Viscosity bifurcation in granular materials, foams, and emulsions

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Abstract
We show that the rheological properties of dry granular materials, as well as foams and emulsions, are similar to typical thixotropic fluids: under a sufficiently strong shear the viscosity decreases in time, leading to a hysteresis in an up-and-down stress ramp. This leads to a viscosity bifurcation around a critical stress: for smaller stresses, the viscosity increases in time and the material eventually stops flowing, whereas for slightly larger stresses the viscosity decreases continuously with time and the flow accelerates. These results show that all jammed systems exhibit strong mechanical similarities around the transition between a “fluid” and a “solid” state, and that the transition between these states is discontinuous. This similarity is further emphasized by the fact that both a simple model for the dynamics of a grain on a sandpile [Quartier et al., Phys. Rev. E 62, 8299 (2000)] and a simple model for the thixotropic behavior of (colloidal) pastes [Coussot et al., Phys. Rev. Lett. 88, 175501 (2002)] extrapolated to granular flows qualitatively predict this viscosity bifurcation.

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