Shear bands in granular flow through a mixing length model

We discuss the advantages and results of using a mixing-length, compressible model to account for shear banding behaviour in granular flow. We formulate a general approach based on two function of the solid fraction to be determined. Studying the vertical chute flow, we show that shear band thickness is always independent from flowrate in the quasistatic limit, for Coulomb wall boundary conditions. The effect of bin width is addressed using the functions developed by Pouliquen and coworkers, predicting a linear dependence of shear band thickness by channel width, while literature reports contrasting data. We also discuss the influence of wall roughness on shear bands. Through a Coulomb wall friction criterion we show that our model correctly predicts the effect of increasing wall roughness on the thickness of shear bands. Then a simple mixing-length approach to steady granular flows can be useful and representative of a number of original features of granular flow.Comment: submitted to EP

Characterising powder flowability at high shear rates by the ball indentation method

Unreliable powder flow is a major problem during processing of powders. The shear cell is the most widely used method for powders subjected to moderate or high stresses, and under quasi-static conditions, with established methods for designing large bins and hoppers based on the measurement. However, this method is not suitable for measuring the flowability of dynamic systems, such as powder mixing. Here, the ball indentation method is investigated as a technique for evaluating powders in the intermediate and dynamic regime of flow. The method, which simply consists of dropping a ball onto a cylindrical bed of powder previously consolidated, directly measures hardness, which is related to the unconfined yield stress of the powder by the constrain factor (Hassanpour and Ghadiri, 2007). The impact of the ball on the bed is recorded with a high-speed camera to determine velocity and penetration depth. The shear rate is varied by using a range of indenter materials and sizes, and a range of drop heights. The hardness against the strain rate is considered for several materials. It was found that the indenter size does not influence the hardness results, which are consistent with the flowability evaluation achieved with the rheometer. Furthermore the hardness, which is independent of the strain rate in quasi-static conditions, becomes shear rate dependent in intermediate regime of flow. Further work is needed to evaluate hardness in the rapid granular flow regime

Dynamic ball indentation for powder flow characterization

In industrial processing and manufacturing, characterizing the flowability of particulate solids is of particular importance both for reliable powder flow and for a consistent production rate. Shear testing is the most widely used method for powders subjected to moderate or high stresses, and under quasi-static conditions. However, this method is not suitable for measuring the powder flow properties occurring in dynamic systems, such as powder mixers and screw conveyors. In this study, the rheological behaviour of powders at high shear rates has been evaluated by the ball indentation method. The technique, which simply consists of dropping a ball onto a cylindrical bed of previously consolidated powder, directly measures the material hardness, which is related to the unconfined yield stress by the constraint factor. The impact of the ball on the bed is recorded with a high-speed camera to determine velocity and penetration depth. The hardness against the strain rate is considered for four different materials. Because of their difference in particle size, and by using a range of drop heights and a range of indenter densities, the intermediate regime of flow has been fully analyzed. Although hardness is constant in the quasi-static condition, it results to be strain rate dependent in the intermediate regime of flow. Finally, a predictive correlation that allows the operator to choose the best operating conditions for achieving the desired flow regime is proposed, and the unconfined yield strength of the materials is inferred

Bulk Powder Flow Characterisation Techniques

This chapter provides a review of the state of the art apparatus and procedures for the characterisation of powder flow properties. Classified according to the relevant state of consolidation, their measurement principles and the consequent procedure for different powder flow properties are described in detail. In addition, major available commercial devices are introduced, discussed and summarised based on the powder flow properties that can be measured. Finally, a comparison between the main features of different measurement methods with reference to the relevant powder consolidation, suitable usage, availability of standardised procedures and ease of self-construction of the rig is provided

Shear-induced particle segregation in binary mixtures: Verification of a percolation theory

Granular materials composed of different-sized grains may experience undesired segregation. Segregation is detrimental for a lot of industries because it leads to an increase in production costs and wastes. For these reasons, the segregation phenomena have been intensively studied in the last decades, and a lot of models have been provided by many researchers. However, these models are mainly based on empirical relations rather than physical considerations. This paper aims to confirm the main assumptions made by Volpato, Tirapelle, and Santomaso (2020) in their percolation theory by means of DEM simulations. The simulated geometry is a tilting shear box filled with few tracer particles in a bed of coarser sized grains, and simulations are performed for a range of tilting frequencies and size ratios. The results provide meaningful insight on the mathematical model parameters and allow us to say that the percolation theory relies on physically consistent assumptions

Experimental investigation and numerical modelling of density-driven segregation in an annular shear cell

Granular materials segregate spontaneously due to differences in particle size, shape, density and flow behaviour. In this paper we experimentally investigate density-difference-driven segregation for a range of density ratios and a range of heavy particle concentrations. The experiments are conducted in an annular shear cell with rotating bumpy bottom that yields an exponential shear profile. The cell is initially filled with a layer of light particles and an upper layer of heavier grains and, on top, a load provides confinement. The segregation process is filmed through the transparent side-wall with a camera, and the evolution of particle concentration in space and time is evaluated by means of post-processing image analysis. We also propose a continuum-approach to model density-driven segregation. We use a segregation-diffusion transport equation, constitutive relations for effective viscosity and friction coefficient, and a segregation velocity analogous to the Stokes\u2019 law. The model, which is validated by comparison with experimental findings, can successfully predict density-driven segregation at different density ratios and volumetric fraction