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

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.

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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 110:034501

    Article  Google Scholar 

  2. Balmforth N, Frigaard I, Ovarlez G (2014) Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu Rev Fluid Mech 46:121–146

    Article  Google Scholar 

  3. Barral Q, Boujlel J, Chateau X, Rabideau BD, Coussot P (2010) Adhesion of yield stress fluids. Soft Matter 6:1343–1351

    Google Scholar 

  4. Benbow J, Bridgewater J (1993) Paste flow and extrusion. Clarendon Press, Oxford

    Google Scholar 

  5. Bittleston S, Guillot D (1991) Mud removal: research improves traditional cementing guidelines. Oilfield Review 3:44–54

    Google Scholar 

  6. Blaes O, Blandford R, Madau P, Koonin S (1990) Slowly accreting neutron-stars and the origin of gamma-ray bursts. Astrophys J 363:612–627

    Article  Google Scholar 

  7. Boger DV, Walters K (1993) Rheological phenomena in focus. Elsevier, Amsterdam

    Google 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 89:035005

    Article  Google Scholar 

  9. Boujlel J, Coussot P (2013) Measuring the surface tension of yield stress fluids. Soft Matter 9:5898–5908

    Article  Google 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 56:1083–1108

    Article  Google 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 275:370

    Article  Google Scholar 

  12. Chevalier T, Rodts S, Chateau X, Boujlel J, Maillard M, Coussot P (2013) Boundary layer (shear-band) in frustrated viscoplastic flows. EPL 102:48002

    Article  Google Scholar 

  13. Cloitre M, Bonnecaze RT (2017) A review on wall slip in high solid dispersions. Rheol Acta 56:283–305

    Article  Google Scholar 

  14. Coleman BD, Markowitz H, Noll W (1966) Viscometric flows of non-Newtonian Fluids. Springer Verlag, Berlin

  15. Cottrell AH (1964) The mechanical properties of matter. Wiley, New York

    Google Scholar 

  16. Coussot P (1999) Saffman-Taylor instability for yield stress fluids. J Fluid Mech 380:363–376

    Article  Google Scholar 

  17. Coussot P (2014) Yield stress fluid flows: a review of experimental data. J Non-Newt Fluid Mech 221:31–49

    Article  Google Scholar 

  18. Coussot P (2017) Bingham’s heritage. Rheol Acta 56:163–176

    Article  Google Scholar 

  19. Coussot P, Malki A, Ovarlez G (2017) Yield Stress Fluids: a 100 Years after Bingham’s Landmark Paper 56:(3)

  20. Coussot P, Gaulard F (2005) Gravity flow instability of viscoplastic materials: the “ketchup drip”. Phys Rev E 72:031409

    Article  Google Scholar 

  21. Coussot P, Tabuteau H, Chateau X, Tocquer L, Ovarlez G (2006) Aging and solid or liquid behavior in pastes. J Rheol 50:975–994

    Article  Google Scholar 

  22. Coussot P, Ovarlez G (2010) Physical origin of shear-banding of jammed systems. Eur Phys J E 33:183–188

    Article  Google Scholar 

  23. Coussot P, Tocquer L, Lanos C, Ovarlez G (2009) Macroscopic vs local rheology of yield stress fluids. J Non-Newtonian Fluid Mech 158:85–90

    Article  Google 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 93:1557–1566

    Article  Google Scholar 

  25. Dimonte G, Gore R, Schneider M (1998) Rayleigh-Taylor instability in elastic-plastic materials. Phys Rev Lett 80:1212–1215

    Article  Google Scholar 

  26. Ebrahimi B, Mostaghimi P, Gholamian H, Sadeghy K (2016) Viscous fingering in yield stress fluids: a numerical study. J Eng Math 97:161–176

    Article  Google Scholar 

  27. Fontana JV, Lira SA, Miranda JA (2013) Radial viscous fingering in yield stress fluids: onset of pattern formation. Phys Rev E 87:013016

    Article  Google Scholar 

  28. Hébraud P, Lequeux F, Munch JP, Pine DJ (1997) Yielding and rearrangements in disordered emulsions. Phys Rev Lett 78:4657–4660

    Article  Google Scholar 

  29. Homsy GM (1987) Viscous fingering in porous media. Ann Rev Fluid Mech 19:271–311

    Article  Google Scholar 

  30. Israelachvili JN (2001) Intermolecular and surface forces. Academic Press, Amsterdam

    Google Scholar 

  31. Jorgensen L, Le Merrer M, Delanoe-Ayari H, Barentin C (2015) Yield stress and elasticity influence on surface tension measurements. Soft Matter 11:5111–5121

