Viscosity bifurcation in granular materials, foams, and emulsions

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.

Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films between Neighboring Bubbles and Drops

“…Non-homogeneous flow, often discussed in terms of "shear banding" or "jammingunjamming transitions", attracted researchers' attention in several areas, because it appears as a generic phenomenon in various systems, such as glassy and granular materials, concentrated suspensions, foams, emulsions, and micellar solutions [1][2][3][4][5][6][7][8][9][10]. This phenomenon is still poorly understood and appropriate theoretical modeling, beyond the phenomenological description, is missing.…”

“…This agreement proves that properly chosen foams, with bubble radius in the range 20-150 μm, are indeed very appropriate for quantitative investigation of jamming and the related phenomena, because the bubble dynamics could be described theoretically in great detail and could be observed directly with optical devices. After simple modifications, the same approach could be applied to other types of dispersions, such as suspensions of soft particles (vesicles, microgel particles) or spherical solid particles [1][2][3]6]. For this purpose, appropriate material parameters and expressions for the surface forces should be implemented in the consideration.…”

An attempt to categorize yield stress fluid behaviour

“…Granular avalanches and thus also the viscosity bifurcation observed in granular systems (Da Cruz et al 2002) occur through a dilatancy of the system: gravity compacts the system, whereas the flow dilates it. This is in fact a rather peculiar type of thixotropy, but does manifest itself macroscopically in a similar way: the viscosity bifurcation in a dry granular system is not very different from that of bentonite.…”

“…A very striking demonstration of how the simple yield stress fluid picture often fails in predicting even qualitatively the flow of actual yield stress fluids is the 'avalanche behaviour' (Coussot et al 2002a,b), which has recently been observed for thixotropic yield stress fluids and leads to the so-called 'viscosity bifurcation' (Coussot et al 2002b;Da Cruz et al 2002). One of the simplest tests to determine the yield stress of a given fluid is the so-called inclined plane test (Coussot & Boyer 1995).…”

“…(i) Thixotropic yield stress fluids: particle and polymer gels (Moller et al 2008), attractive glasses (this paper), 'soft' colloidal glasses , adhesive emulsions (Ragouilliaux et al 2007), dry granular systems (Da Cruz et al 2002), pastes (Huang et al 2005), hard-sphere colloidal glasses (this paper). (ii) Simple yield stress fluids: emulsions and foams (Bertola et al 2003;Moller et al 2009), hair gel (Moller et al 2009), carbopol (Moller et al 2009).…”