Skip to main content
SpringerLink
Log in

Sliding droplets of Xanthan solutions: A joint experimental and numerical study

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

Abstract.

We have investigated the sliding of droplets made of solutions of Xanthan, a stiff rodlike polysaccharide exhibiting a non-Newtonian behavior, notably characterized by a shear thinning viscosity accompanied by the emergence of normal stress difference as the polymer concentration is increased. These experimental results are quantitatively compared with those of Newtonian fluids (water). The impact of the non-Newtonian behavior on the sliding process was shown through the relation between the average dimensionless velocity (i.e. the capillary number) and the dimensionless volume forces (i.e. the Bond number). To this aim, it is needed to define operative strategies to compute the capillary number for the shear thinning fluids and compare with the corresponding Newtonian case. The resulting capillary number for the Xanthan solutions scales linearly with the Bond number at small inclinations, as well known for Newtonian fluids, while it shows a plateau as the Bond number is increased. Experimental data were complemented with lattice Boltzmann numerical simulations of sliding droplets, aimed to disentangle the specific contribution of shear thinning and elastic effects on the sliding behavior. In particular the deviation from the linear (Newtonian) trend is more likely attributed to the emergence of normal stresses inside the non-Newtonian droplet.

Graphical abstract

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N.J. Cira, A. Benusiglio, M. Prakash, Nature 519, 446 (2015)

    Article  ADS  Google Scholar 

  2. D. ’t Mannetje, S. Ghosh, R. Lagraauw, S. Otten, A. Pit, C. Berendsen, J. Zeegers, D. van den Ende, F. Mugele, Nat. Commun. 5, 3559 (2014)

    Article  Google Scholar 

  3. M.J. Jebrail, H. Yang, J.M. Mudrik, N.M. Lafrenière, C. McRoberts, O.Y. Al-Dirbashi, L. Fisher, P. Chakraborty, A.R. Wheeler, Lab on a Chip 11, 3218 (2011)

    Article  Google Scholar 

  4. D.K.N. Sinz, A.A. Darhuber, Lab on a Chip 12, 705 (2012)

    Article  Google Scholar 

  5. H. Gau, S. Herminghaus, P. Lenz, R. Lipowsky, Science 283, 46 (1999)

    Article  ADS  Google Scholar 

  6. G. Lagubeau, M. Le Merrer, C. Clanet, D. Quéré, Nat. Phys. 7, 395 (2011)

    Article  Google Scholar 

  7. K. Piroird, B.D. Texier, C. Clanet, D. Quéré, Physics Fluids (1994-present) 25, 032108 (2013)

    Article  ADS  Google Scholar 

  8. P. Sartori, D. Quagliati, S. Varagnolo, M. Pierno, G. Mistura, F. Magaletti, C.M. Casciola, New J. Phys. 17, 113017 (2015)

    Article  ADS  Google Scholar 

  9. S.F. Kistler, P.M. Schweizer, Liquid Film Coating (Chapman and Hall, London, 1997)

  10. P.G. De Gennes, Rev. Mod. Phys. 57, 827 (1985)

    Article  ADS  Google Scholar 

  11. C. Furmidge, J. Colloid Interface Sci. 17, 309 (1962)

    Article  Google Scholar 

  12. C. Huh, C. Scriven, J. Colloid Interface Sci. 35, 85 (1971)

    Article  Google Scholar 

  13. J. Buehrle, S. Herminghaus, F. Mugele, Langmuir 18, 9771 (2002)

    Article  Google Scholar 

  14. R. Seemann, M. Brinkmann, E.J. Kramer, F.F. Lange, R. Lipowsky, Proc. Nat. Acad. Sci. U.S.A. 102, 1848 (2005)

    Article  ADS  Google Scholar 

  15. T. Podgorski, J.M. Flesselles, L. Limat, Phys. Rev. Lett. 87, 036102 (2001)

    Article  ADS  Google Scholar 

  16. H. Kim, H. Lee, B. Kang, J. Colloid Interface Sci. 247, 372 (2002)

    Article  Google Scholar 

  17. E. Rio, A. Daerr, B. Andreotti, L. Limat, Phys. Rev. Lett. 94, 024503 (2005)

    Article  ADS  Google Scholar 

  18. S. Varagnolo, D. Ferraro, P. Fantinel, M. Pierno, G. Mistura, G. Amati, L. Biferale, M. Sbragaglia, Phys. Rev. Lett. 111, 066101 (2013)

    Article  ADS  Google Scholar 

  19. M. Sbragaglia, L. Biferale, G. Amati, S. Varagnolo, D. Ferraro, G. Mistura, M. Pierno, Phys. Rev. E 89, 012406 (2014)

    Article  ADS  Google Scholar 

  20. S. Varagnolo, V. Schiocchet, D. Ferraro, M. Pierno, G. Mistura, M. Sbragaglia, A. Gupta, G. Amati, Langmuir 30, 2401 (2014)

