Mixing of granular materials, part II: effect of particle size under periodic shear

Although the study of mixing of granular particles in the last years has shown notable advances, it continues being moderately understood. In this work, a low shear mixing device consisting of a box with two moving walls and three static walls was used again to study granular mixing as a function of particle size. The goal is to obtain a more in depth understanding of the internal behavior of granular material in the three dimensions when particle size is changed. Experiments at different particle size distributions and wall displacements were run. Results show that faster mixing is achieved with particles of high diameter. The particle size affected the granular movement at the three directions. The phenomenon of dilation varied proportionally with the particle size.     

Quantitative validation of the discrete element method using an annular shear cell

The discrete element method (DEM) is often used as the “gold standard” for comparison to continuum-level theories and/or coarse-grained models of granular material flows due to its derivation from first-principal constructs, like contact mechanics. Despite its prevalence, the method is most often validated against experiment in only qualitative ways - comparison of mixing rates, gross features of concentration profiles, etc. - for exactly the reason it has found its popularity; detailed experimental measurements are difficult and often expensive. In this paper, we outline work aimed at using detailed, particle-level experimental measurements to quantitatively validate DEM simulations. Specifically, we examine the flow in a horizontally-aligned annular shear cell. Measurements are performed using digital particle tracking velocimetry (DPTV) so that the velocity, granular temperature, and solids fractions profiles may be extracted. Computationally, we attempt to match the experimental measurements as closely as possible and study the impact of a variety of contact mechanics-inspired force laws as well as perform sensitivity analysis on device and particle geometry and material properties employed.     

Transport property measurements in sheared granular flows

Experiments were performed in a shear cell device under four different solid fractions. The glass spheres with a mean diameter of 3 mm were used as granular materials. The motions of the granular materials were recorded by a high-speed camera. By using image processing technology and a particle tracking method, the average and fluctuation velocities in the streamwise and the transverse directions could be successfully measured and analyzed. Three bi-directional stress gages were used to measure the normal and shear stresses along the upper boundary. The effective viscosity of the granular material flow can be calculated. By tracking the movements of particles continually, the curves of the mean-square diffusive displacements versus time were plotted and were used to determine the self-diffusion coefficients from the slopes of the curves. The fluctuations and the self-diffusion coefficients in the streamwise direction were much higher than those in the transverse direction. The fluctuations were found to increase with the solid fraction, but the diffusion coefficients were greater in a more dilute flow system.     

Analysis of the kinetics of agglomerate erosion in simple shear flows

A model for the erosion kinetics of particle agglomerates in simple shear flows has been developed. The erosion rate is taken to be proportional to the difference between hydrodynamic and cohesive forces and to the rotation velocity of the dispersing agglomerate. For dispersion under identical hydrodynamic conditions, the model predicts faster erosion for larger agglomerates. Moreover, at equivalent hydrodynamic stress, erosion is enhanced at higher shear rates. Dispersion experiments using silica agglomerates of various densities and liquid low molecular weight polymers (e.g., poly(dimethyl siloxane)) of different viscosities were conducted in an oscillatory shear flow device. The experimental results validate the erosion model; the general shape of the erosion kinetic curve, and the effect of viscosity, shear rate and agglomerate size on dispersion kinetics are well predicted. The model can also predict erosion for agglomerates with fractal structure.     

The maximum thickness of upper shear layers of granular materials in rotating cylinders

Published data from Henein et al. (Metallurgical Transactions 14B (1983a) 191-206), Woodle and Munro (Powder Technology 76 (1993) 241-245), Boateng and Barr (Journal of Fluid Mechanics 330 (1997) 233-249), Van Puyvelde et al. (Transactions of the Institute of Chemical Engineers 78A (2000) 643-650), and Felix et al. (Powder Technology 128 (2002) 314-319) on the maximum thickness of shear layers at the upper surface of a freely flowing granular material being rotated in a cylindrical drum are modeled and analyzed. A theory is developed which suggests that all distances should be scaled by x_m, or half the length of the shear layer, which should remove most of the explicit dependence on the filled fraction. The rolling regime is predicted to contain two extreme regimes. The dispersive (inertial) regime occurs when the parameter Fr_s(x_m/σ)^4/3 is small (large), and is characterized by the dominance of dispersive (inertial) effects. Here Fr_s is a particle-dependent Froude number scaled by x_m, and σ is the particle diameter. An author-dependent and particle-dependent parameter λ is introduced to account for the different definitions and particle types used. Regression analysis shows that most of the data sets above (for the rolling regime) are approximately described by the dispersive regime. Our theory predicts that shear layers in the rolling regime should be almost identical for fill fractions symmetric about the half-filled level. All of the data analyzed satisfy essentially the same scale-up relationship, and does not support the idea that the maximum shear layer thickness should be about ten particle diameters.     

