Insights into the rheology of cohesive granular media
Résumé
Characterization and prediction of the "flowability" of powders are of paramount importance in many industries. However, our understanding of the flow of powders like cement or flour is sparse compared to the flow of coarse, granular media like sand. The main difficulty arises because of the presence of adhesive forces between the grains, preventing smooth and continuous flows. Several tests are used in industrial contexts to probe and quantify the "flowability" of powders. However, they remain empirical and would benefit from a detailed study of the physics controlling flow dynamics. Here, we attempt to fill the gap by performing intensive discrete numerical simulations of cohesive grains flowing down an inclined plane. We show that, contrary to what is commonly perceived, the cohesive nature of the flow is not entirely controlled by the interparticle adhesion, but that stiffness and inelasticity of the grains also play a significant role. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow. This observation is rationalized by introducing the concept of a dynamic, "effective" adhesive force, a single parameter, which combines the effects of adhesion, elasticity, and dissipation. Based on this concept, a rheological description of the flow is proposed for the cohesive grains. Our results elucidate the physics controlling the flow of cohesive granular materials, which may help in designing new approaches to characterize the "flowability" of powders. granular flows | rheology | cohesion | powder M any industrial (wet granulation, food processing, construction , etc.) and geophysical (landslides, mudflow, etc.) processes involve the flows of an assembly of cohesive grains. The cohesion between the grains has different origins. Van der Waals or electrostatic forces are responsible for cohesion in fine grains (1, 2). Liquid capillary (3-5) or solid bridges (6) between the grains give rise to cohesion in large grains. In all cases, the cohesion introduces an additional complexity to gran-ular materials-the flows of cohesive grains are intermittent and less homogeneous (7, 8) in comparison with coarse, cohesion-less grains, leading to frequent jamming of industrial units. It is, therefore, necessary to a priori characterize and quantify the capability of flow, so-called "flowability," of a powder to yield better handling. Different methods are used in industrial contexts for this purpose (1, 9-11). A first method measures the tapped bulk density and the freely settled bulk density of a powder to define the Hausner ratio (or Carr index), which is the ratio of the two. A powder with high Hausner ratio is shown to have poor "flowability." A second one employs a series of measurements , using the Hosokawa powder tester, comprising angle of repose, aerated bulk density, tapped bulk density, etc., to define a weighted "flowability" index, which ranges from 0 to 100. Very cohesive powders yield "flowability" indices close to zero and the free-flowing ones close to 100. Other methods estimate the macroscopic cohesion from the yield loci of a powder using shear testers (Jenike shear tester or ring shear tester) for various pre-consolidation normal stresses, which are useful in understanding the arch formation in silos. All these methods, carried out in the quasistatic limit, are useful for comparing the macroscopic properties of different powders and for characterizing their plastic behavior. However, they do not provide any information about the flow dynamics. Understanding the concept of "flowability" from a physical point of view is still a challenge. The flow dynamics of rigid, cohesionless grains, interacting solely by contact and friction, is less complex in comparison with cohesive grains, as shown by numerous experimental and numerical studies (12). Flow rules have been evidenced and constitutive laws have been proposed for different flow regimes (13, 14). In the dense flow regime, the rheology of the grains of diameter d and density ρp, sheared at a shear rateγ by imposing a shear stress τ under a confining normal stress σzz , is well described by a coefficient of friction µ(I) and a volume fraction φ(I), which depend on a single dimensionless parameter, the inertial number I =γd / σzz /ρp (15, 16). These constitutive relations are found to be unaffected by the mechanical properties of the grains-for example, stiffness and inelasticity-as long as the grains are sufficiently rigid and inelastic (14, 17-19). This rough description of the rheology has proven to be useful in describing flows in different configurations from inclines to silos (20-23). This rheological framework has been extended to the flows of cohesive grains (24-27) by using discrete numerical simulations. Different force models with different levels of realism have been used in the simulations to account for the cohesive interactions between the grains (28, 29). In the simplest approach used in rheological studies (24, 27), the adhesion is characterized by a minimum pull-off force Nc necessary to detach two grains. The existence of this additional force scale implies that a second dimensionless number, called cohesion number C = Nc/(σzz d 2), exists besides the inertial number, which compares the adhesive force between the grains with the confining normal stress. The rheology is then described by a coefficient of friction µ(I , C) and a volume fraction φ(I , C), which are functions of I and C only (24-27, 30). Significance An uninterrupted flow of powders is the key to smooth production operations of many industries. However, powders have more difficulty flowing than coarse, granular media like sand because of the interparticle cohesive interactions. What precisely controls the "flowability" of powders remains unclear. Here, we address this issue by performing numerical simulations of the flow of cohesive grains. We show that the cohesiveness during flow is not only controlled by the inter-particle adhesion, but also by the stiffness and inelasticity of the grains. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow, i.e., higher "flowability." This combined effect can be embedded in a single dimensionless number-a result that enriches our understanding of powder rheology.
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