Viscoinertial regime of immersed granular flows

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.

Numerical model for solid-like and fluid-like behavior of granular flows

We propose a constitutive model for both the solid-like and fluid-like behavior of granular materials by decomposing the stress tensor into quasi-static and collisional components. A hypoplastic model is adopted for the solid-like behavior in the quasi-static regime, while the viscous and dilatant behavior in the fluid-like regime is represented by a modified μ ( I ) rheology model. This model effectively captures the transition between solid-like and fluid-like flows. Performance and validation of the proposed model are demonstrated through numerical simulations of element tests.

Shear dilation of subglacial till results in time-dependent sliding laws

The dynamics of glacial sliding over water-saturated tills are poorly constrained and difficult to capture realistically in large-scale models. Experiments characterize till as a plastic material with a pressure-dependent yield stress, but the subglacial water pressure may fluctuate on annual to daily timescales, leading to transient adjustment of the till. We construct a continuum two-phase model of coupled fluid and solid deformation, describing the movement of water through the pore space of a till that is itself dilating and deforming. By forcing the model with time-dependent effective pressure at the ice–till interface, we infer the resulting relationships between basal traction, solid fraction and rate of deformation. We find that shear dilation introduces internal pressure variations and transient dilatant strengthening emerges, leading to hysteretic behaviour in low-permeability materials. The result is a time-dependent effective sliding law, with permeability-dependent lag between changes in effective pressure and the slidingspeed. This deviation from traditional steady-state sliding laws may play an important role in a wide range of transient ice-sheet phenomena, from glacier surges to the tidal response of ice streams.

Viscous to Inertial Transition in Dense Granular Suspension

Granular suspensions present a transition from a Newtonian rheology in the Stokes limit to a Bagnoldian rheology when inertia is increased. A custom rheometer that can be run in a pressure- or a volume-imposed mode is used to examine this transition in the dense regime close to jamming. By varying systematically the interstitial fluid, shear rate, and packing fraction in volume-imposed measurements, we show that the transition takes place at a Stokes number of 10 independent of the packing fraction. Using pressure-imposed rheometry, we investigate whether the inertial and viscous regimes can be unified as a function of a single dimensionless number based on stress additivity.

Directional shear jamming of frictionless ellipses

In this work we study shear reversals of dense non-Brownian suspensions composed of cohesionless elliptical particles. By numerical simulations, we show that a new fragility appears for frictionless ellipses in the flowing states, where particles can flow indefinitely in one direction at applied shear stresses but shear jam in the other direction upon shear stress reversal. This new fragility, absent in the isotropic particle case, is linked to the directional order of the elongated particles at steady shear and its reorientation at shear stress reversal, which forces the suspensions to pass through a more disordered state with an increased number of contacts in which it might get arrested.

Scaling behavior of the tensile strength of viscocohesive granular aggregates

We numerically analyze the tensile strength of a single wet agglomerate modeled as a viscocohesive aggregate impacting a flat surface by using the discrete-element simulations. The viscocohesive agglomerate composed of primary spherical particles with the inclusion of the interstitial liquid in the form of the capillary bridges characterized by the cohesive and viscous forces between particles is extracted from a cuboidal sample of granular materials by applying a spherical probe. The tensile strength is measured from the impact test of a wet agglomerate by systematically varying different values of the surface tension of the interstitial liquid, the liquid viscosity, and the impact speed. We show that the tensile stress increases immediately when the collision occurs between the agglomerate and the flat surface. The peak of the tensile stress obtained after the collision, then decreases smoothly with increasing the particle movement. The maximum tensile stress is defined to be the tensile strength of such agglomerate. It is remarkable that the normalized tensile strength of such agglomerate can be well described as a function of a dimensionless impact number that incorporates the capillary number and Stokes number (calculated from the surface tension and the viscosity of the liquid and the impact rate of the agglomerate), thus providing the confirmation for the unified representation of the liquid properties and the impact rate of wet granular media.

Time scales and rheology of visco-cohesive granular flows

In the presence of viscous and cohesive interactions between particles, a granular flow is governed by several characteristic time and stress scales that determine its rheological properties (shear stress, packing fraction, effective viscosities). In this paper, we revisit and extend the scaling arguments used previously for dry cohesionless granular flows and suspensions. We show that the rheology can be in principle described by a single dimensionless control parameter that includes all characteristic times. We also briefly present simulation results for 2D sheared suspensions and 3D wet granular flows where the effective friction coefficient and packing fraction are consistently described as functions of this unique control parameter.

The role of inter-particle friction on rheology and texture of wet granular flows

In order to get insight into the rheology and texture of rough unsaturated granular flows, we study the effects of the inter-particle friction coefficient on the macroscopic attributes and the texture variables of steady-state shearing flow of wet granular materials by relying on three-dimensional (3D) particle dynamics simulations. The macroscopic attributes are characterized by the macroscopic friction coefficient, macroscopic cohesion, and the packing fraction. The microstructural variables are characterized by the fabric and force anisotropies, the coordination number, and the stress transmission ratio. We show that the macroscopic observables behave as a function of the inertial number as a dry case for different values of the inter-particle friction coefficient. In particular, the macroscopic friction coefficient increases and the packing fraction decreases rapidly for small values of the friction coefficient, then they almost reach plateaus for higher values of the friction coefficient. Interestingly, all the macroscopic observables nicely behave as a function of the small values of the friction coefficient. Similarly, we also observe these characteristics for the fabric and force anisotropies and the coordination number as well as the stress transmission ratio which reflects the intermediate relationship between the microstructure and the mechanical behavior of such flows.