    Article  Google Scholar 

  21. R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of polymeric liquids (J. Wiley & Sons, 1987)

  22. M. Herrchen, H. Oettinger, J. Non-Newton. Fluid Mech. 68, 17 (1997)

    Article  Google Scholar 

  23. A. Lindner, J. Vermant, D. Bonn, Physica A 319, 125 (2003)

    Article  ADS  Google Scholar 

  24. P. Arratia, L.A. Cramer, J. Gollub, D.J. Durian, New J. Phys. 11, 115006 (2009)

    Article  ADS  Google Scholar 

  25. Y. Wei, E. Ramé, L. Walker, S. Garoff, J. Phys.: Condens. Matter 21, 464126 (2009)

    ADS  Google Scholar 

  26. Y. Wei, G. Seevaratnam, S. Garoff, E. Ramé, L. Walker, J. Colloid Interface Sci. 313, 274 (2007)

    Article  Google Scholar 

  27. D.E. Weidner, L.W. Schwartz, Phys. Fluids 6, 3535 (1994)

    Article  MATH  ADS  Google Scholar 

  28. L. Ansini, L. Giacomelli, Nonlinearity 15, 2147 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. A. Carré, P. Woehl, Langmuir 18, 3600 (2002)

    Article  Google Scholar 

  30. A. Carré, F. Eustache, C. R. Acad. Sci. Paris 325, 709 (1997)

    Google Scholar 

  31. A. Carré, F. Eustache, Langmuir 16, 2936 (2000)

    Article  Google Scholar 

  32. S. Rafai, D. Bonn, A. Boudaoud, J. Fluid Mech. 513, 77 (2004)

    Article  MATH  ADS  Google Scholar 

  33. S. Rafai, D. Bonn, Physica A 358, 58 (2005)

    Article  ADS  Google Scholar 

  34. L.H. Tanner, J. Phys. D 12, 1473 (1979)

    Article  ADS  Google Scholar 

  35. A. Baudaud, Eur. Phys. J. E 22, 107 (2007)

    Article  Google Scholar 

  36. J.S. Ro, G. Homsy, J. Non-Newton. Fluid Mech. 57, 203 (1995)

    Article  Google Scholar 

  37. A. Borkar, J. Tsamopoulos, S. Gupta, R. Gupta, Phys. Fluids 6, 3539 (1994)

    Article  ADS  Google Scholar 

  38. M. Bajaj, J. Prakash, M. Pasquali, J. Non-Newton. Fluid Mech. 149, 104 (2008)

    Article  MATH  Google Scholar 

  39. A. Abedijaberi, G. Bhatara, E. Shaqfeh, B. Khomami, J. Non-Newton. Fluid Mech. 166, 614 (2011)

    Article  MATH  Google Scholar 

  40. N. Fraysse, G. Homsy, Phys. Fluids 6, 1491 (1994)

    Article  ADS  Google Scholar 

  41. G. Seevaratnam, L. Walker, E. Ramé, S. Garoff, J. Colloid Interface Sci. 284, 265 (2005)

    Article  Google Scholar 

  42. G. Seevaratnam, Y. Suo, E. Ramé, L. Walker, S. Garoff, Phys. Fluids 19, 012103 (2007)

    Article  ADS  Google Scholar 

  43. P. Yue, J.J. Feng, J. Non-Newton. Fluid Mech. 189, 8 (2012)

    Article  Google Scholar 

  44. J. Han, C. Kim, J. Non-Newton. Fluid Mech. 202, 120 (2013)

    Article  Google Scholar 

  45. J. Han, C. Kim, Rheol Acta 53, 55 (2014)

    Article  Google Scholar 

  46. H. Kusumaatmaja, J. Leopoldes, A. Dupuis, J. Yeomans, Europhys. Lett. 73, 740 (2006)

    Article  ADS  Google Scholar 

  47. H. Kusumaatmaja, J. Yeomans, Langmuir 23, 956 (2007)

    Article  Google Scholar 

  48. H.A. Stone, Annu. Rev. Fluid Mech. 26, 65 (1994)

    Article  ADS  Google Scholar 

  49. V. Kheyfets, S. Kieweg, J. Biomech. Engin. 135, 061009 (2013)

    Article  Google Scholar 

  50. G. Ahmed, M. Sellier, Y. Lee, M. Jermy, T. M., Colloids Surf. A: Physicochem. Eng. Aspects 432, 2 (2013)

    Article  Google Scholar 

  51. L.W. Schwartz, J. Charpin, S. O’Brien, in XXII ICTAM, 25-29 august 2008, Adelaide, Australia (2008)

  52. G. Perazzo, G. Gratton, Phys. Rev. E 67, 016307 (2003)

    Article  ADS  Google Scholar 

  53. G. Perazzo, G. Gratton, Phys. Fluids 17, 013102 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  54. K. Rajagopal, G. Saccomandi, L. Vergori, J. Fluid. Mech. 706, 173 (2012)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  55. H. Morita, S. Plog, T. Kajiya, D. M., J. Phys. Soc. Jpn. 78, 014804 (2009)

