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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 viscosity4-8. 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 rigidity9-11, 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 transient2,15-17. 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.
Jamming transitions transform fluid-like particle systems into amorphous solids with finite yield stress when the particle packing fraction φ increases beyond a critical value, φJ. In the standard scenario10, the jammed state is reached via isotropic compression, and for frictionless particle interactions the jammed system will weaken and eventually unjam when shear stress is applied. In suspensions, on the other hand, shear can have the opposite role, by inducing viscosity increases and even solidification. Here the idea has been that shear reorganizes particles into anisotropic configurations that form large clusters and potentially a load-bearing network. With frictionless, purely hydrodynamic interactions between suspended particles, such 'hydroclusters'21,22 can, however, give rise...