Skip to main content
SpringerLink
Log in

Hidden hierarchy in the rheology of dense suspensions

  • Early Career Materials Researcher Prospective
  • Published:
MRS Communications Aims and scope Submit manuscript

Abstract

Dense suspensions of fine particles are significant in numerous biological, industrial, and natural phenomena. They are often out-of-equilibrium and display various rheological features including liquid–solid phase transition under external deformation being one of the most interesting one. Developing an understanding of the mechanisms that drive these phenomena has over the last several years led to a surge in research activity at the intersection of fluid mechanics, granular materials, driven disordered systems, tribology, and soft condensed matter physics. One central aspect that emerged is that these phenomena occur due to a shear-activated or deactivated network of contacts between particles. The perspective briefly presents the current state of understanding and challenges associated with relating the flow of material at the bulk scale with the microscopic physics at the particle scale.

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

Figure 1
Figure 2
Figure 3

Similar content being viewed by others

Data availability

Yes.

References

  1. M.M. Denn, J.F. Morris, D. Bonn, Shear thickening in concentrated suspensions of smooth spheres in Newtonian suspending fluids. Soft Matter 14(2), 170–184 (2018)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  4. D.J. Jerolmack, K.E. Daniels, Viewing earth’s surface as a soft-matter landscape. Nat. Rev. Phys. 1(12), 716–730 (2019)

    Article  Google Scholar 

  5. F. Toussaint, C. Roy, P.-H. Jézéquel, Reducing shear thickening of cement-based suspensions. Rheol. Acta 48(8), 883–895 (2009)

    Article  CAS  Google Scholar 

  6. J.F. Morris, Shear thickening of concentrated suspensions: recent developments and relation to other phenomena. Annu. Rev. Fluid Mech. 52, 121–144 (2020)

    Article  Google Scholar 

  7. J.J. Stickel, R.L. Powell, Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149 (2005)

    Article  Google Scholar 

  8. J.F. Brady, G. Bossis, The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105–129 (1985)

    Article  Google Scholar 

  9. J.F. Brady, G. Bossis, Stokesian dynamics. Ann. Rev. Fluid Mech. 20, 111–157 (1988)

    Article  Google Scholar 

  10. T.N. Phung, J.F. Brady, G. Bossis, Stokesian dynamics simulation of Brownian suspensions. J. Fluid Mech. 313, 181–207 (1996)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. G.I. Taylor, The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Charact. 138(834), 41–48 (1932)

    CAS  Google Scholar 

  13. G.K. Batchelor, The stress system in a suspension of force-free particles. J. Fluid Mech. 41(3), 545–570 (1970)

    Article  Google Scholar 

  14. G. Batchelor, The effect of brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83(1), 97–117 (1977)

    Article  Google Scholar 

  15. H.A. Barnes, J.F. Hutton, K. Walters, An Introduction to Rheology, vol. 3 (Elsevier, Amsterdam, 1989)

    Book  Google Scholar 

  16. R.I. Tanner, Engineering Rheology, vol. 52 (Oxford University Press, Oxford, 2000)

    Book  Google Scholar 

  17. S. Gürgen, M.C. Kuşhan, W. Li, Shear thickening fluids in protective applications: a review. Prog. Polym. Sci. 75, 48–72 (2017)

    Article  Google Scholar 

  18. Y.S. Lee, E.D. Wetzel, N.J. Wagner, The ballistic impact characteristics of Kevlar® woven fabrics impregnated with a colloidal shear thickening fluid. J. Mater. Sci. 38, 2825–2833 (2003)

    Article  CAS  Google Scholar 

  19. A. Srivastava, A. Majumdar, B. Butola, Improving the impact resistance of textile structures by using shear thickening fluids: a review. Crit. Rev. Solid State Mater. Sci. 37(2), 115–129 (2012)

    Article  CAS  Google Scholar 

  20. M. Zarei, J. Aalaie, Application of shear thickening fluids in material development. J. Market. Res. 9(5), 10411–10433 (2020)

