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Shear jamming and fragility in dense suspensions

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Abstract

The phenomenon of shear-induced jamming is a factor in the complex rheological behavior of dense suspensions. Such shear-jammed states are fragile, i.e., they are not stable against applied stresses that are incompatible with the stress imposed to create them. This peculiar flow-history dependence of the stress response is due to flow-induced microstructures. To examine jammed states realized under constant shear stress, we perform dynamic simulations of non-Brownian particles with frictional contact forces and hydrodynamic lubrication forces. We find clear signatures that distinguish these fragile states from the more conventional isotropic jammed states.

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References

  1. Denn, M.M., Morris, J.F., Bonn, D.: Shear thickening in concentrated suspensions of smooth spheres in newtonian suspending fluids. Soft Matter 14, 170–184 (2018)

    Article  ADS  Google Scholar 

  2. Guazzelli, É., Pouliquen, O.: Rheology of dense granular suspensions. J. Fluid Mech. 852, P1 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Einstein, A.: Eine neue bestimmung der moleküldimensionen. Ann. Phys. 19, 289–305 (1906)

    Article  MATH  Google Scholar 

  4. Einstein, A.: Berichtigung zu meiner arbeit: ‘eine neue bestimmung der moleküldimensionen’. Ann. Physik 34, 591–592 (1911)

    Article  ADS  MATH  Google Scholar 

  5. Denn, M.M., Morris, J.F.: Rheology of non-brownian suspensions. Annu. Rev. Chem. Biomol. Eng. 5(1), 203–228 (2014)

    Article  Google Scholar 

  6. Goddard, J.D.: A dissipative anisotropic fluid model for non-colloidal particle dispersions. J. Fluid Mech. 568, 1–17 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Bertrand, E., Bibette, J., Schmitt, V.: From shear thickening to shear-induced jamming. Phys. Rev. E 66(6), 060401 (2002)

    Article  ADS  Google Scholar 

  8. Peters, I.R., Majumdar, S., Jaeger, H.M.: Direct observation of dynamic shear jamming in dense suspensions. Nature 532, 214 (2016)

    Article  ADS  Google Scholar 

  9. Singh, A., Mari, R., Denn, M.M., Morris, J.F.: A constitutive model for simple shear of dense frictional suspensions. J. Rheol. 62(2), 457–468 (2018)

    Article  ADS  Google Scholar 

  10. Cates, M.E.: Stress transmission in jammed and granular matter, p. 369. IOP Publishing, Bristol (2000)

    Google Scholar 

  11. Cates, M.E., Wittmer, J.P., Bouchaud, J.P., Claudin, P.: Jamming, force chains, and fragile matter. Phys. Rev. Lett. 81, 1841–1844 (1998)

    Article  ADS  Google Scholar 

  12. Ness, C., Mari, R., Cates, M.E.: Shaken and stirred: random organization reduces viscosity and dissipation in granular suspensions. Sci. Adv. 4(3), eaar3296 (2018)

    Article  ADS  Google Scholar 

  13. Bi, D., Zhang, J., Chakraborty, B., Behringer, R.P.: Jamming by shear. Nature 480, 355–358 (2011)

    Article  ADS  Google Scholar 

  14. Ren, J., Dijksman, J.A., Behringer, R.P.: Reynolds pressure and relaxation in a sheared granular system. Phys. Rev. Lett. 110, 018302 (2013)

    Article  ADS  Google Scholar 

  15. Sarkar, S., Bi, D., Zhang, J., Behringer, R., Chakraborty, B.: Origin of rigidity in dry granular solids. Phys. Rev. Lett. 111(6), 068301 (2013)

    Article  ADS  Google Scholar 

  16. Sarkar, S., Bi, D., Zhang, J., Ren, J., Behringer, R.P., Chakraborty, B.: Shear-induced rigidity of frictional particles: analysis of emergent order in stress space. Phys. Rev. E 93, 042901 (2016)

    Article  ADS  Google Scholar 

  17. Sarkar, S., Chakraborty, B.: Shear-induced rigidity in athermal materials: a unified statistical framework. Phys. Rev. E 91(4), 042201 (2015)

    Article  ADS  Google Scholar 

  18. Otsuki, M., Hayakawa, H.: Shear jamming, discontinuous shear thickening, and fragile state in dry granular materials under oscillatory shear. arXiv:1810.03846 [cond-mat.soft] (2018)

  19. Srivastava, I., Silbert, L.E., Grest, G.S., Lechman, J.B.: Flow-arrest transitions in frictional granular matter. Phys. Rev. Lett. 122, 048003 (2019)

