Nonlinear glassy rheology

Dense colloidal suspensions and related glass-forming fluids show pronounced nonlinear (non-Newtonian) flow effects, since slow internal relaxation competes with the imposed external driving. The microscopic processes governing the macroscopic material behavior are nonlocal both in time and space, encoding the divergence of viscosity in the fluid, and the rigidity of the amorphous solid that forms at the glass transition. Current theoretical approaches starting from either extreme, the homogeneous fluid flow and the spatially heterogeneous amorphous solid, are reviewed. [Display omitted] •The rheology of dense suspensions shows fluid-like and solid-like aspects.•Fluid flow is governed by temporal-history effects.•Amorphous-solid deformation is ruled by mesoscale localized plastic events.•Future development concerns the theoretical description covering both regimes.