Size segregation of granular matter in silo discharges

Flow dynamics of different particle shapes in a rectangular silo

The present work investigates the effect of using six different particle shapes of equal volume on the discharge process of a rectangular silo with adjustable width, equipped with a flat bottom orifice opening of varying size. We find that the discharge rate decreases with the increasing aspect ratio of the particles for both lentil-shaped (oblate) and rice-shaped (prolate ellipsoidal) particles and macaroni-shaped particles show the lowest discharge rate among all the particle shapes. In addition, the silo width influences the discharge in such a way that the rates at which different particle shapes flow out from the system become more distinguishable at smaller silo widths. We observe that the velocity profile near the orifice opening becomes narrower and less sharp with increasing aspect ratio for both lentil- and rice-shaped particles. Moreover, the silo width does not have a significant influence on the velocity profile very near to the orifice, but, its influence becomes more noticeable with increasing height within the silo.

Risk-Based Approach for Defining Retest Dates for Active Pharmaceutical Ingredients and Excipients

Drug substances and excipients must be stored in recommended storage conditions and should comply with their specifications during the retest period for their use in the manufacture of drug products. The ICH (International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use) and WHO (World Health Organization) regulatory guidelines mandate that after the retest period, the drug substances must be retested for compliance with the specification and then used immediately in the manufacture of the finished product. Although these substances can be retested multiple times, an emphasis is placed on immediate use following a retest and compliance with standards. The phrase "used immediately" is ambiguous and is left for interpretation. In this article, we will look at the various processes that must be completed to determine the retest date. In addition, we present a risk-based method for establishing retest dates and the time during which material can be used.

Study of Diminutive Granules as Feed Powders for Manufacturability of High Drug Load Minitablets

The maximal amount of drug contained in a minitablet is limited. To reduce the total number of minitablets in a single dose, high drug load minitablets can be prepared from high drug load feed powders by various pharmaceutical processing techniques. Few researchers have however examined the influence of pharmaceutical processing techniques on the properties of high drug load feed powders, and consequently the manufacturability of high drug load minitablets. In this study, silicification of the high drug load physical mix feed powders alone did not yield satisfactory quality attributes and compaction parameters to produce good quality minitablets. The abrasive nature of fumed silica increased ejection force and damage to the compaction tools. Granulation of fine paracetamol powder was crucial for the preparation of good quality high drug load minitablets. The diminutive granules had superior powder packing and flow properties for homogenous and consistent filling of the small die cavities when preparing minitablets. Compared to the physical mix feed powders for direct compression, the granules which possessed higher plasticity, lower rearrangement and elastic energies, yielded better quality minitablets with high tensile strength and rapid disintegration time. High shear granulation demonstrated greater process robustness than fluid bed granulation, with less discernment on the quality attributes of feed powder. It could proceed without fumed silica, with the high shear forces reducing interparticulate cohesivity. An in-depth understanding on the properties of high drug load feed powders with inherently poor compactability and poor flowability is important for the manufacturability of high drug load minitablets.

Effects of size polydispersity on segregation of spherical particles in rotating drum

To get insight into the segregation process of a polydisperse granular materials flow, we numerically investigated the migration process of particles in a rotating drum operating in the rolling regime by means of the discrete element method. Particle migration is analyzed through the variation of the proportion of particles in different zones where the flow property is characterized. The proportion of particles in different zones of the drum shows to increase in the center of the flow radially and axially where a higher concentration of small particles is observed, while its decreases in other zones with a higher concentration of larger particles. Interestingly, we find that the migration process of particles leads to radial and axial segregation which is caused by a combination between the exerted fluctuation forces on particles and its surrounding pressure gradient.

Local Percolation of a Binary Particle Mixture in a Rectangular Hopper with Inclined Bottom during Discharging

To reveal the local percolation characteristics of a binary particle mixture in a rectangular hopper with inclined bottom, the discrete element method (DEM) is used to simulate the discharging process. A local percolation evaluation method is proposed, and the percolation strength grid maps are drawn. The effects of geometric parameters, particle properties, and interaction parameters on percolation are investigated. Apart from the free surface, percolation is mainly concentrated near the wall and at the bottom. With the increase in the orifice width, the average local percolation strength index (ALPSI) of the near-wall region increases and that of the bottom region decreases. The effect of the angle on percolation in the near-wall region can be ignored. The effect of friction on local percolation is significant. Increasing the fine particle mass fraction and reducing the difference in particle size can effectively avoid percolation.

