Interparticle Friction Leads to Nonmonotonic Flow Curves and Hysteresis in Viscous Suspensions

Abstract

Hysteresis is a major feature of the solid-liquid transition in granular materials. This property, by allowing metastable states, can potentially yield catastrophic phenomena such as earthquakes or aerial landslides. The origin of hysteresis in granular flows is still debated. However, most mechanisms put forward so far rely on the presence of inertia at the particle level. In this paper, we study the avalanche dynamics of non-Brownian suspensions in slowly rotating drums and reveal large hysteresis of the avalanche angle even in the absence of inertia. By using micro-silica particles whose interparticle friction coefficient can be turned off, we show that microscopic friction, conversely to inertia, is key to triggering hysteresis in granular suspensions. To understand this link between friction and hysteresis, we use the rotating drum as a rheometer to extract the suspension rheology close to the flow onset for both frictional and frictionless suspensions. This analysis shows that the flow rule for frictionless particles is monotonous and follows a power law of exponent α = 0.37 ± 0.05, in close agreement with the previous theoretical prediction, α = 0.35. By contrast, the flow rule for frictional particles suggests a velocity-weakening behavior, thereby explaining the flow instability and the emergence of hysteresis. These findings show that hysteresis can also occur in particulate media without inertia, questioning the intimate nature of this phenomenon. By highlighting the role of microscopic friction, our results may be of interest in the geophysical context to understand the failure mechanism at the origin of undersea landslides. arXiv:1904.03918v1 [cond-mat.soft]

Viscometric flow of dense granular materials under controlled pressure and shear stress

“…The quasi-static stress ratio increases with friction from μ 0 1 = 0.09 for frictionless particles to μ 0 1 = 0.33 for particles with high friction, as shown in figure 3(c). The non-zero value of μ 0 1 for frictionless particles is consistent with previous simulations (Peyneau & Roux 2008) and experiments (Clavaud et al 2017;Perrin et al 2019) that demonstrated a non-zero internal friction angle for frictionless granular material. The value of μ 0 1 at high friction is consistent with previous simulations and experiments (Boyer, Guazzelli & Pouliquen 2011a;Salerno et al 2018;Srivastava et al 2019), and is also similar to the critical stress ratio from the critical state theory (Schofield & Wroth 1968).…”

“…Therefore, the rheology at low inertial numbers is not well-resolved for low pressures, especially for intermediate interparticle friction, as seen in figure 3(a). Recent experiments (Perrin et al 2019) and simulations (Degiuli & Wyart 2017) have indicated that the local rheology of frictional granular materials possibly exhibits hysteresis at very low inertial numbers, which would also prohibit very slow flows in the present stress-controlled simulations.…”

“…These topics are currently a subject of our ongoing study. Lastly, the constitutive model described here could also be extended to include other important granular flow phenomena such as hysteresis (Degiuli & Wyart 2017;Perrin et al 2019) and non-locality (Henann & Kamrin 2013)…”

Surface-wave instability without inertia in shear-thickening suspensions

“…The Oobleck waves instability mechanism highlighted in this study is not limited to shear-thickening suspensions and could be extended to any other complex fluids having a rheology with a negatively sloped region (e.g., granular materials and geomaterials exhibiting velocity-weakening rheology 43,44 , concentrated polymers or surfactant solutions 35,36 , liquid crystals 45 , active selfpropelled suspensions 46 ). More generally, our analysis shows that gravity forces, which are usually stabilizing for gravity-driven free-surface flows, can become destabilizing in the presence of a non-monotonic rheology.…”

Shear thickening of suspensions of dimeric particles

“…It is also possible to look at the same data as a function of the viscous number J = η f γ P p [Boyer, Guazzelli, and Pouliquen, 2011]. For rate-independent suspensions, µ M is a function of J [Boyer, Guazzelli, and Pouliquen, 2011;Trulsson, Andreotti, and Claudin, 2012;Gallier et al, 2014b;Ness and Sun, 2015;Amarsid et al, 2017;Seto and Giusteri, 2018;Chèvremont, Chareyre, and Bodiguel, 2019], which monotonicity has been recently argued to depend on the interparticle friction coefficient [Perrin et al, 2019]. Also, for these suspensions, one can measure µ M (J) in two equivalent ways: either in a usual, fixed volume, rate-(or stress-) controlled rheometer, by measuring independently P p (hence J) and µ M for several φ, or in a fixed pressure, rate-controlled rheometer by measuring µ M and φ for several J [Boyer, Guazzelli, and Pouliquen, 2011].…”