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Abstract

In our daily lives, most materials we see are in one of the three states of matter: solid, liquid, or gas. When a material in one state is broken up into small particles and mixed with material in another state, rich and interesting phenomena can happen. For example, the air is so “soft” that most of the time one can hardly feel its existence. However, when many air bubbles are distributed in water, the foam that forms develops a rigidity that can hold its shape against gravity. Another famous example of such mixtures is a suspension of hard cornstarch particles in water, which is sometimes referred to as the “Oobleck” in Dr. Seuss’ stories. One striking behavior of this solid-liquid mixture is that it flows like a viscous fluid under normal conditions, but solidifies under a sudden impact. The transition is so dramatic that people can jog or jump on the surface of such mixtures. When they stop moving, the material can no longer support their weight, and they slowly sink in. This reversible, dynamic fluid-solid transition is the main focus of this thesis.

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Notes

  1. 1.

    Note that Eq. (1.2) is valid only when the viscosity η r(ϕ) is measured in the “Newtonian regime.”

  2. 2.

    Strong force is defined as F > F ave, where F is the local contact forces, and F ave is the average of F across the whole system [27].

  3. 3.

    Some literature does not clearly distinguish shear thickening and jamming. Sometimes discontinuous shear thickening is referred to as “temporary jamming.” In this thesis, jamming is only designated to a state that does not flow under applied stress (with a non-zero shear modulus) during the time scale of the experiments.

References

  1. H.A. Barnes, J.F. Hutton, K. Walters, An Introduction to Rheology (Elsevier, Amsterdam, 1989)

    MATH  Google Scholar 

  2. L.D. Landau, E.M. Lifshitz, Theory of Elasticity, 2nd edn. (Pergamon Press, Oxford, 1970)

    MATH  Google Scholar 

  3. D.J. Acheson, Elementary Fluid Dynamics (Oxford University Press, Oxford, 2005)

    MATH  Google Scholar 

  4. A. Einstein, A new determination of the molecular dimensions. Ann. Phys. 19, 289–306 (1906)

    Article  Google Scholar 

  5. G.K. Batchelor, The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83(01), 97 (1977)

    Google Scholar 

  6. R.C. Ball, P. Richmond, Dynamics of colloidal dispersions. Phys. Chem. Liq. 9(2), 99–116 (1980)

    Article  Google Scholar 

  7. A.J. Liu, S.R. Nagel, Jamming is not just cool any more. Nature 396(6706), 21–22 (1998)

    Article  ADS  Google Scholar 

  8. M.E. Cates, J.P. Wittmer, J.P. Bouchaud, P. Claudin, Jamming force chains and fragile matter. Phys. Rev. Lett. 81(9), 4 (1998)

    Google Scholar 

  9. S.H. Maron, P.E. Pierce, Application of ree-eyring generalized flow theory to suspensions of spherical particles. J. Colloid Sci. 11, 80–95 (1956)

    Article  Google Scholar 

  10. I.M. Krieger, T.J. Dougherty, A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3(1), 137–152 (1959)

    Article  Google Scholar 

  11. J.F. Brady, The rheological behavior of concentrated colloidal dispersions. J. Chem. Phys. 99(1), 567–581 (1993)

    Article  ADS  Google Scholar 

  12. H.M. Shewan, J.R. Stokes, Analytically predicting the viscosity of hard sphere suspensions from the particle size distribution. J. Non-Newtonian Fluid Mech. 222, 72–81 (2015)

    Article  MathSciNet  Google Scholar 

  13. E. Brown, H.M. Jaeger, Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming. Rep. Prog. Phys. 77(4), 046602 (2014)

    Google Scholar 

  14. V. Trappe, V. Prasad, L. Cipelletti, P.N. Segre, D.A. Weitz, Jamming phase diagram for attractive particles. Nature 411, 772–775 (2001)

    Article  ADS  Google Scholar 

  15. E. Brown, N.A. Forman, C.S. Orellana, H. Zhang, B.W. Maynor, D.E. Betts, J.M. DeSimone, H.M. Jaeger, Generality of shear thickening in dense suspensions. Nat. Mater. 9(3), 220–224 (2010)

    Article  ADS  Google Scholar 

  16. B.J. Maranzano, N.J. Wagner, The effects of particle size on reversible shear thickening of concentrated colloidal dispersions. J. Chem. Phys. 114(23), 10514–10527 (2001)