Modeling methods for gravity flow of granular solids in silos

This paper provides a review on the flow of free-flowing particles inside silos. We have previously reviewed in detail the experimental studies in this field. In the present work, the focus is placed on the theoretical approaches allowing numerical simulation and modeling of these systems. Modeling of granular flow in silos is very significant due to the advantages of modeling compared to experiments. The simulation methods are divided into four main groups: analytical methods, finite element method, discrete element method, and hybrid models. In each section, the most significant researches are reviewed. The drawbacks and advantages of each method are discussed, and the effects of different parameters are reviewed. Finally, the perspective of future work and the main challenges in this area are discussed.

Intermittency and velocity fluctuations in hopper flows prone to clogging

We study experimentally the dynamics of granular media in a discharging hopper. In such flows, there often appears to be a critical outlet size D_{c} such that the flow never clogs for D>D_{c}. We report on the time-averaged velocity distributions, as well as temporal intermittency in the ensemble-averaged velocity of grains in a viewing window, for both D<D_{c} and D>D_{c}, near and far from the outlet. We characterize the velocity distributions by the standard deviation and the skewness of the distribution of vertical velocities. We propose a measure for intermittency based on the two-sample Kolmogorov-Smirnov D_{KS} statistic for the velocity distributions as a function of time. We find that there is no discontinuity or kink in these various measures as a function of hole size. This result supports the proposition that there is no well-defined D_{c} and that clogging is always possible. Furthermore, the intermittency time scale of the flow is set by the speed of the grains at the hopper exit. This latter finding is consistent with a model of clogging as the independent sampling for stable configurations at the exit with a rate set by the exiting grain speed [C. C. Thomas and D. J. Durian, Phys. Rev. Lett. 114, 178001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.178001].

Discharge flow of a bidisperse granular media from a silo

The discharge flow in a cylindrical and a rectangular silo using both monodisperse and bidisperse mixtures of spherical glass beads is studied experimentally. The flow rate is measured using a precision balance for a large range of particle diameters, size ratios, and outlet diameters. A simple physical model is proposed to describe the flow of bidisperse mixtures. It gives an expression for the flow rate and predicts that the bulk velocity follows a simple mixture law. This model implies that a mixture diameter cannot be simply defined. Moreover it is shown that bidisperse granular media allow for the transport of coarse particles below their jamming conditions.

Experimental and Numerical Study of Stagnant Zones in Pebble Bed

The experimental method (side area method) and DEM simulation have been carried out to analyse the stagnant zone in the quasi-two-dimensional silos. The side area method is a phenomenological method by means of investigating the interface features of different areas composed of different coloured pebbles. Two methods have been discussed to define the stagnant zone. In particular, the area of the stagnant zone has been calculated with the mean-streamline method, and the tracking time of different marking pebbles has been investigated with the stagnant time method to explore the kinematics characteristics of the pebbles. The stagnant zone is crucial for the safety of the pebble-bed reactor, and the practical reactor core must avoid the existence of the stagnant zone. Furthermore, this paper also analyses the effects of bed configuration (the bed height, the base angle, and the friction coefficient) on stagnant zone with the two methods mentioned above. In detail, the bed height shows little impact on the stagnant zones when the bed height exceeds a certain limit, while the base angle has negative prominent correlation with the stagnant zone. The friction coefficient effect seems complicated and presents the great nonlinearity, which deserves to be deeply investigated.