    Article  ADS  Google Scholar 

  20. Brady, J.F., Bossis, G.: Stokesian dynamics. Annu. Rev. Fluid Mech. 20(1), 111–157 (1988)

    Article  ADS  Google Scholar 

  21. Melrose, J.R., Ball, R.C.: The pathological behaviour of sheared hard spheres with hydrodynamic interactions. Europhys. Lett. 32, 535–540 (1995)

    Article  ADS  Google Scholar 

  22. Morris, J.F.: Lubricated-to-frictional shear thickening scenario in dense suspensions. Phys. Rev. Fluids 3, 110508 (2018)

    Article  ADS  Google Scholar 

  23. Seto, R., Mari, R., Morris, J.F., Denn, M.M.: Discontinuous shear thickening of frictional hard-sphere suspensions. Phys. Rev. Lett. 111, 218301 (2013)

    Article  ADS  Google Scholar 

  24. Mari, R., Seto, R., Morris, J.F., Denn, M.M.: Nonmonotonic flow curves of shear thickening suspensions. Phys. Rev. E 91, 052302 (2015)

    Article  ADS  Google Scholar 

  25. Ball, R.C., Melrose, J.R.: A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces. Physica A 247(1), 444–472 (1997)

    Article  ADS  Google Scholar 

  26. Jeffrey, D.J., Onishi, Y.: Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech. 139, 261–290 (1984)

    Article  ADS  MATH  Google Scholar 

  27. Wilson, H.J., Davis, R.H.: Shear stress of a monolayer of rough spheres. J. Fluid Mech. 452, 425–441 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Mari, R., Seto, R., Morris, J.F., Denn, M.M.: Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions. J. Rheol. 58(6), 1693–1724 (2014)

    Article  ADS  Google Scholar 

  29. Seto, R., Giusteri, G.G., Martiniello, A.: Microstructure and thickening of dense suspensions under extensional and shear flows. J. Fluid Mech. 825, R3 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Luding, S.: Cohesive, frictional powders: contact models for tension. Granul. Matter 10, 235–246 (2008)

    Article  MATH  Google Scholar 

  31. Gadala-Maria, F., Acrivos, A.: Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24(6), 799–814 (1980)

    Article  ADS  Google Scholar 

  32. Henkes, S., van Hecke, M., van Saarloos, W.: Critical jamming of frictional grains in the generalized isostaticity picture. Europhys. Lett. 90(1), 14003 (2010)

    Article  ADS  Google Scholar 

  33. Ciamarra, M.P., Coniglio, A.: Random very loose packings. Phys. Rev. Lett. 101, 128001 (2008)

    Article  ADS  Google Scholar 

  34. Onoda, G.Y., Liniger, E.G.: Random loose packings of uniform spheres and the dilatancy onset. Phys. Rev. Lett. 64, 2727–2730 (1990)

    Article  ADS  Google Scholar 

  35. Giusteri, G.G., Seto, R.: A theoretical framework for steady-state rheometry in generic flow conditions. J. Rheol. 62(3), 713–723 (2018)

    Article  ADS  Google Scholar 

  36. Behringer, R.P., Chakraborty, B.: The physics of jamming for granular materials: a review. Rep. Prog. Phys. 82(1), 012601 (2019)

    Article  ADS  Google Scholar 

  37. Baity-Jesi, M., Goodrich, C.P., Liu, A.J., Nagel, S.R., Sethna, J.P.: Emergent SO(3) symmetry of the frictionless shear jamming transition. J. Stat. Phys. 167(3), 735–748 (2017)

    Article  ADS  MATH  Google Scholar 

  38. Barnes, H.A.: Shear-thickening (“Dilatancy”) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids. J. Rheol. 33(2), 329–366 (1989)

    Article  ADS  Google Scholar 

  39. Reynolds, O.: On the dilatancy of media composed of rigid particles in contact, with experimental illustrations. Philos. Mag. 20(5), 469–481 (1885)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank M. Otsuki, H. Hayakawa, and R. Mari for fruitful discussions. This study was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grants Nos. 17H01083 and 17K05618. BC was supported by NSF-CBET-1605428, while JFM was supported by NSF-CBET-1605283. The research was also supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. RS thanks R. Yamamoto for his full support.

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Correspondence to Ryohei Seto.

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This article is part of the Topical Collection: In Memoriam of Robert P. Behringer.

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Seto, R., Singh, A., Chakraborty, B. et al. Shear jamming and fragility in dense suspensions. Granular Matter 21, 82 (2019). https://doi.org/10.1007/s10035-019-0931-5

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