    Google Scholar 

  21. T. Sato, Rheology of suspensions. JCT 67(847), 69–79 (1995)

    CAS  Google Scholar 

  22. L. Heymann, S. Peukert, N. Aksel, On the solid–liquid transition of concentrated suspensions in transient shear flow. Rheol. Acta 41(4), 307–315 (2002)

    Article  CAS  Google Scholar 

  23. R.I. Tanner, Aspects of non-colloidal suspension rheology. Phys. Fluids (2018). https://doi.org/10.1063/1.5047535

    Article  Google Scholar 

  24. C. Ness, R. Seto, R. Mari, The physics of dense suspensions. Annu. Rev. Condens. Matter Phys. 13, 97–117 (2022)

    Article  Google Scholar 

  25. V. Gopalakrishnan, C. Zukoski, Effect of attractions on shear thickening in dense suspensions. J. Rheol. 48(6), 1321–1344 (2004)

    Article  CAS  Google Scholar 

  26. 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)

    Article  Google Scholar 

  27. L.C. Hsiao, S. Pradeep, Experimental synthesis and characterization of rough particles for colloidal and granular rheology. Curr. Opin. Colloid Interface Sci. 43, 94–112 (2019)

    Article  CAS  Google Scholar 

  28. D. Lootens, H. Van Damme, P. Hébraud, Giant stress fluctuations at the jamming transition. Phys. Rev. Lett. 90, 178301 (2003)

    Article  Google Scholar 

  29. S.R. Raghavan, H.J. Walls, S.A. Khan, Rheology of silica dispersions in organic liquids: new evidence for solvation forces dictated by hydrogen bonding. Langmuir 16(21), 7920–7930 (2000)

    Article  CAS  Google Scholar 

  30. S.S. Shenoy, N.J. Wagner, Influence of medium viscosity and adsorbed polymer on the reversible shear thickening transition in concentrated colloidal dispersions. Rheol. Acta 44, 360–371 (2005)

    Article  CAS  Google Scholar 

  31. T. Jiang, C.F. Zukoski, Role of particle size and polymer length in rheology of colloid-polymer composites. Macromolecules 45(24), 9791–9803 (2012)

    Article  CAS  Google Scholar 

  32. M. Naald, L. Zhao, G.L. Jackson, H.M. Jaeger, The role of solvent molecular weight in shear thickening and shear jamming. Soft Matter 17, 3144–3152 (2021)

    Article  Google Scholar 

  33. 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  CAS  Google Scholar 

  34. A. Singh, C. Ness, R. Seto, J.J. Pablo, H.M. Jaeger, Shear thickening and jamming of dense suspensions: the “roll” of friction. Phys. Rev. Lett. 124, 248005 (2020)

    Article  CAS  Google Scholar 

  35. S.H. Maron, P.E. Pierce, Application of REE-Eyring generalized flow theory to suspensions of spherical particles. J. Colloid Sci. 11(1), 80–95 (1956)

    Article  CAS  Google Scholar 

  36. J. Chong, E. Christiansen, A. Baer, Rheology of concentrated suspensions. J. Appl. Polym. Sci. 15(8), 2007–2021 (1971)

    Article  CAS  Google Scholar 

  37. 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  CAS  Google Scholar 

  38. N. Frankel, A. Acrivos, On the viscosity of a concentrated suspension of solid spheres. Chem. Eng. Sci. 22(6), 847–853 (1967)

    Article  Google Scholar 

  39. M. Mooney, The viscosity of a concentrated suspension of spherical particles. J. Colloid Sci. 6(2), 162–170 (1951)

    Article  CAS  Google Scholar 

  40. A.J. Liu, S.R. Nagel, The jamming transition and the marginally jammed solid. Annu. Rev. Condens. Matter Phys. 1(1), 347–369 (2010)

    Article  Google Scholar 

  41. M. Hecke, Jamming of soft particles: geometry, mechanics, scaling and isostaticity. J. Phys.: Condens. Matter 22(3), 033101 (2009)