Granular mixing and segregation in zigzag chute flow

Periodic flow inversions have been shown as an effective means to eliminate both density (D system) and size (S system) segregation. The frequency of these inversions, however, is the key to applying this technique and is directly related to the inverse of the characteristic time of segregation. In this work, we study size segregation (S system) and adapt a size segregation model to compliment existing work on density segregation and, ultimately, aid in determining the critical forcing frequency for S systems. We determine the impact on mixing and segregation of both the binary size ratio and the length of each leg of a "zigzag chute". Mixing is observed when L < U tS, where L, U, and t(S) denote the length of each leg of the zigzag chute, the average streamwise flow velocity of the particle, and the characteristic time of segregation, respectively.

Segregation in arch formation

We report new segregation phenomena in the clogging arches formed during the discharge of granular piles. Results from molecular dynamics simulations show segregation effects with respect to both size and density ratios used in piles built with bidisperse mixtures of grains. The clogging arch is preferentially constituted of large grains when size bidisperse piles were discharged, whereas for density bidisperse mixtures there is a predominance of light grains in the arch for large orifice widths but, for small widths, an inversion in the preference is observed, with a slightly higher incidence of heavy grains forming the arches. We present arguments based on the reverse buoyancy effect and the statistics collected for the avalanche size distributions to explain how these effects can be understood as a crossover between two different segregation mechanisms acting independently at small and large orifice width limits.

Rheology of evolving bidisperse granular media

We investigate the mixing of bidisperse distributions of spherical particles for slowly rotating vanes by pouring smaller beads, diameter d(1), onto a monodisperse bed composed of larger beads, diameter d(0), and monitoring the torque and lift forces. If the mixing beads are too small, d(1)/d(0)<0.05, the drag and lift are unaltered. Otherwise smaller beads displace larger beads from the shearing region, and if present in sufficient quantity both the drag and lift diminish to values of a monodisperse bed composed entirely of the smaller beads. We observe reductions in the torque up to 70%. The rate at which smaller beads leave the shearing region decreases as their size relative to the larger beads increases, and for d(1)/d(0)>0.155 the smaller beads remain inside the shearing region.

Prediction of Segregation Tendency Occurrence in Dry Particulate Pharmaceutical Mixtures: Development of a Mathematical Tool Adapted for Granular Systems Application

Segregation phenomena are of importance in nearly all processes involving dry granular and powder mixtures. The extent of segregation directly influences the eventual rejection of a considerable percentage of the final product in the majority of pharmaceutical processes; among these are those mixtures destined for powder compression processing for the production of tablets. Although the parameters influencing segregation are relatively well-known qualitatively, there are, so far, no widely accepted quantitative prediction tools that permit process improvement and optimization of production as a function of the mixture's composition and the particulars of individual processes (e.g., geometry of the vessels). Thus, within present practice, only general design considerations and the technical expertise of engineers and operators are relied upon to optimize these processes on a case-by-case basis. It is in these circumstances that a study of the tendency towards segregation in free flowing granular materials was conducted, using a simple tool previously developed for the study of the behavior of continuous chemical reactors with classical fluid flows. The measurement of average residence times and their variance is used to calculate the deviation of chemical reactors from the ideal behavior of a perfectly mixed vessel or a plug flow pattern. In this work, these measurements are adapted to evaluate the tendency of a granular mixture to segregate. The method consists of introducing a pulse perturbation (of another material) to the established regular flow of a single granular material or a granular mixture and to then calculate the response of the system in terms of the concentration of the pulsed material at the process outlet. The average granular particle residence time and its standard deviation are then related to the segregation tendency.

Anomalous diffusion in silo drainage

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well-defined relationship (gamma = 2/(3 - q)) between the anomalous diffusion exponent gamma and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.

Stochastic flow rule for granular materials

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-two-dimensional granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials-discreteness and randomness-via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments--with essentially no fitting parameters--although it is only expected to function where material is at incipient failure and slip lines are inadmissible. For special cases of admissible slip lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, mesoscale spot random walks, and microscopic particle relaxation.

