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  • Open Access

Unified model for full-stage shear thickening via surface chemistry and friction

Kang Wang*, Bing Liu*, and Quan Liu

Huaxia Deng†

Xinglong Gong‡

  • *These authors contributed equally to this work.
  • †Contact author: hxdeng@ustc.edu.cn
  • ‡Contact author: gongxl@ustc.edu.cn

Phys. Rev. Research 8, 023263 – Published 8 June, 2026

DOI: https://doi.org/10.1103/tzxq-dmgc

Abstract

Shear thickening fluid exhibits complex properties in a wide range of external conditions, leading to the significance for probing its state-transition property at the molecular level. Here, we propose a constitutive model that unifies the three rheological stages of shear thinning, shear thickening, and secondary shear thinning by considering the short-range attractive forces governed by particle surface chemistry in shear thickening dense suspensions. The proposed model reproduces the secondary shear thinning phenomenon precisely and predicts the evolution of cluster number, size, and dispersion with a marked error reduction. Besides, based on the proposed model, the distribution of particles can be divided into isolated, uniform-aggregated, and overaggregated states according to the dissipative particle dynamics simulation results. This model provides a framework to design rheological behavior via particle surface chemistry, bridge the relationship between microstructure and macroscopic performance at various scales, and accelerate the understanding to the state-transition phenomenon in shear thickening dense suspension.

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References (46)