Additive rheology of complex granular flows

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Granular materials are abundant in nature, but we haven’t fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

Evolution of wet agglomerates inside inertial shear flow of dry granular materials

We use particle dynamics simulations to investigate the evolution of a wet agglomerate inside homogeneous shear flows of dry particles. The agglomerate is modeled by introducing approximate analytical expressions of capillary and viscous forces between particles in addition to frictional contacts. During shear flow, the agglomerate may elongate, break, or be eroded by loss of its capillary bonds and primary particles. By systematically varying the shear rate and surface tension of the binding liquid, we characterize the rates of these dispersion modes. All the rates increase with increasing inertial number of the flow and decreasing cohesion index of the agglomerate. We show that the data points for each mode collapse on a master curve for a dimensionless scaling parameter that combines the inertial number and the cohesion index. The erosion rate vanishes below a cutoff value of the scaling parameter. This leads to a power-law borderline between the vanishing erosion states and erosion states in the phase space defined by the inertial number and the cohesion index.

Transparent experiments: releasing data from mechanical tests on three dimensional hydrogel sphere packings

We describe here experiments on the mechanics of hydrogel particle packings from the Behringer lab, performed between 2012 and 2015. These experiments quantify the evolution of all contact forces inside soft particle packings exposed to compression, shear, and the intrusion of a large intruder. The experimental set-ups and processes are presented and the data are concomitantly published in a repository (Barés et al. in Dryad, Dataset 10.5061/dryad.6djh9w0x8, 2019).

A general constitutive model for dense, fine-particle suspensions validated in many geometries

Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect-for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of "shear jamming fronts," 3) the time-dependent propagation of "impact-activated jamming fronts," and 4) the non-Newtonian, "running on oobleck" effect, wherein fast locomotors stay afloat while slow ones sink.

Agglomeration of wet particles in dense granular flows

In order to get insight into the wet agglomeration process, we numerically investigate the growth of a single granule inside a dense flow of an initially homogeneous distribution of wet and dry particles. The simulations are performed by means of the discrete element method and the binding liquid is assumed to be transported by the wet particles, which interact via capillary and viscous force laws. The granule size is found to be an exponential function of time, reflecting the conservation of the amount of liquid and the decrease of the number of available wet particles inside the flow during agglomeration. We analyze this behavior in terms of the accretion and erosion rates of wet particles for a range of different values of material parameters such as mean particle size, size polydispersity, friction coefficient and liquid viscosity. In particular, we propose a phase diagram of the granule growth as a function of the mean primary particle diameter and particle size span, which separates the parametric domain in which the granule grows from the domain in which the granule does not survive.

Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows

Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient μ scales with the square root of the local Péclet number Pe provided that the particle diameter exceeds the particle mean free path. With decreasing Pe and granular temperature gradient M, this general scaling breaks down, leading to a yield condition with a variable yield stress ratio characterized by M.

Fluid flow through packings of elastic shells

Fluid transport in porous materials is commonly studied in geological samples (soil, sediments, etc.) or idealized systems, but the fluid flow through compacted granular materials, consisting of substantially strained granules, remains relatively unexplored. As a step toward filling this gap, we study a model of liquid transport in packings of deformable elastic shells using finite-element and lattice-Boltzmann methods. We find that the fluid flow abruptly vanishes as the porosity of the material falls below a critical value, and the flow obstruction exhibits features of a percolation transition. We further show that the fluid flow can be captured by a simplified permeability model in which the complex porous material is replaced by a collection of disordered capillaries, which are distributed and shaped by the percolation transition. To that end, we numerically explore the divergence of hydraulic tortuosity τ_{H} and the decrease of a hydraulic radius R_{h} as the percolation threshold is approached. We interpret our results in terms of scaling predictions derived from the percolation theory applied to random packings of spheres.

The dynamics of granular flow from a silo with two symmetric openings

The dynamics of granular flow in a rectangular silo with two symmetrically placed exit openings is investigated using particle image velocimetry (PIV), flow rate measurements and discrete element modelling (DEM). The flow of mustard seeds in a Perspex silo is recorded using a high-speed camera and the resulting image frames are analysed using PIV to obtain velocity, velocity divergence and shear rate plots. A change in flow structure is observed as the distance L between the two openings is varied. The mass flow rate is shown to be at a maximum at zero opening separation, decreasing as L is increased; it then reaches a minimum before rising to an equilibrium rate close to two times that of an isolated (non-interacting) opening. The flow rate experiment is repeated using amaranth and screened sand and similar behaviour is observed. Although this result is in contrast with some recent DEM and physical experiments in silo systems, this effect has been reported in an analogous system: the evacuation of pedestrians from a room through two doors. Our experimental results are replicated using DEM and we show that inter-particle friction controls the flow rate behaviour and explains the discrepancies in the literature results.