The effect of particle shape on the pressure drop across the dust cake

In order to observe the effect of particle shape of poly-dispersed dusts on filter performance, the pressure drop across the dust cakes of fly ashes from a conventional power plant (PC), fluidized bed combustion (FBC), and paint incinerator (FI) was measured over a metal filter element in the accurate conditions. A fluidized bed column was used to prepare the dust feed stream of uniform particle distribution. The fine particles of FI ash have a tendency to be agglomerated at low transport velocity. The aggregates were broken at high velocity of more than 21 cm/sec. FBC ash composed of jagged type particles and containing high concentration of unburned-carbon showed higher pressure drop than that of PC ash composed mostly of spherical particles. FI ash composed of aggregates of very fine carbon particles presented the highest pressure drop among the fly ashes tested. The shape factors of PC, FBC, and FI ash were estimated as 0.91, 0.76, and 0.65, respectively, by the Ergun equation. The results implied that the irregular particle tends to form a higher pressure drop and to be more compressible than spherical one. This paper is dedicated to Professor Wha Young Lee on the occasion of his retirement from Seoul National University.     

Effects of particle shape and size on devolatilization of biomass particle

Experimental and theoretical investigations indicate particle shape and size influence biomass particle dynamics, including drying, heating rate, and reaction rate. Experimental samples include disc/flake-like, cylindrical/cylinder-like, and equant (nearly spherical) shapes of wood particles with similar particle masses and volumes but different surface areas. Small samples (320 μm) passed through a laboratory entrained-flow reactor in a nitrogen atmosphere and a maximum reactor wall temperature of 1600 K. Large samples were suspended in the center of a single-particle reactor. Experimental data indicate that equant particles react more slowly than the other shapes, with the difference becoming more significant as particle mass or aspect ratio increases and reaching a factor of two or more for particles with sizes over 10 mm. A one-dimensional, time-dependent particle model simulates the rapid pyrolysis process of particles with different shapes. The model characterizes particles in three basic shapes (sphere, cylinder, and flat plate). With the particle geometric information (particle aspect ratio, volume, and surface area) included, this model simulates the devolatilization process of biomass particles of any shape. Model simulations of the three shapes show satisfactory agreement with the experimental data. Model predictions show that both particle shape and size affect the product yield distribution. Near-spherical particles exhibit lower volatile and higher tar yields relative to aspherical particles with the same mass under similar conditions. Volatile yields decrease with increasing particle size for particles of all shapes. Assuming spherical or isothermal conditions for biomass particles leads to large errors at most biomass particle sizes of practical interest.     

Application of incomplete similarity theory for estimating maximum shear layer thickness of granular flows in rotating drums

Granular flow in a rotating drum provides a convenient system for investigating mixing, segregation and general properties of granular materials. This study is concerned with the maximum thickness of the flowing surface layer observed at the rolling regime. A scaling relation is first derived with the consideration of incomplete similarity associated with the drum-particle size ratio and the Froude number. Calibration is then carried out with published laboratory data, which were collected for the case of rotating drums half-filled with glass beads. The scaling relation is also compared with other kinds of datasets, showing good agreement and possibilities of the proposed approach to be further extended to more complex cases.     

Wet granular materials in sheared flows

The transport properties of wet granular materials in a shear cell apparatus have been studied. If the particles are wet, the flow becomes more viscous forming liquid bridges between particles. The dynamic liquid bridge forces are considered as the cohesive forces between particles to restrict their movements. The cohesive forces make the particles stick tighter with each other and hamper the movement of particles. The mixing and transport properties are influenced seriously by the amount of moisture added in the flow. This paper discusses a series of experiments performed in a shear cell device with five different moisture contents using 3-mm glass spheres as the granular materials. The motion of granular materials was recorded by a high-speed camera. Using the image processing technology and particle tracking method, the average and fluctuation velocities in the streamwise and transverse directions could be measured. The self-diffusion coefficient could be found from the history of the particle displacements. The self-diffusion coefficients and fluctuations in the streamwise direction were much larger than those in the transverse direction. Three bi-directional stress gages were installed to the upper wall to measure the normal and shear stresses of the granular materials along the upper wall. For wetter granular material flows, the fluctuation velocities and the self-diffusion coefficients were smaller.     