    Article  ADS  Google Scholar 

  17. X. Cheng, J.H. McCoy, J.N. Israelachvili, I. Cohen, Imaging the microscopic structure of shear thinning and thickening colloidal suspensions. Science 333, 1276–1279 (2011)

    Article  ADS  Google Scholar 

  18. E. Brown, H.M. Jaeger, Through thick and thin. Science 333, 1230–1231 (2011)

    Article  ADS  Google Scholar 

  19. N.J. Wagner, J.F. Brady, Shear thickening in colloidal dispersions. Phys. Today 62(10), 27–32 (2009)

    Article  Google Scholar 

  20. J.F. Brady, G. Bossis, The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105 (1985)

    Article  ADS  Google Scholar 

  21. J.F. Brady, G Bossis, Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111 (1988)

    Article  ADS  Google Scholar 

  22. H.A. Barnes, Shear-thickening (“dilatancy”) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids. J. Rheol. 33(2), 329 (1989)

    Google Scholar 

  23. E. Brown, H.M. Jaeger, The role of dilation and confining stresses in shear thickening of dense suspensions. J. Rheol. 56(4), 875 (2012)

    Google Scholar 

  24. Q. Xu, S. Majumdar, E. Brown, H.M. Jaeger, Shear thickening in highly viscous granular suspensions. Europhys. Lett. 107(6), 68004 (2014)

    Google Scholar 

  25. N.Y. Lin, B.M. Guy, M. Hermes, C. Ness, J. Sun, W.C. Poon, I. Cohen, Hydrodynamic and contact contributions to continuous shear thickening in colloidal suspensions. Phys. Rev. Lett. 115(22), 228304 (2015)

    Google Scholar 

  26. C.S. O’Hern, L.E. Silbert, A.J. Liu, S.R. Nagel, Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys. Rev. E 68(1), 011306 (2003)

    Google Scholar 

  27. D. Bi, J. Zhang, B. Chakraborty, R.P. Behringer, Jamming by shear. Nature 480(7377), 355–358 (2011)

    Article  ADS  Google Scholar 

  28. I.R. Peters, S. Majumdar, H.M. Jaeger, Direct observation of dynamic shear jamming in dense suspensions. Nature 532(7598), 214–217 (2016)

    Article  ADS  Google Scholar 

  29. N. Kumar, S. Luding, Memory of jamming–multiscale models for soft and granular matter. Granul. Matter 18(3), 58 (2016)

    Google Scholar 

  30. W. Zheng, H. Liu, N. Xu, Shear-induced solidification of athermal systems with weak attraction. Phys. Rev. E 94(6), 062608 (2016)

    Google Scholar 

  31. E. DeGiuli, G. Düring, E. Lerner, M. Wyart, Unified theory of inertial granular flows and non-Brownian suspensions. Phys. Rev. E 91(6), 062206 (2015)

    Google Scholar 

  32. E. Lerner, G. Düring, M. Wyart, A unified framework for non-Brownian suspension flows and soft amorphous solids. Proc. Natl. Acad. Sci. 109(13), 4798–4803 (2012)

    Article  ADS  Google Scholar 

  33. N. Fernandez, R. Mani, D. Rinaldi, D. Kadau, M. Mosquet, H. Lombois-Burger, J. Cayer-Barrioz, H.J. Herrmann, N.D. Spencer, L. Isa, Microscopic mechanism for shear thickening of non-Brownian suspensions. Phys. Rev. Lett. 111(10), 108301 (2013)

    Google Scholar 

  34. F. Boyer, E. Guazzelli, O. Pouliquen, Unifying suspension and granular rheology. Phys. Rev. Lett. 107(18), 188301 (2011)

    Google Scholar 

  35. J. Comtet, G. Chatte, A. Nigues, L. Bocquet, A. Siria, A. Colin, Pairwise frictional profile between particles determines discontinuous shear thickening transition in non-colloidal suspensions. Nat. Commun. 8, 15633 (2017)

    Article  ADS  Google Scholar 

  36. C. Clavaud, A. Berut, B. Metzger, Y. Forterre, Revealing the frictional transition in shear-thickening suspensions. Proc. Natl. Acad. Sci. 114(20), 5147–5152 (2017)

