Advertisement

Rheologica Acta

, Volume 57, Issue 1, pp 1–14 | Cite as

Slow flows of yield stress fluids: yielding liquids or flowing solids?

  • P. Coussot
Review

Abstract

Yield stress fluids (YSF) exhibit strongly non-linear rheological characteristics. As a consequence, they develop original flow features (as compared to simple fluids) under various boundary conditions. This paper reviews and analyzes the characteristics of a series of slow flows (just beyond yielding) under more or less complex conditions (simple shear flow, flow through a cavity, dip-coating, blade-coating, Rayleigh-Taylor instability, Saffman-Taylor instability) and highlights some of their common original characteristics: (i) a transition from a solid regime to a flowing regime which does not correspond to a true “liquid state,” the flow in this regime may rather be seen as a succession of solid states during very large deformation; (ii) a strong tendency to localization of the yielded regions in some small region of the material while the rest of the material undergoes some deformation in its solid state; (iii) the deformation of YSF interface with another fluid, in the form of fingers tending to penetrate the material via a local liquefaction process. Finally, these observations suggest that slow flows of YSF are a kind of extension of plastic flows for very large deformations and without irreversible changes of the structure. This suggests that the field of plasticity and the field of slow flows of YSF could benefit from each other.

Keywords

Yield stress slow flows plasticity localization 

References

  1. Aytouna M, Paredes J, Shahidzadeh-Bonn N, Moulinet S, Wagner C, Amarouchene Y, Eggers J, Bonn D (2013) Drop formation in non-Newtonian fluids. Phys Rev Lett 110:034501CrossRefGoogle Scholar
  2. Balmforth N, Frigaard I, Ovarlez G (2014) Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu Rev Fluid Mech 46:121–146CrossRefGoogle Scholar
  3. Barral Q, Boujlel J, Chateau X, Rabideau BD, Coussot P (2010) Adhesion of yield stress fluids. Soft Matter 6:1343–1351Google Scholar
  4. Benbow J, Bridgewater J (1993) Paste flow and extrusion. Clarendon Press, OxfordGoogle Scholar
  5. Bittleston S, Guillot D (1991) Mud removal: research improves traditional cementing guidelines. Oilfield Review 3:44–54Google Scholar
  6. Blaes O, Blandford R, Madau P, Koonin S (1990) Slowly accreting neutron-stars and the origin of gamma-ray bursts. Astrophys J 363:612–627CrossRefGoogle Scholar
  7. Boger DV, Walters K (1993) Rheological phenomena in focus. Elsevier, AmsterdamGoogle Scholar
  8. Bonn D, Paredes J, Denn M, Berthier L, Divoux T, Manneville S (2017) Yield stress materials in soft condensed matter. Rev Modern Phys 89:035005CrossRefGoogle Scholar
  9. Boujlel J, Coussot P (2013) Measuring the surface tension of yield stress fluids. Soft Matter 9:5898–5908CrossRefGoogle Scholar
  10. Boujlel J, Maillard M, Lindner A, Ovarlez G, Chateau X, Coussot P (2012) Boundary layer in pastes-displacement of a long object through a yield stress fluid. J Rheol 56:1083–1108CrossRefGoogle Scholar
  11. Burov EB, Molnar P (2008) Small and large-amplitude gravitational instability of an elastically compressible viscoelastic Maxwell solid overlying an inviscid incompressible fluid: dependence of growth rates on wave number and elastic constants at low Deborah numbers. Earth Planetary Sci Lett 275:370CrossRefGoogle Scholar
  12. Chevalier T, Rodts S, Chateau X, Boujlel J, Maillard M, Coussot P (2013) Boundary layer (shear-band) in frustrated viscoplastic flows. EPL 102:48002CrossRefGoogle Scholar
