Liquid-like at rest, dense suspensions of hard particles can undergo striking transformations in behaviour when agitated or sheared1. These phenomena include solidification during rapid impact2,3, as well as strong shear thickening characterized by discontinuous, orders-of-magnitude increases in suspension viscosity4,5,6,7,8. Much of this highly non-Newtonian behaviour has recently been interpreted within the framework of a jamming transition. However, although jamming indeed induces solid-like rigidity9,10,11, even a strongly shear-thickened state still flows and thus cannot be fully jammed12,13. Furthermore, although suspensions are incompressible, the onset of rigidity in the standard jamming scenario requires an increase in particle density9,10,14. Finally, whereas shear thickening occurs in the steady state, impact-induced solidification is transient2,15,16,17. As a result, it has remained unclear how these dense suspension phenomena are related and how they are connected to jamming. Here we resolve this by systematically exploring both the steady-state and transient regimes with the same experimental system. We demonstrate that a fully jammed, solid-like state can be reached without compression and instead purely with shear, as recently proposed for dry granular systems18,19. This state is created by transient shear-jamming fronts, which we track directly. We also show that shear stress, rather than shear rate, is the key control parameter. From these findings we map out a state diagram with particle density and shear stress as variables. We identify discontinuous shear thickening with a marginally jammed regime just below the onset of full, solid-like jamming20. This state diagram provides a unifying framework, compatible with prior experimental and simulation results on dense suspensions, that connects steady-state and transient behaviour in terms of a dynamic shear-jamming process.
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We thank E. Brown, E. Han, N. James, S. Mukhopadhyay and Q. Xu for discussions. This work was supported by the US Army Research Office through grant W911NF-12-1-0182 and the Chicago Materials Research Science and Engineering Center, which is funded by the NSF through grant DMR-1420709. S.M. acknowledges support through a Kadanoff-Rice fellowship.
The authors declare no competing financial interests.
Extended data figures and tables
a, Ratio between front speed and driving speed as a function of the solvent viscosity. Error bars are standard deviations of 7–19 repeated experiments at different driving speeds ui. b, Bouncing transition curves for two different solvent viscosities. The horizontal axis gives the applied shear stress, the vertical axis the maximum upward velocity we observed from the trajectory of the impacting sphere. Error bars are standard deviations of 5–10 repeated experiments.
Experimental trajectories showing the long-time behaviour of spheres impacting the suspension under three different shear stresses. Zero shear stress (blue curve) and a stress of 90 Pa (DST, green curve) both show a slowly sinking sphere. The shear-jammed state (4,400 Pa, red curve) shows a rebound followed by yield stress behaviour, shown by the sphere not sinking in.
This video shows the determination of the onset of shear-jamming through the impact of spheres on the suspension surface. (MP4 13217 kb)
Difference between a diffusive-like velocity profile and a travelling jamming front at high driving speed
This video shows the difference between a diffusive-like velocity profile at low driving speed and a traveling jamming front at high driving speed. (MP4 8152 kb)
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Peters, I., Majumdar, S. & Jaeger, H. Direct observation of dynamic shear jamming in dense suspensions. Nature 532, 214–217 (2016). https://doi.org/10.1038/nature17167
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