Scholar 

  46. P. Saramito, J. Non-Newtonian Fluid Mech. 145, 1 (2007)

    Article  MATH  Google Scholar 

  47. J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, Nature 454, 84 (2008)

    Article  ADS  Google Scholar 

  48. E. Janiaud, D. Weaire, S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)

    Article  ADS  Google Scholar 

  49. D. Weaire, S. Hutzler, V.J. Langlois, R.J. Clancy, Philos. Mag. Lett. 88, 387 (2008)

    Article  ADS  Google Scholar 

  50. A. Prosperetti, Advanced Mathematics for Applications (Cambridge University Press, 2011)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Benjamin Dollet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dollet, B., Bocher, C. Flow of foam through a convergent channel. Eur. Phys. J. E 38, 123 (2015). https://doi.org/10.1140/epje/i2015-15123-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2015-15123-3

Keywords

Navigation