    Google Scholar 

  42. 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, 011306 (2003)

    Article  Google Scholar 

  43. J. Mewis, N.J. Wagner, Colloidal Suspension Rheology (Cambridge University Press, Cambridge, 2011)

    Book  Google Scholar 

  44. D. Prasad, H. Kytömaa, Particle stress and viscous compaction during shear of dense suspensions. Int. J. Multiph. Flow 21(5), 775–785 (1995)

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  46. B. Etcheverry, Y. Forterre, B. Metzger, Capillary-stress controlled rheometer reveals the dual rheology of shear-thickening suspensions. Phys. Rev. X 13(1), 011024 (2023)

    CAS  Google Scholar 

  47. S. Athani, B. Metzger, Y. Forterre, R. Mari, Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy. J. Fluid Mech. 949, 9 (2022)

    Article  Google Scholar 

  48. C. Clavaud, B. Metzger, Y. Forterre, The Darcytron: a pressure-imposed device to probe the frictional transition in shear-thickening suspensions. J. Rheol. 64(2), 395–403 (2020)

    Article  CAS  Google Scholar 

  49. J. Dong, M. Trulsson, Analog of discontinuous shear thickening flows under confining pressure. Phys. Rev. Fluids 2(8), 081301 (2017)

    Article  Google Scholar 

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

    Article  Google Scholar 

  51. B.M. Guy, J. Richards, D. Hodgson, E. Blanco, W.C.K. Poon, Constraint-based approach to granular dispersion rheology. Phys. Rev. Lett. 121(12), 128001 (2018)

    Article  CAS  Google Scholar 

  52. A. Singh, G.L. Jackson, M. Naald, J.J. Pablo, H.M. Jaeger, Stress-activated constraints in dense suspension rheology. Phys. Rev. Fluids 7(5), 054302 (2022)

    Article  Google Scholar 

  53. R. Seto, R. Botet, M. Meireles, G.K. Auernhammer, B. Cabane, Compressive consolidation of strongly aggregated particle gels. J. Rheol. 57(5), 1347–1366 (2013)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  56. R. Mari, R. Seto, J.F. Morris, M.M. Denn, Discontinuous shear thickening in Brownian suspensions by dynamic simulation. Proc. Natl. Acad. Sci. U.S.A. 112(50), 15326–15330 (2015)

    Article  CAS  Google Scholar 

  57. C. Ness, J. Sun, Shear thickening regimes of dense non-Brownian suspensions. Soft Matter 12(3), 914–924 (2016)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  59. 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. U.S.A. 115, 5117–5122 (2018)

    Article  CAS  Google Scholar 

  60. S. Jamali, J.F. Brady, Alternative frictional model for discontinuous shear thickening of dense suspensions: hydrodynamics. Phys. Rev. Lett. 123(13), 138002 (2019)

    Article  CAS  Google Scholar 

  61. J.C. Maxwell, On the calculation of the equilibrium and stiffness of frames. Philos. Mag. 27(182), 294–299 (1864)

    Article  Google Scholar 

  62. A.P. Santos, D.S. Bolintineanu, G.S. Grest, J.B. Lechman, S.J. Plimpton, I. Srivastava, L.E. Silbert, Granular packings with sliding, rolling, and twisting friction. Phys. Rev. E 102(3), 032903 (2020)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  64. R. More, A. Ardekani, Roughness induced shear thickening in frictional non-Brownian suspensions: a numerical study. J. Rheol. 64(2), 283–297 (2020)

    Article  CAS  Google Scholar 

  65. S. Pradeep, M. Nabizadeh, A.R. Jacob, S. Jamali, L.C. Hsiao, Jamming distance dictates colloidal shear thickening. Phys. Rev. Lett. 127(15), 158002 (2021)

    Article  CAS  Google Scholar 

  66. W.H. Boersma, J. Laven, H.N. Stein, Shear thickening (dilatancy) in concentrated dispersions. AIChE J. 36, 321–332 (1990)