    Article  ADS  Google Scholar 

  37. R. Seto, R. Mari, J.F. Morris, M.M. Denn, Discontinuous shear thickening of frictional hard-sphere suspensions. Phys. Rev. Lett. 111(21), 218301 (2013)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  39. S. Sarkar, D. Bi, J. Zhang, J. Ren, R.P. Behringer, B. Chakraborty, Shear-induced rigidity of frictional particles: analysis of emergent order in stress space. Phys. Rev. E 93(4), 042901 (2016)

    Google Scholar 

  40. M. Wyart, M.E. Cates, Discontinuous shear thickening without inertia in dense non-Brownian suspensions. Phys. Rev. Lett. 112(9), 098302 (2014)

    Google Scholar 

  41. C. Song, P. Wang, H.A. Makse, A phase diagram for jammed matter. Nature 453(7195), 629–632 (2008)

    Article  ADS  Google Scholar 

  42. L.C. Hsiao, S. Jamali, E. Glynos, P.F. Green, R.G. Larson, M.J. Solomon, Rheological state diagrams for rough colloids in shear flow. Phys. Rev. Lett. 119(15), 158001 (2017)

    Google Scholar 

  43. C.P. Hsu, S.N. Ramakrishna, M. Zanini, N.D. Spencer, L. Isa, Roughness-dependent tribology effects on discontinuous shear thickening. Proc. Natl. Acad. Sci. 115(20), 5117–5122 (2018)

    Article  ADS  Google Scholar 

  44. N.M. James, E. Han, R.A.L. de la Cruz, J. Jureller, H.M. Jaeger, Interparticle hydrogen bonding can elicit shear jamming in dense suspensions. Nat. Mater. 17(11), 965–970 (2018)

    Article  ADS  Google Scholar 

  45. M. Trulsson, E. DeGiuli, M. Wyart, Effect of friction on dense suspension flows of hard particles. arXiv preprint arXiv:1606.07650 (2016)

    Google Scholar 

  46. F. Blanc, F. Peters, E. Lemaire, Local transient rheological behavior of concentrated suspensions. J. Rheol. 55(4), 835–854 (2011)

    Article  ADS  Google Scholar 

  47. B.M. Guy, M. Hermes, W.C. Poon, Towards a unified description of the rheology of hard-particle suspensions. Phys. Rev. Lett. 115(8), 088304 (2015)

    Google Scholar 

  48. Z. Pan, H. de Cagny, B. Weber, D. Bonn, S-shaped flow curves of shear thickening suspensions: direct observation of frictional rheology. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 92(3), 032202 (2015)

    Google Scholar 

  49. B. Liu, M. Shelley, J. Zhang, Focused force transmission through an aqueous suspension of granules. Phys. Rev. Lett. 105(18), 188301 (2010)

    Google Scholar 

  50. S. von Kann, J.H. Snoeijer, D. Lohse, D. van der Meer, Nonmonotonic settling of a sphere in a cornstarch suspension. Phys. Rev. E 84(6), 060401 (2011)

    Google Scholar 

  51. S.R. Waitukaitis, H.M. Jaeger, Impact-activated solidification of dense suspensions via dynamic jamming fronts. Nature 487(7406), 205–209 (2012)

    Article  ADS  Google Scholar 

  52. B. Allen, B. Sokol, S. Mukhopadhyay, R. Maharjan, E. Brown, System-spanning dynamically jammed region in response to impact of cornstarch and water suspensions. Phys. Rev. E 97(5), 052603 (2018)

    Google Scholar 

  53. M.I. Smith, R. Besseling, M.E. Cates, V. Bertola, Dilatancy in the flow and fracture of stretched colloidal suspensions. Nat. Commun. 1, 114 (2010)

    Article  ADS  Google Scholar 

  54. I.R. Peters, H.M. Jaeger, Quasi-2d dynamic jamming in cornstarch suspensions: visualization and force measurements. Soft Matter 10(34), 6564–6570 (2014)

    Article  ADS  Google Scholar 

  55. S.R. Waitukaitis, L.K. Roth, V. Vitelli, H.M. Jaeger, Dynamic jamming fronts. Europhys. Lett. 102(4), 44001 (2013)

    Google Scholar 

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Han, E. (2020). Introduction. In: Transient Dynamics of Concentrated Particulate Suspensions Under Shear. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-38348-0_1

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