Viscous to Inertial Transition in Dense Granular Suspension

Origins of complexity in the rheology of Soft Earth suspensions

When wet soil becomes fully saturated by intense rainfall, or is shaken by an earthquake, it may fluidize catastrophically. Sand-rich slurries are treated as granular suspensions, where the failure is related to an unjamming transition, and friction is controlled by particle concentration and pore pressure. Mud flows are modeled as gels, where yielding and shear-thinning behaviors arise from inter-particle attraction and clustering. Here we show that the full range of complex flow behaviors previously reported for natural debris flows can be reproduced with three ingredients: water, silica sand, and kaolin clay. Going from sand-rich to clay-rich suspensions, we observe continuous transition from brittle (Coulomb-like) to ductile (plastic) yielding. We propose a general constitutive relation for soil suspensions, with a particle rearrangement time that is controlled by yield stress and jamming distance. Our experimental results are supported by models for amorphous solids, suggesting that the paradigm of non-equilibrium phase transitions can help us understand and predict the complex behaviors of Soft Earth suspensions.

Rheology of Suspensions of Non-Brownian Soft Spheres across the Jamming and Viscous-to-Inertial Transitions

The rheology of suspensions of non-Brownian soft spheres is studied across jamming but also across the viscous and inertial regimes using a custom pressure- and volume-imposed rheometer. The study shows that the granular rheology found for suspensions of hard spheres can be extended to a soft granular rheology (SGranR) by renormalizing the critical volume fraction and friction coefficient to pressure-dependent values and using the addition of the viscous and inertial stress scales. This SGranR encompasses rheological behaviors on both sides of the jamming transition, resulting in an approximate collapse of the rheological data into two branches when scaled with the distance to jamming, as observed for soft colloids. This research suggests that suspensions of soft particles across flow regimes can be described by a unified SGranR framework around the jamming transition.

Rheology of debris flow materials is controlled by the distance from jamming

Debris flows are fast-flowing and dangerous slurries of soil and water that often form when intense rainfall soaks hillsides burned by wildfire. As climate change intensifies this hazard, models capable of predicting failure and flow behaviors are needed. Here we capitalize on recent progress in the physics of dense suspensions, to determine how the physical and chemical composition of natural hillslope soils controls the viscosity and yield stress of debris flows. We show how a simple flow model—previously developed for idealized suspensions—can be extended to highly heterogeneous, natural debris flow materials. This model reconciles previously contradictory observations and could help to improve computer models that assess the hazard potential of debris flows in the field.

Debris flows are dense and fast-moving complex suspensions of soil and water that threaten lives and infrastructure. Assessing the hazard potential of debris flows requires predicting yield and flow behavior. Reported measurements of rheology for debris flow slurries are highly variable and sometimes contradictory due to heterogeneity in particle composition and volume fraction (ϕ) and also inconsistent measurement methods. Here we examine the composition and flow behavior of source materials that formed the postwildfire debris flows in Montecito, CA, in 2018, for a wide range of ϕ that encapsulates debris flow formation by overland flow. We find that shear viscosity and yield stress are controlled by the distance from jamming, Δϕ=ϕm−ϕ, where the jamming fraction ϕm is a material parameter that depends on grain size polydispersity and friction. By rescaling shear and viscous stresses to account for these effects, the data collapse onto a simple nondimensional flow curve indicative of a Bingham plastic (viscoplastic) fluid. Given the highly nonlinear dependence of rheology on Δϕ, our findings suggest that determining the jamming fraction for natural materials will significantly improve flow models for geophysical suspensions such as hyperconcentrated flows and debris flows.

Granular effects in sea ice rheology in the marginal ice zone

Sea ice in the marginal ice zone (MIZ) consists of relatively small floes with a wide size span. In response to oceanic and atmospheric forcing, it behaves as an approximately two-dimensional, highly polydisperse granular material. The established viscous-plastic rheologies used in continuum sea ice models are not suitable for the MIZ; the collisional rheology, in which sea ice is treated as a granular gas, captures only one aspect of the granular behaviour, typical for a narrow range of conditions when dynamics is dominated by binary floe collisions. This paper reviews rheology models and concepts from research on granular materials relevant for MIZ dynamics (average stress as a result of 'microscopic' interactions of grains; [Formula: see text] and collisional rheologies). Idealized discrete-element simulations are used to illustrate granular effects and strong influence of the floe size distribution on strain-stress relationships in sheared sea ice, demonstrating the need for an MIZ rheology model capturing the whole range of 'regimes', from quasi-static/dense flow in the inner MIZ to the inertial flow in the outer MIZ. This article is part of the theme issue 'Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks'.