    Article  CAS  Google Scholar 

  67. H.M. Laun, Rheological properties of aqueous polymer dispersions. Angew. Makromol. Chem. 123(1), 335–359 (1984)

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  69. R.L. Hoffman, Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observation of a flow instability. Trans. Soc. Rheol. 16, 155–173 (1972)

    Article  CAS  Google Scholar 

  70. B.J. Maranzano, N.J. Wagner, The effects of particle size on reversible shear thickening of concentrated colloidal dispersions. J. Chem. Phys. 114, 10514–527 (2001)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  72. R.G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York/Oxford, 1999)

    Google Scholar 

  73. E. Zaccarelli, Colloidal gels: equilibrium and non-equilibrium routes. J. Phys.: Condens. Matter 19(32), 323101 (2007)

    Google Scholar 

  74. J.A. Richards, B.M. Guy, E. Blanco, M. Hermes, G. Poy, W.C. Poon, The role of friction in the yielding of adhesive non-Brownian suspensions. J. Rheol. 64(2), 405–412 (2020)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  76. F. Radjai, D.E. Wolf, M. Jean, J.-J. Moreau, Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80(1), 61 (1998)

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  79. 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)

    Article  Google Scholar 

  80. J.E. Thomas, K. Ramola, A. Singh, R. Mari, J.F. Morris, B. Chakraborty, Microscopic origin of frictional rheology in dense suspensions: correlations in force space. Phys. Rev. Lett. 121(12), 128002 (2018)

    Article  CAS  Google Scholar 

  81. J.R. Royer, D.L. Blair, S.D. Hudson, Rheological signature of frictional interactions in shear thickening suspensions. Phys. Rev. Lett. 116(18), 188301 (2016)

    Article  Google Scholar 

  82. S. Jamali, E. Del Gado, J.F. Morris, Rheology discussions: the physics of dense suspensions. J. Rheol. 64(6), 1501–1524 (2020)

    Article  CAS  Google Scholar 

  83. Y.-F. Lee, Y. Luo, S.C. Brown, N.J. Wagner, Experimental test of a frictional contact model for shear thickening in concentrated colloidal suspensions. J. Rheol. 64(2), 267–282 (2020)

    Article  CAS  Google Scholar 

  84. A. Boromand, S. Jamali, B. Grove, J.M. Maia, A generalized frictional and hydrodynamic model of the dynamics and structure of dense colloidal suspensions. J. Rheol. 62(4), 905–918 (2018)

    Article  CAS  Google Scholar 

  85. M. Gameiro, A. Singh, L. Kondic, K. Mischaikow, J.F. Morris, Interaction network analysis in shear thickening suspensions. Phys. Rev. Fluids 5(3), 034307 (2020)

    Article  Google Scholar 

  86. L.E. Edens, S. Pednekar, J.F. Morris, G.K. Schenter, A.E. Clark, J. Chun, Global topology of contact force networks: insight into shear thickening suspensions. Phys. Rev. E 99(1), 012607 (2019)

    Article  CAS  Google Scholar 

  87. L.E. Edens, E.G. Alvarado, A. Singh, J.F. Morris, G.K. Schenter, J. Chun, A.E. Clark, Shear stress dependence of force networks in 3D dense suspensions. Soft Matter 17(32), 7476–7486 (2021)

    Article  CAS  Google Scholar 

  88. A. Singh, S. Pednekar, J. Chun, M.M. Denn, J.F. Morris, From yielding to shear jamming in a cohesive frictional suspension. Phys. Rev. Lett. 122(9), 098004 (2019)

    Article  CAS  Google Scholar 

  89. M. Nabizadeh, A. Singh, S. Jamali, Structure and dynamics of force clusters and networks in shear thickening suspensions. Phys. Rev. Lett. 129(6), 068001 (2022)