Analysis of granular flow in a pebble-bed nuclear reactor

Pebble-bed nuclear reactor technology, which is currently being revived around the world, raises fundamental questions about dense granular flow in silos. A typical reactor core is composed of graphite fuel pebbles, which drain very slowly in a continuous refueling process. Pebble flow is poorly understood and not easily accessible to experiments, and yet it has a major impact on reactor physics. To address this problem, we perform full-scale, discrete-element simulations in realistic geometries, with up to 440,000 frictional, viscoelastic 6-cm-diam spheres draining in a cylindrical vessel of diameter 3.5m and height 10 m with bottom funnels angled at 30 degrees or 60 degrees. We also simulate a bidisperse core with a dynamic central column of smaller graphite moderator pebbles and show that little mixing occurs down to a 1:2 diameter ratio. We analyze the mean velocity, diffusion and mixing, local ordering and porosity (from Voronoi volumes), the residence-time distribution, and the effects of wall friction and discuss implications for reactor design and the basic physics of granular flow.

Evidence of two effects in the size segregation process in dry granular media

In a half-filled rotating drum, the size segregation of particles of equal density builds a ring pattern of the large particles, whose location continuously varies from the periphery to the center depending on the size ratio between particles [N. Thomas, Phys. Rev. E 62, 961 (2000)]. For small size ratios (typically < 5) position. The existence of circles with an intermediate radius shows that the segregation at an intermediate level within a flow is possible. In this paper, we experimentally study the segregation of particles of different densities and sizes in a half-filled rotating drum and other devices (chute flow, pile). In the drum, the location of the segregated ring continuously varies from the periphery to the center and is very sensitive to both the size (from 1 to 33) and density (from 0.36 to 4.8) ratios. The densest large beads segregate on a circle close to the center, the lightest large beads on a circle close to the periphery. Consequently, we found that for any tracer, its excess of mass, due to only a size excess, a density excess, or both, leads to a deep inside segregation of the tracer. There is a push-away process that makes heavy beads of any type go downwards, while the excess of size is already known to push large beads towards the surface, by a dynamical sieving process. Each segregation at an intermediate ring corresponds to a balance between these mass and geometrical effects. The segregation level in the flow is determined by the ratio of the intensities of both effects.

Diffusion and mixing in gravity-driven dense granular flows

We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from superdiffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Péclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with long-lasting contacts but not thermal collisions, as in normal fluids.

Angle of repose and segregation in cohesive granular matter

We study the effect of fluids on the angle of repose and the segregation of granular matter poured into a silo. The experiments are conducted in two regimes where: (i) the volume fraction of the fluid (liquid) is small and it forms liquid bridges between particles thus giving rise to cohesive forces, and (ii) the particles are completely immersed in the fluid. The data is obtained by imaging the pile formed inside a quasi-two-dimensional silo through the transparent glass side walls and using color-coded particles. In the first series of experiments, the angle of repose is observed to increase sharply with the volume fraction of the fluid and then saturates at a value that depends on the size of the particles. We systematically study the effect of viscosity by using water-glycerol mixtures to vary it over at least three orders of magnitude while keeping the surface tension almost constant. Besides surface tension, the viscosity of the fluid is observed to have an effect on the angle of repose and the extent of segregation. In case of bidisperse particles, segregation is observed to decrease and finally saturate depending on the size ratio of the particles and the viscosity of the fluid. The sharp initial change and the subsequent saturation in the extent of segregation and angle of repose occurs over similar volume fraction of the fluid. Preferential clumping of small particles causes layering to occur when the size of the clumps of small particles exceeds the size of large particles. We calculate the azimuthal correlation function of particle density inside the pile to characterize the extent of layering. In the second series of experiments, particles are poured into a container filled with a fluid. Although the angle of repose is observed to be unchanged, segregation is observed to decrease with an increase in the viscosity of the fluid. The viscosity at which segregation decreases to zero depends on the size ratio of the particles.

Segregation transitions in wet granular matter

We report the effect of interstitial fluid on the extent of segregation by imaging the pile that results after bidisperse color-coded particles are poured into a silo. Segregation is sharply reduced and preferential clumping of small particles is observed when a small volume fraction of fluid V(f) is added. We find that viscous forces in addition to capillary forces have an important effect on the extent of segregation s and the angle of repose straight theta. We show that the sharp initial change and the subsequent saturation in s and straight theta occurs over similar V(f). We also find that a transition back to segregation can occur when the particles are completely immersed in a fluid at low viscosities.