Experimental models for cohesive granular materials: a review

TL;DR

This review addresses how to design and interpret experiments on cohesive granular materials by surveying model grains that enable controlled adhesion. It delineates five experimental approaches—capillary bridges, solid bridges, polymer coatings, magnetic forces, and geometric cohesion—and connects particle-scale adhesion to bulk properties using dimensionless and continuum concepts such as $Bo_g$ and Mohr-Coulomb cohesion. Key contributions include synthesizing mechanisms for tuning $F_{\rm adh}$, outlining methods to measure adhesion at the particle scale, and describing how cohesion manifests in macroscopic yield, confinement effects, and free-surface behavior (e.g., $\tau_c$, $\sigma_t$, and $\ell_c$). The review highlights gaps in understanding aging/consolidation and the challenge of reconciling inter-particle forces with bulk rheology, while proposing directions for experimental benchmarks and cross-validation with numerical models to advance cohesive granular flow understanding.

Abstract

Granular materials are involved in most industrial and environmental processes, as well as many civil engineering applications. Although significant advances have been made in understanding the statics and dynamics of cohesionless grains over the past decades, most granular systems we encounter often display some adhesive forces between grains. The presence of cohesion has effects at distances substantially larger than the closest neighbors and consequently can greatly modify their overall behavior. While considerable progress has been made in understanding and describing cohesive granular systems through idealized numerical simulations, controlled experiments corroborating and expanding the wide range of behavior remain challenging to perform. In recent years, various experimental approaches have been developed to control inter-particle adhesion that now pave the way to further our understanding of cohesive granular flows. This article reviews different approaches for making particles sticky, controlling their relative stickiness, and thereby studying their granular and bulk mechanics. Some recent experimental studies relying on model cohesive grains are synthesized, and opportunities and perspectives in this field are discussed.

Figures (8)

• Figure 1: Illustration of the effects of grain size and a small amount of water on the macroscopic behavior of granular materials. A mass $m=350$ g of grains is poured into a cylinder, which is then lifted quasi-statically at $0.1$ mm.s$^{-1}$. Top figures: dry granular columns of the same aspect ratio and different grain sizes collapse into similar piles, described by the macroscopic friction. Bottom figures: When a small amount of water is mixed into the grains, a wide range of behavior is observed due to cohesion. In this figure, $W= m_{\rm liq}/m_{\rm liq + solid} = 1\, \%$, where $m_{\rm liq}$ and $m_{\rm sol}$ are the masses of the liquid and solid phases respectively for all the grains. The pictures are taken as soon as the cylinder has been lifted. For large grains, the capillary bridges have only a minor effect. For small grains, the column behaves as a solid and resists any deformation when lifting the confining cylinder. The scale bar shown is the initial diameter of the column, 5 cm.
• Figure 2: (a) Comparison of the order of magnitude of the particle weight, the air drag force, and different interparticle forces when varying the size of a spherical particle of roughness $50\,{\rm nm}$. The expressions used to make this schematic, alongside the magnitudes and descriptions of the constants, are summarized in Table \ref{['table:Tab1_Forces']} (b) Schematic illustration of micromechanical tests of adhesion between particles in a normal and shear configuration. Pictures of such experiments are shown in (c) and (d), respectively. (c) and (d) are reproduced from hemmerle2021measuring with permission from the Royal Society of Chemistry.
• Figure 3: Schematic representation of the distribution of liquid within a wet granular material as a function of the liquid fraction $W$ and corresponding examples: (a) dry grains; (b) pendular state [reproduced with permission from herminghaus2005dynamics. Copyright 2005 from Taylor & Francis]; (c) funicular state; (d) capillary state [reproduced from sauret2020erosion]. If the liquid fills all the pore spaces and makes a suspension, the effects of cohesion are no longer observed, and this state is consequently outside our interest here. (e) Evolution of the capillary force with the distance between the particles and different volumes of capillary bridges [Adapted with permission from willett2000capillary. Copyright 2000 American Chemical Society.]. While more liquid ensures a bridge can last for a greater separation length, the maximum force appears to be approximately the same. (g) Cohesive yield stress $\tau_{\rm c}$ measured with a shear cell when varying the liquid fraction $W$ [Reprinted with permission from richefeu2006shear. Copyright 2006 by the American Physical Society. ]. The dashed line is drawn to suggest that beyond some minimal amount of liquid content, $W_m$, the yield stress is observed to saturate to $c_m$, for the ratio of liquid to total mass tested here.
• Figure 4: (a) Experiments showing microbial-induced calcite precipitation (MICP) to cement grains for tension tests as described earlier [Reprinted with permission from kwon2024pore] (b)-(c) Typical set of measurements from particle-scale tensile tests. (b) Evolution of the force between two grains connected by a solid bond. As the distance between rigidly connected spheres increases, the force measured rises until the bond ruptures. The amplitude of the force between before and after the rupture gives the adhesive force. (c) 3D tomographic reconstructions of broken bonds of paraffin wax between 7 mm glass beads. Rupture often occurs as de-bonding from one of the grains (top and middle) or as fracture within the bond (bottom). Figs (b) and (c) are reproduced with permission from farhat2024micro, copyright 2024 Springer Nature.
• Figure 5: SEM images of glass beads (a) before and (b) after polymer coating [Reprinted from ma2019fluidization, Copyright 2019, with permission from Elsevier]. (c) Macroscopic cohesive stress $\tau_{\rm c}$ of CCGM measured from inclined plane experiments as a function of the interparticle cohesive force $F_{\rm c}$. The dashed line is Eq. \ref{['eq:eq_Adh_cap_macro']} with $\phi=0.6$ and $Z=6$, which seemingly provides a reasonable prediction for polymer-coated grains as well. The inset shows that for the range of coatings tested here, no major effect on macroscopic friction $\mu$ is observed. [Reproduced from gans2020cohesion, Copyright 2020, with permission from American Physical Society]