    Article  CAS  Google Scholar 

  90. M. Naald, A. Singh, T. Eid, K. Tang, J. Pablo, H. Jaeger, Minimally rigid clusters in dense suspension flow (2023). https://doi.org/10.21203/rs.3.rs-2468688/v1

    Article  Google Scholar 

  91. A. Goyal, N.S. Martys, E. Del Gado, Flow induced rigidity percolation in shear thickening suspensions. arXiv Preprint (2022). http://arxiv.org/abs/2210.00337

  92. J. Comtet, G. Chatté, A. Niguès, 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  CAS  Google Scholar 

  93. A. Singh, Shear thickening in dense suspension: a master-curve and “roll” of friction. Sci. Talks 3, 100028 (2022)

    Article  Google Scholar 

  94. J. Castle, A. Farid, L.V. Woodcock, The effect of surface friction on the rheology of hard-sphere colloids. Prog. Colloid Polym. Sci. 100, 259–265 (1996)

    Article  CAS  Google Scholar 

  95. D. Lootens, P. Hébraud, E. Lécolier, H. Van Damme, Gelation, shear-thinning and shear-thickening in cement slurries. Oil Gas Sci. Technol. Rev. IFP 59(1), 31–40 (2004)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  97. N.M. James, C.-P. Hsu, N.D. Spencer, H.M. Jaeger, L. Isa, Tuning interparticle hydrogen bonding in shear-jamming suspensions: kinetic effects and consequences for tribology and rheology. J. Phys. Chem. Lett. 10(8), 1663–1668 (2019)

    Article  CAS  Google Scholar 

  98. Q. Xu, A. Singh, H.M. Jaeger, Stress fluctuations and shear thickening in dense granular suspensions. J. Rheol. 64(2), 321–328 (2020)

    Article  CAS  Google Scholar 

  99. C. Chen, M. Naald, A. Singh, N.D. Dolinski, G.L. Jackson, H.M. Jaeger, S.J. Rowan, J.J. Pablo, Leveraging the polymer glass transition to access thermally switchable shear jamming suspensions. ACS Cent. Sci. 9(4), 639–647 (2023)

    Article  CAS  Google Scholar 

Download references

Acknowledgments

I acknowledge Case Western Reserve University for the start-up funding for the project. I am grateful to my mentors Heinrich M. Jaeger and Juan J. de Pablo (University of Chicago); Jeffrey F. Morris and Morton M. Denn (Levich Institute, City College of New York); Stefan Luding and Vanessa Magnanimo (University of Twente, The Netherlands) for their valuable guidance that has been critical in shaping my thoughts. The work presented here has been performed in several collaborations with Romain Mari, Ryohei Seto, Christopher Ness, Sidhant Pednekar, Jaehun Chun, Grayson L. Jackson, and Michael van der Naald. I would also like to thank Stuart Rowan, Bulbul Chakraborty, Emanuela del Gado, Safa Jamali, Lilian Hsiao, Lou Kondic, Aurora Clark, Jacinta Konrad, Sarah Hormozi, Douglas Jerolmack, and Karen Daniels for many insightful discussions. I appreciate the collaborations with Omer Sedes, Jetin E Thomas, Kabir Ramola, Qin Xu, Marcio Gameiro, and Konstantin Mischaikow. I have thoroughly enjoyed working with my colleagues and friends: Elise Chen, Abhishek Sharma, Endao Han, Nicole M James, Neil Dolinski, Melody X Lim, and Bryan VanSaders for many fruitful discussions over the years.

Funding

Case Western Reserve University startup grant.

Author information

Authors and Affiliations

  1. Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, OH, 10040, USA

    Abhinendra Singh

Authors
  1. Abhinendra Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Not applicable.

Corresponding author

Correspondence to Abhinendra Singh.

Ethics declarations

Conflict of interest

There are no conflict of interest to declare.

Consent for publication

Yes.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, A. Hidden hierarchy in the rheology of dense suspensions. MRS Communications 13, 971–979 (2023). https://doi.org/10.1557/s43579-023-00450-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/s43579-023-00450-2

Keywords

Search

Navigation