  13. Cloitre M, Bonnecaze RT (2017) A review on wall slip in high solid dispersions. Rheol Acta 56:283–305CrossRefGoogle Scholar
  14. Coleman BD, Markowitz H, Noll W (1966) Viscometric flows of non-Newtonian Fluids. Springer Verlag, BerlinGoogle Scholar
  15. Cottrell AH (1964) The mechanical properties of matter. Wiley, New YorkGoogle Scholar
  16. Coussot P (1999) Saffman-Taylor instability for yield stress fluids. J Fluid Mech 380:363–376CrossRefGoogle Scholar
  17. Coussot P (2014) Yield stress fluid flows: a review of experimental data. J Non-Newt Fluid Mech 221:31–49CrossRefGoogle Scholar
  18. Coussot P (2017) Bingham’s heritage. Rheol Acta 56:163–176CrossRefGoogle Scholar
  19. Coussot P, Malki A, Ovarlez G (2017) Yield Stress Fluids: a 100 Years after Bingham’s Landmark Paper 56:(3)Google Scholar
  20. Coussot P, Gaulard F (2005) Gravity flow instability of viscoplastic materials: the “ketchup drip”. Phys Rev E 72:031409CrossRefGoogle Scholar
  21. Coussot P, Tabuteau H, Chateau X, Tocquer L, Ovarlez G (2006) Aging and solid or liquid behavior in pastes. J Rheol 50:975–994CrossRefGoogle Scholar
  22. Coussot P, Ovarlez G (2010) Physical origin of shear-banding of jammed systems. Eur Phys J E 33:183–188CrossRefGoogle Scholar
  23. Coussot P, Tocquer L, Lanos C, Ovarlez G (2009) Macroscopic vs local rheology of yield stress fluids. J Non-Newtonian Fluid Mech 158:85–90CrossRefGoogle Scholar
  24. Derks D, Lindner A, Creton C, Bonn D (2003) Cohesive failure of thin layers of soft model adhesives under tension. J Appl Phys 93:1557–1566CrossRefGoogle Scholar
  25. Dimonte G, Gore R, Schneider M (1998) Rayleigh-Taylor instability in elastic-plastic materials. Phys Rev Lett 80:1212–1215CrossRefGoogle Scholar
  26. Ebrahimi B, Mostaghimi P, Gholamian H, Sadeghy K (2016) Viscous fingering in yield stress fluids: a numerical study. J Eng Math 97:161–176CrossRefGoogle Scholar
  27. Fontana JV, Lira SA, Miranda JA (2013) Radial viscous fingering in yield stress fluids: onset of pattern formation. Phys Rev E 87:013016CrossRefGoogle Scholar
  28. Hébraud P, Lequeux F, Munch JP, Pine DJ (1997) Yielding and rearrangements in disordered emulsions. Phys Rev Lett 78:4657–4660CrossRefGoogle Scholar
  29. Homsy GM (1987) Viscous fingering in porous media. Ann Rev Fluid Mech 19:271–311CrossRefGoogle Scholar
  30. Israelachvili JN (2001) Intermolecular and surface forces. Academic Press, AmsterdamGoogle Scholar
  31. Jorgensen L, Le Merrer M, Delanoe-Ayari H, Barentin C (2015) Yield stress and elasticity influence on surface tension measurements. Soft Matter 11:5111–5121CrossRefGoogle Scholar
  32. Lidon P, Villa L, Manneville S (2017) Power-law creep and residual stresses in a carbopol gel. Rheol Acta 56:307–323CrossRefGoogle Scholar
  33. Lubliner J (1990) Plasticity theory. Macmillan, New YorkGoogle Scholar
  34. Lindner A, Bonn D, Coussot P (2000) Viscous fingering in a yield stress fluid. Phys Rev Lett 85:314–317CrossRefGoogle Scholar
  35. Lindner A, Bonn D, Poire EC, Ben Amar M (2002) Meunier J. Viscous fingering in non-Newtonian fluids 469:237–256Google Scholar
  36. Liu AJ, Nagel SR (1998) Jamming is not just cool any more. Nature 396:21–22CrossRefGoogle Scholar
  37. Maillard M (2015) Spreading flows of yield stress fluids, PhD thesis, Univ. Paris-Est (in French)Google Scholar
  38. Maillard M, Mézière C, Moucheront P, Courrier C, Coussot P (2016) Blade-coating of yield stress fluids. J Non-Newt Fluid Mech 237:16–25CrossRefGoogle Scholar