    Article  Google Scholar 

  32. Lidon P, Villa L, Manneville S (2017) Power-law creep and residual stresses in a carbopol gel. Rheol Acta 56:307–323

    Article  Google Scholar 

  33. Lubliner J (1990) Plasticity theory. Macmillan, New York

    Google Scholar 

  34. Lindner A, Bonn D, Coussot P (2000) Viscous fingering in a yield stress fluid. Phys Rev Lett 85:314–317

    Article  Google Scholar 

  35. Lindner A, Bonn D, Poire EC, Ben Amar M (2002) Meunier J. Viscous fingering in non-Newtonian fluids 469:237–256

    Google Scholar 

  36. Liu AJ, Nagel SR (1998) Jamming is not just cool any more. Nature 396:21–22

    Article  Google Scholar 

  37. Maillard M (2015) Spreading flows of yield stress fluids, PhD thesis, Univ. Paris-Est (in French)

  38. Maillard M, Mézière C, Moucheront P, Courrier C, Coussot P (2016) Blade-coating of yield stress fluids. J Non-Newt Fluid Mech 237:16–25

    Article  Google 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 116:154502

    Article  Google Scholar 

  40. Maloney CE, Lemaître A (2006) Amorphous systems in athermal, quasistatic shear. Phys Rev E 74:016118

    Article  Google 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–S1228

    Article  Google Scholar 

  42. Marsh BD (1979) Island-arc development––some observations, experiments, and speculations. J Geol 87:687–713

    Article  Google 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 367:5139–5155

    Google Scholar 

  44. Mora S, Phou T, Fromental JM, Pomeau Y (2014) Gravity driven instability in elastic solid layers. Phys Rev Lett 113:178301

    Article  Google Scholar 

  45. Nadai A (1950) Theory of flow and fracture of solids. McGraw Hill, New York

    Google Scholar 

  46. Oldroyd JG (1947) A rational formulation of the equations of plastic flow for a Bingham solid. Proc Camb Philos Soc 43:100–105

  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 193:68–79

    Article  Google 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 48:831–844

    Article  Google Scholar 

  49. Piriz AR, López Cela JJ, Cortázar OD, Tahir NA, Hoffmann DHH (2005) Rayleigh-Taylor instability in elastic solids. Phys Rev E 72:056313

    Article  Google Scholar 

  50. Piriz AR, Sun YB, Tahir NA (2013) Rayleigh-Taylor stability boundary at solid-liquid interfaces. Phys Rev E 88:023026

    Article  Google Scholar 

  51. Rahmani Y, Habibi M, Javadi A, Bonn D (2011) Coiling of yield stress fluids. Phys Rev E 83:056327

    Article  Google Scholar 

  52. Rayleigh SJW (1883) Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc Lond Math Soc 14:170–177

    Google Scholar 

  53. Robinson AC, Swegle JW (1989) Acceleration instability in elastic-plastic solids 2. Analytical techniques. J Appl Phys 66:2859–2872

    Article  Google Scholar 

  54. Sharp DH (1984) An overview of Rayleigh-Taylor instability. Physica 12D:3–18

    Google Scholar 

  55. Sollich P, Lequeux F, Hébraud P, Cates ME (1997) Rheology of soft glassy materials. Phys Rev Lett 78:2020

    Article  Google Scholar 

  56. Tabor D (1991) Gases, liquids and solids. Cambridge University Press, Cambridge

    Google Scholar 

  57. Terrones G (2005) Fastest growing linear Rayleigh-Taylor modes at solid/fluid and solid/solid interfaces. Phys Rev E 71:036306

    Article  Google 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 78:041405

    Article  Google Scholar 

  59. Zaleski S, Julien P (1992) Numerical simulation of Rayleigh-Taylor instability for single and multiple salt diapirs. Tectonophysics 206:55–69

    Article  Google 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 Lett

Download references

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Correspondence to P. Coussot.

Appendix 1. Interfacial tension of a yield stress fluid with another phase

Appendix 1. Interfacial tension of a yield stress fluid with another phase

Since interfacial tension is related to the interactions between the molecules situated along the interface (Israelachvili 2001) and since YSF are made of suspended elements in a liquid, it is natural to consider that the interfacial tension of a YSF with another (simple) phase is given by that of the interstitial liquid with this other phase since there is always at least a few layers of liquid molecules surrounding the suspended elements. This assumption appears to be in agreement with existing measurements (Yoshitake et al. 2008; Boujlel and Coussot 2013; Aytouna et al. 2013; Jorgensen et al. 2015). It remains that a direct measure of interfacial tension with YSF is a challenge because, in such materials, there might exist, even at rest, residual stresses which can preclude a straightforward appreciation of interfacial stresses.

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Coussot, P. Slow flows of yield stress fluids: yielding liquids or flowing solids?. Rheol Acta 57, 1–14 (2018). https://doi.org/10.1007/s00397-017-1055-7

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Keywords

  • Yield stress
  • slow flows
  • plasticity
  • localization