Simulation of entrainment of agglomerates from plate surfaces by shear flows

The entrainment process of agglomerates deposited on plate surfaces by shear flows was simulated using the three-dimensional modified discrete element method (mDEM) and influences of several factors on entrainment process were examined. In the case shear induced force is too weak, deposits are only deformed and particles are barely entrained, however, above some critical value particles are entrained by flows forming agglomerates. It was also clarified that the steric-bulky deposit undergoes the stronger hydrodynamic force and is easy to be entrained. There are two entrainment mechanisms corresponding to the parameter A_s/A which indicates the relative strength of adhesive force between particle and plate surface to that between particles. In case of large A_s/A where the adhesion between particle and plate surface is predominant, the number of entrained particles monotonically decreases as A_s/A increases due to the enhanced binding force. By contrast for small A_s/A, the number of entrained particles is not heavily dependent on A_s/A due to the mechanism in which the upstream side of deposit is lifted and the deposit is deformed extensively then large agglomerates are entrained. The boundary between those two entrainment mechanisms exists at A_s/A=0.5-0.6 which is in good agreement with the theoretical prediction.     

Investigating the effect of shape on particle segregation using a Monte Carlo simulation

A Monte Carlo simulation has been used to investigate the segregation potential of a range of particulate systems under conditions in which the particles undergo high amplitude low frequency shaking. These systems involve a wide range of binary powder mixtures in which complex particle shapes have been investigated, including plates and rods which represent the real world materials encountered in pharmaceutical systems such as those which include crystalline components. Previous simulations on the segregation propensity of systems with different shapes were limited to spheres and spherocylinders, with relatively low vibrational amplitude drops. A commercial computer application for particle packing—called MacroPac—has been successfully employed here, as it has been able to model systems that are more complex where the shape variation is much wider. These simulations apply to the case of macroscopic particles, in the absence of air resistance and inter-particle forces. For non-spherical shapes, an ‘effective size’ which relates to the radius of gyration of the particles is determined. Our studies indicate that with high amplitude low frequency shaking, in a mixture of particles with different shapes but with equal volumes, the particles with the larger ‘effective size’, which tend to have a lower packing fraction, segregate to the top.     

Instability-induced clustering and segregation in high-shear Couette flows of model granular materials

Controlling unwanted segregation of components within a particle mixture is a longstanding goal in particle processing technologies. We investigate flow-induced clustering and consequent segregation of cohesionless particulate mixtures flowing rapidly in high-shear Couette geometries, comparing results from particle-dynamic (PD) simulations, kinetic theory and experiments. Using spheres and disks and a simplified plug instability as a surrogate for the variety of coherent flow structures, we find that density, velocity, and granular temperature gradients, and possibly, initiation of vorticity, influence the onset and nature of segregation. For equal density particles, simulations and experiments show that there exists a critical solids fraction at which the direction of segregation is reversed and streamwise diffusivity drops significantly, which appears to correspond to a point where the thermal diffusion flux no longer dominates over other terms. Results compare favorably to those from binary kinetic theories with one exception. We find that the 1D steady-state theoretical solutions do not capture the flux reversal observed in PD simulations of the equal density mixtures. Finally, we illustrate how local density variations can severely affect particle size distribution measurements.     

The effect of liquid viscosity on sheared granular flows

This work investigates the effect of transport properties in sheared granular flows with adding different silicone oils. We performed a series of experiments in a shear cell device using 2-mm soda lime beads as the granular materials by adding little amount of different silicone oils. The viscosity of silicone oils added was changed in different tests. By particle tracking method, the velocities, the velocity fluctuations and the self-diffusion coefficients were measured and analyzed. It was found that for the granular system with adding the more viscous silicone oil, the system became less active due to the greater shear force and cohesive force, which resulted in the decrease of velocity fluctuations and diffusions. Three bi-directional stress gages were installed to the upper wall to measure the normal and shear stresses of the granular materials along the upper wall. Thus, the effective viscosities of the wet granular material systems could be evaluated. The dimensionless normal and shear stresses, and the effective viscosity in the wet sheared granular flow were found to decrease with the increase of the viscosity of the added silicone oil. The influence of the viscosity of added fluid on these transport properties of wet granular systems will be discussed.     