  39. Maimouni I, Goyon J, Lac E, Pringuey T, Boujlel J, Chateau X, Coussot P (2016) Rayleigh-Taylor instability in elastoplastic solids: a local, catastrophic process. Phys Rev Lett 116:154502CrossRefGoogle Scholar
  40. Maloney CE, Lemaître A (2006) Amorphous systems in athermal, quasistatic shear. Phys Rev E 74:016118CrossRefGoogle Scholar
  41. Maleki-Jirsaraei N, Lindner A, Rouhani S, Bonn D (2005) Saffman-Taylor instability in yield stress fluids. J Phys Cond Matt 17:S1219–S1228CrossRefGoogle Scholar
  42. Marsh BD (1979) Island-arc development––some observations, experiments, and speculations. J Geol 87:687–713CrossRefGoogle Scholar
  43. Moller P, Fall A, Chikkadi V, Derks D, Bonn D (2009) An attempt to categorize yield stress fluid behavior, philosophical trans. Royal Soci. A: Math Phys Eng Sci 367:5139–5155Google Scholar
  44. Mora S, Phou T, Fromental JM, Pomeau Y (2014) Gravity driven instability in elastic solid layers. Phys Rev Lett 113:178301CrossRefGoogle Scholar
  45. Nadai A (1950) Theory of flow and fracture of solids. McGraw Hill, New YorkGoogle Scholar
  46. Oldroyd JG (1947) A rational formulation of the equations of plastic flow for a Bingham solid. Proc Camb Philos Soc 43:100–105Google Scholar
  47. Ovarlez G, Cohen-Addad S, Krishan K, Goyon J, Coussot P (2013) On the existence of a simple yield stress fluid behavior. J Non-Newt Fluid Mech 193:68–79CrossRefGoogle Scholar
  48. Ovarlez G, Rodts S, Chateau X, Coussot P (2009) Phenomenology and physical origin of shear-localization and shear-banding in complex fluids. Rheol Acta 48:831–844CrossRefGoogle Scholar
  49. Piriz AR, López Cela JJ, Cortázar OD, Tahir NA, Hoffmann DHH (2005) Rayleigh-Taylor instability in elastic solids. Phys Rev E 72:056313CrossRefGoogle Scholar
  50. Piriz AR, Sun YB, Tahir NA (2013) Rayleigh-Taylor stability boundary at solid-liquid interfaces. Phys Rev E 88:023026CrossRefGoogle Scholar
  51. Rahmani Y, Habibi M, Javadi A, Bonn D (2011) Coiling of yield stress fluids. Phys Rev E 83:056327CrossRefGoogle Scholar
  52. Rayleigh SJW (1883) Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc Lond Math Soc 14:170–177Google Scholar
  53. Robinson AC, Swegle JW (1989) Acceleration instability in elastic-plastic solids 2. Analytical techniques. J Appl Phys 66:2859–2872CrossRefGoogle Scholar
  54. Sharp DH (1984) An overview of Rayleigh-Taylor instability. Physica 12D:3–18Google Scholar
  55. Sollich P, Lequeux F, Hébraud P, Cates ME (1997) Rheology of soft glassy materials. Phys Rev Lett 78:2020CrossRefGoogle Scholar
  56. Tabor D (1991) Gases, liquids and solids. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  57. Terrones G (2005) Fastest growing linear Rayleigh-Taylor modes at solid/fluid and solid/solid interfaces. Phys Rev E 71:036306CrossRefGoogle Scholar
  58. Yoshitake Y, Mitani S, Salai K, Takagi K (2008) Surface tension and elasticity of gel studied with laser-induced surface-deformation spectroscopy. Phys Rev E 78:041405CrossRefGoogle Scholar
  59. Zaleski S, Julien P (1992) Numerical simulation of Rayleigh-Taylor instability for single and multiple salt diapirs. Tectonophysics 206:55–69CrossRefGoogle Scholar
  60. Zhang X, Lorenceau E, Basset P, Bourouina T, Rouyer F, Goyon J, Coussot P (2017) Wall slip of soft-jammed systems: a generic, apparent simple shear process, to appear in Phys Rev LettGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Université Paris-EstLaboratoire Navier (ENPC-IFSTTAR-CNRS)Champs-sur-MarneFrance

Personalised recommendations