  1. R. L. Hoffman, Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observation of a flow instability, Trans. Soc. Rheol. 16, 155 (1972).
  2. H. A. Barnes, Shear-thickening “dilatancy” in suspensions of nonaggregating solid particles dispersed in Newtonian liquids, J. Rheol. 33, 329 (1989).
  3. J. Yang, J. Zhang, B. Wang, and X. Gong, Constitutive modeling of shear thickening fluid using continuum mechanics, Int. J. Mech. Sci. 289, 110057 (2025).
  4. N. Fernandez, R. Mani, D. Rinaldi, D. Kadau, M. Mosquet, H. Lombois-Burger, J. Cayer-Barrioz, H. J. Herrmann, N. D. Spencer, and L. Isa, Microscopic mechanism for shear thickening of non-Brownian suspensions, Phys. Rev. Lett. 111, 108301 (2013).
  5. R. Mari, R. Seto, J. F. Morris, and M. M. Denn, Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions, J. Rheol. 58, 1693 (2014).
  6. L. Lobry, E. Lemaire, F. Blanc, S. Gallier, and F. Peters, Shear thinning in non-Brownian suspensions explained by variable friction between particles, J. Fluid Mech. 860, 682 (2019).
  7. R. Seto, R. Mari, J. F. Morris, and M. M. Denn, Discontinuous shear thickening of frictional hard-sphere suspensions, Phys. Rev. Lett. 111, 218301 (2013).
  8. R. Mari, R. Seto, J. F. Morris, and M. M. Denn, Nonmonotonic flow curves of shear thickening suspensions, Phys. Rev. E 91, 052302 (2015).
  9. Z. Pan, H. de Cagny, B. Weber, and D. Bonn, S-shaped flow curves of shear thickening suspensions: Direct observation of frictional rheology, Phys. Rev. E 92, 032202 (2015).
  10. G. Ovarlez, A. V. N. Le, W. J. Smit, A. Fall, R. Mari, G. Chatté, and A. Colin, Density waves in shear-thickening suspensions, Sci. Adv. 6, eaay5589 (2020).
  11. B. M. Guy, C. Ness, M. Hermes, L. J. Sawiak, J. Sun, and W. C. K. Poon, Testing the Wyart–Cates model for non-Brownian shear thickening using bidisperse suspensions, Soft Matter 16, 229 (2020).
  12. S. Jamali and J. F. Brady, Alternative frictional model for discontinuous shear thickening of dense suspensions: Hydrodynamics, Phys. Rev. Lett. 123, 138002 (2019).
  13. R. V. More and A. M. Ardekani, Unifying disparate rate-dependent rheological regimes in non-Brownian suspensions, Phys. Rev. E 103, 062610 (2021).
  14. V. Babu, H. A. Vinutha, D. Bi, and S. Sastry, Discontinuous rigidity transition associated with shear jamming in granular simulations, Soft Matter 19, 9399 (2023).
  15. H. Dashti, A. A. Saberi, S. H. E. Rahbari, and J. Kurths, Emergence of rigidity percolation in flowing granular systems, Sci. Adv. 9, eadh5586 (2023).
  16. V. A. Tolpekin, M. H. G. Duits, D. van den Ende, and J. Mellema, Aggregation and breakup of colloidal particle aggregates in shear flow, studied with video microscopy, Langmuir 20, 2614 (2004).
  17. G. Frungieri and M. Vanni, Aggregation and breakup of colloidal particle aggregates in shear flow: A combined Monte Carlo–Stokesian dynamics approach, Powder Technol. 388, 357 (2021).
  18. N. M. James, E. Han, R. A. L. de la Cruz, J. Jureller, and H. M. Jaeger, Interparticle hydrogen bonding can elicit shear jamming in dense suspensions, Nat. Mater. 17, 965 (2018).
  19. C.-P. Hsu, S. N. Ramakrishna, M. Zanini, N. D. Spencer, and L. Isa, Roughness-dependent tribology effects on discontinuous shear thickening, Proc. Natl. Acad. Sci. USA 115, 5117 (2018).
  20. C. Clavaud, A. Bérut, B. Metzger, and Y. Forterre, Revealing the frictional transition in shear-thickening suspensions, Proc. Natl. Acad. Sci. USA 114, 5147 (2017).
  21. M. M. Cross, Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems, J. Colloid Sci. 20, 417 (1965).
  22. J. J. Stickel and R. L. Powell, Fluid mechanics and rheology of dense suspensions, Annu. Rev. Fluid Mech. 37, 129 (2005).
  23. E. Brown and H. M. Jaeger, Shear thickening in concentrated suspensions: Phenomenology, mechanisms and relations to jamming, Rep. Prog. Phys. 77, 046602 (2014).
  24. J. F. Morris, Shear thickening of concentrated suspensions: Recent developments and relation to other phenomena, Annu. Rev. Fluid Mech. 52, 121 (2020).
  25. M. M. Denn and J. F. Morris, Rheology of non-Brownian suspensions, Annu. Rev. Chem. Biomol. Eng. 5, 203 (2014).
  26. Q. Liu, B. Liu, Y. Pan, J. Zhang, K. Wang, C. Lou, J. Zhou, H. Deng, and X. Gong, Probing the roles of surface characteristic of suspended nanoparticle in shear thickening suspensions, Appl. Surf. Sci. 659, 159910 (2024).
  27. A. K. Townsend and H. J. Wilson, Frictional shear thickening in suspensions: The effect of rigid asperities, Phys. Fluids 29, 121607 (2017).
  28. R. Mari, R. Seto, J. F. Morris, and M. M. Denn, Discontinuous shear thickening in Brownian suspensions by dynamic simulation, Proc. Natl. Acad. Sci. USA 112, 15326 (2015).
  29. M. Wyart and M. E. Cates, Discontinuous shear thickening without inertia in dense non-Brownian suspensions, Phys. Rev. Lett. 112, 098302 (2014).
  30. C. S. O’Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Jamming at zero temperature and zero applied stress: The epitome of disorder, Phys. Rev. E 68, 011306 (2003).
  31. G. D. Scott and D. M. Kilgour, The density of random close packing of spheres, J. Phys. D: Appl. Phys. 2, 863 (1969).
  32. J. N. Israelachvili, Intermolecular and Surface Forces, 3rd ed. (Academic Press, Burlington, MA, 2011).
  33. T. Kawasaki and L. Berthier, Discontinuous shear thickening in Brownian suspensions, Phys. Rev. E 98, 012609 (2018).
  34. M. Hermes, B. M. Guy, W. C. K. Poon, G. Poy, M. E. Cates, and M. Wyart, Unsteady flow and particle migration in dense, non-Brownian suspensions, J. Rheol. 60, 905 (2016).
  35. I. M. Krieger and T. J. Dougherty, A mechanism for non-Newtonian flow in suspensions of rigid spheres, Trans. Soc. Rheol. 3, 137 (1959).
  36. B. M. Guy, M. Hermes, and W. C. K. Poon, Towards a unified description of the rheology of hard-particle suspensions, Phys. Rev. Lett. 115, 088304 (2015).
  37. B. J. Maranzano and N. J. Wagner, The effects of particle size on reversible shear thickening of concentrated colloidal dispersions, J. Chem. Phys. 114, 10514 (2001).
  38. R. C. Ball and J. R. Melrose, A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces, Physica A 247, 444 (1997).
  39. K. Chen, Y. Wang, S. Xuan, S. Cao, and X. Gong, Contribution of frictional contact during steady and oscillatory shear in the discontinuous shear thickening fluid, Smart Mater. Struct. 28, 045009 (2019).
  40. R. D. Groot and P. B. Warren, Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation, J. Chem. Phys. 107, 4423 (1997).
  41. E. Kiyani, M. Kooshkbaghi, K. Shukla, R. B. Koneru, Z. Li, L. Bravo, A. Ghoshal, G. E. Karniadakis, and M. Karttunen, Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs, J. Fluid Mech. 985, A7 (2024).
  42. D. R. Foss and J. F. Brady, Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation, J. Fluid Mech. 407, 167 (2000).
  43. L. E. Silbert, D. Ertaş, G. S. Grest, T. C. Halsey, D. Levine, and S. J. Plimpton, granular flow down an inclined plane: Bagnold scaling and rheology, Phys. Rev. E 64, 051302 (2001).
  44. M. Blair and C. Ness, Shear thickening in dense suspensions driven by particle interlocking, J. Fluid Mech. 948, A48 (2022).
  45. T. C. Beutler, A. E. Mark, R. C. van Schaik, P. R. Gerber, and W. F. van Gunsteren, Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations, Chem. Phys. Lett. 222, 529 (1994).
  46. S. Pednekar, J. Chun, and J. F. Morris, Simulation of shear thickening in attractive colloidal suspensions, Soft Matter 13, 1773 (2017).

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