Slow and intermediate flow of a frictional bulk powder in the Couette geometry

Most current research in the field of dry, non-aerated powder flows is directed toward rapid granular flows of large particles. Slow, frictional, dense flows of powders in the so-called quasi-static regime were also studied extensively using Soil Mechanics principles. The present paper describes the rheological behavior of powders in the “intermediate” regime lying between the slow and rapid flow regimes. Flows in this regime have direct industrial relevance. Such flows occur when powders move relative to solid walls in hoppers, bins and around inserts or are mixed in high and low shear mixers using moving paddles. A simple geometry that of a Couette device is used as a benchmark of more complicated flows.The constitutive equations derived by Schaeffer [J. Differ. Equ. 66 (1987) 19] for slow, incompressible powder flows were used in a new approach proposed by Savage [J. Fluid Mech. 377 (1998) 1] to describe flows in the intermediate regime. The theory is based on the assumption that both stress and strain-rate fluctuations are present in the powder. Using Savage's approach, we derive an expression for the average stress that reduces to the quasi-static flow limit when fluctuations go to zero while, in the limit of large fluctuations, a “liquid-like”, “viscous” character is manifested by the bulk powder.An analytical solution of the averaged equations for the specific geometry of the Couette device is presented. We calculate both the velocity profile in the powder and the shear stress in the sheared layer and compare these results to experimental data. We show that normal stresses in the sheared layer depend linearly on depth (somewhat like in a fluid) and that the shear stress in the powder is shear rate dependent. We also find that the velocity of the powder in the vicinity of a rough, moving boundary, decays exponentially so that the flow is restricted to a small area adjacent to the wall. The width of this area is of the order of 10-13 particle diameters. In the limit of very small particles, this is tantamount to a shear band-type behavior near the wall.     

Mixing in vibrated granular beds with the effect of electrostatic force

In this study, the DEM (Discrete Elementary Method) is used to simulate the behavior of granular mixing in vibrated beds. First, the velocity fields are simulated by the DEM model to examine the convective currents in a three-dimensional vibrated granular bed. Then, in order to characterize the effect of electrostatic force on the granular flow, the electrostatic number Es is defined as the ratio of the electrostatic force to the particle weight. Also, to quantify the quality of mixing, the mixing degree M is used by the well-known Lacey index. The top–bottom and the side–side initial loading patterns of two groups of glass bead with different colors are employed to investigate the influence of the convective currents on the granular mixing. To simplify the electrostatic effect, these two groups of glass beads are given opposite charges and the charged strength is assumed to be constant. The simulation results demonstrate that the granular temperatures increase linearly with the increasing Es number. Meanwhile, the mixing rate constants, calculated from the time evolutions of mixing degree, increase with the increasing Es number in power law relations. The role of granular temperature in the granular mixing is also discussed in this paper.     

The shear force amendments on the slugging behavior of upflow Anammox granular sludge bed reactor

The granulation of Anammox sludge plays an important role in improving the efficiency of high-rate Anammox bioreactors. The present study involved the use of anaerobic granular sludge to start up the Anammox process to accomplish granulation in Anammox reactor. The accumulation of nitrogen gas and subsequent slugging behavior were observed in the upflow Anammox granular sludge bed (AGSB) reactor, resulting in deteriorated effluent quality. Based on shear force analysis of the gas column under the quasi-steady state, the liquid-induced shear force was increased by progressively shortening of hydraulic residence time (HRT) and implementing effluent recycling. It appeared to be the right strategy to eradicate the slugging behavior which disappeared completely when HRT was shortened to 1.10 h with liquid upflow velocity of 1.30 cm min⁻¹. The application of high shear stress enhanced the nitrogen removal performance to 15.40 kg-N m⁻³ d⁻¹. Thus the amendments in the liquid-induced shear force by shortening HRT may be an appropriate strategy to overcome slugging behavior of the Anammox reactor.     

The onset of Taylor-Görtler vortices in the time-dependent Couette flow induced by an impulsively imposed shear stress

The onset of Taylor-Görtler instability induced by an impulsively started rotating cylinder with constant shear stress was analyzed by using propagation theory based on linear theory and momentary instability concept. It is well-known that the primary transient Couette flow is laminar but secondary motion sets in when the inner cylinder velocity exceeds a certain critical value. The dimensionless critical time τ _c to mark the onset of instability is presented here as a function of the modified Taylor number T. For the deep-pool case of small τ, since the inner cylinder velocity increases as V _i ∝√t in the present impulsive shear system, the present system is more stable than impulsive started case (V _i =constant). Based on the present τ _c and the Foster’s [1969] comment, the manifest stability guideline is suggested.     

Digital particle image velocimetry (DPIV) technique in measurements of granular material flows, Part 2 of 3-converging hoppers

The flow evolution of an amaranth seed is being investigated in a wedge-shaped model made of Plexiglas. The objective of this paper is to recognise flow patterns in the flowing material, and also to depict evolution of velocity fields, flow field discontinuities, velocity profiles for cross-sections of the model, shear zones and flow streamlines using the digital particle image velocimetry (DPIV) optical technique. It is demonstrated that the DPIV technique used in the experiments enables quantitative analysis of the flow zones geometry. The technique also allows to reveal boundaries between flowing and stagnant zones and to extract velocity profiles at any selected sections of the model.