    Article  ADS  Google Scholar 

  56. P.T. Callaghan, A.M. Gil, Macromolecules 33, 4116 (2000)

    Article  ADS  Google Scholar 

  57. P.J. Whitcomb, C.W. Macosko, J. Rheol. 22, 493 (1978)

    Article  ADS  Google Scholar 

  58. A. Helmreich, J. Vorwerk, R. Steger, M. Muller, P.O. Brunn, Chem. Engin. J. Biochem. Engin. J. 59, 111 (1995)

    Article  Google Scholar 

  59. D. Bonn, J. Meunier, Phys. Rev. Lett. 79, 2662 (1997)

    Article  ADS  Google Scholar 

  60. M. Zirnsak, D.V. Boger, V. Tirtaatmadja, J. Rheol. 43, 627 (1999)

    Article  ADS  Google Scholar 

  61. F. Varela Lopez, L. Pauchard, M. Rosen, M. Rabaud, J. Non-Newton. Fluid Mech. 103, 123 (2002)

    Article  MATH  Google Scholar 

  62. J. Stokes, L. Macakova, A. Chojnicka-Paszun, C. DeKruif, H. Harmen, H. De Jong, Langmuir 27, 3474 (2011)

    Article  Google Scholar 

  63. R.K. Gupta, M. Ryan, S. T., J. Rheol. 30, 046312 (1986)

    Google Scholar 

  64. D.M. Jones, K. Walters, P.R. Williams, Rheol. Acta 26, 20 (1987)

    Article  Google Scholar 

  65. R.J. Binnington, D.V. Boger, J. Non-Newton. Fluid Mech. 26, 115 (1987)

    Article  Google Scholar 

  66. M.S. Chai, Ph.D. thesis, University of Melbourne, Australia (1990)

  67. H.W. Bewersdorff, R.P. Singh, Rheol. Acta 27, 617 (1988)

    Article  Google Scholar 

  68. D. Won, C. Kim, J. Non-Newton. Fluid Mech. 117, 141 (2004)

    Article  Google Scholar 

  69. T. Toth, D. Ferraro, E. Chiarello, M. Pierno, G. Mistura, G. Bissacco, C. Semprebon, Langmuir 27, 4742 (2011)

    Article  Google Scholar 

  70. D. Ferraro, C. Semprebon, T. Toth, E. Locatelli, M. Pierno, G. Mistura, M. Brinkmann, Langmuir 28, 13919 (2012)

    Article  Google Scholar 

  71. P. Yue, J. Feng, C. Liu, J. Shen, J. Fluid Mech. 515, 293 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  72. P. Yue, J.J. Feng, C. Liu, J. Shen, J. Non-Newton. Fluid Mech. 129, 163 (2005)

    Article  MATH  Google Scholar 

  73. P. Yue, C. Zhou, J.J. Feng, C.F. Ollivier-Gooch, H.H. Hu, J. Comput. Phys. 219, 47 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  74. P. Yue, C. Zhou, J.J. Feng, Phys. Fluids 18, 102102 (2006)

    Article  ADS  Google Scholar 

  75. D. Zhou, P. Yue, J.J. Feng, J. Rheol. 52, 469 (2008)

    Article  ADS  Google Scholar 

  76. N. Moradi, F. Varnik, I. Steinbach, EPL 95, 44003 (2011)

    Article  ADS  Google Scholar 

  77. X. Shan, H. Chen, Phys. Rev. E 47, 1815 (1993)

    Article  ADS  Google Scholar 

  78. X. Shan, H. Chen, Phys. Rev. E 49, 2941 (1994)

    Article  ADS  Google Scholar 

  79. A. Gupta, M. Sbragaglia, A. Scagliarini, J. Comput. Phys. 291, 177 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  80. S. Gabbanelli, G. Drazer, J. Koplik, Phys. Rev. E 72, 046312 (2005)

    Article  ADS  Google Scholar 

  81. C. Wagner, Y. Amarouchene, D. Bonn, J. Eggers, Phys. Rev. Lett. 95, 164504 (2005)

    Article  ADS  Google Scholar 

  82. A. Gupta, M. Sbragaglia, Phys. Rev. E 90, 023305 (2014)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica e Astronomia “G. Galilei” and CNISM, Università di Padova, Via Marzolo, 8, 35131, Padova, Italy

    Silvia Varagnolo, Giampaolo Mistura & Matteo Pierno

  2. Department of Physics and INFN, University of “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

    Mauro Sbragaglia

Authors
  1. Silvia Varagnolo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giampaolo Mistura
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matteo Pierno
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mauro Sbragaglia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Silvia Varagnolo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Varagnolo, S., Mistura, G., Pierno, M. et al. Sliding droplets of Xanthan solutions: A joint experimental and numerical study. Eur. Phys. J. E 38, 126 (2015). https://doi.org/10.1140/epje/i2015-15126-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2015-15126-0

Keywords

Search

Navigation