Combined size and density segregation and mixing in noncircular tumblers

Estimation of Drag Finishing Abrasive Effect for Cutting Edge Preparation in Broaching Tool

In recent years, cutting edge preparation became a topic of high interest in the manufacturing industry because of the important role it plays in the performance of the cutting tool. This paper describes the use of the drag finishing DF cutting edge preparation process on the cutting tool for the broaching process. The main process parameters were manipulated and analyzed, as well as their influence on the cutting edge rounding, material remove rate MRR, and surface quality/roughness (Ra, Rz). In parallel, a repeatability and reproducibility R&R analysis and cutting edge radius r_e prediction were performed using machine learning by an artificial neural network ANN. The results achieved indicate that the influencing factors on r_e, MRR, and roughness, in order of importance, are drag depth, drag time, mixing percentage, and grain size, respectively. The reproducibility accuracy of r_e is reliable compared to traditional processes, such as brushing and blasting. The prediction accuracy of the r_e of preparation with ANN is observed in the low training and prediction errors 1.22% and 0.77%, respectively, evidencing the effectiveness of the algorithm. Finally, it is demonstrated that the DF has reliable feasibility in the application of edge preparation on broaching tools under controlled conditions.

Self-diffusion scalings in dense granular flows

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid volume fractions that are important in those terrestrial gravitational shearing flows that are dominated by collisional interactions. Diffusion over this range of solid fraction has not been well characterized in previous studies. We first compare the measured values with an empirical scaling based on shear rate previously proposed in the literature, and highlight the presence of anisotropy and the solid fraction dependence. We then compare the numerical measurements with those predicted by the kinetic theory for shearing flows of inelastic spheres and offer an explanation for why the measured and predicted values differ.

Influence of particle size and blender size on blending performance of bi-component granular mixing: A DEM and experimental study

The effect of particle size enlargement and blender geometry down-scaling on the blend uniformity (BU) was evaluated by Discrete Element Method (DEM) to predict the blending performance of a binary granular mixture. Three 10 kg blending experiments differentiated by the physical properties specifically particle size were performed as reference for DEM simulations. The segregation behavior observed during the diffusion blending was common for all blends, while the sample BU, i.e., standard deviation of active ingredient content % was different among the three blends reflecting segregation due to the particle size differences between the components. Quantitative prediction of the sample BU probability density distribution in reality based on the DEM simulation results was successfully demonstrated. The average root mean square error normalized by the mean of the mean sample BU in the blends was 0.228. Beside the ratio of blender container to particle size, total number of particles in the blender and the number of particles in a sample were confirmed critical for the blending performance. These in-silico experiments through DEM simulations would help in setting a design space with respect to the particle size and in a broader sense with respect to the physical properties in general.

Modeling Segregation in Granular Flows

Accurate continuum models of flow and segregation of dense granular flows are now possible. This is the result of extensive comparisons, over the last several years, of computer simulations of increasing accuracy and scale, experiments, and continuum models, in a variety of flows and for a variety of mixtures. Computer simulations-discrete element methods (DEM)-yield remarkably detailed views of granular flow and segregation. Conti-nuum models, however, offer the best possibility for parametric studies of outcomes in what could be a prohibitively large space resulting from the competition between three distinct driving mechanisms: advection, diffusion, and segregation. We present a continuum transport equation-based framework, informed by phenomenological constitutive equations, that accurately predicts segregation in many settings, both industrial and natural. Three-way comparisons among experiments, DEM, and theory are offered wherever possible to validate the approach. In addition to the flows and mixtures described here, many straightforward extensions of the framework appear possible.

Dynamics of bidensity particle suspensions in a horizontal rotating cylinder

We report Stokesian dynamics simulations of bidensity suspensions rotating in a horizontal cylinder. We studied the phase space and radial and axial patterns in settling as well as floating systems. Each system was composed of particle mixtures of two different densities. As many as eight unique phases are identified for each system along the radial plane. The bidensity system shows similarity to the monodisperse case only when the radial distribution of the particles is completely uniform. Characteristic behavior of the bidensity systems is identical at low rotation rates and contrasting when centrifugal force dominates. Expressing the phase boundaries in terms of dimensionless parameters U_{s}/(ΩR) and g/(Ω^{2}R) gives a linear fit unifying the data in the gravity-dominated regime. At high rotation rates, the behavior is opposing for either system though linear in nature. In the axial direction, number density profiles of both systems affirm the phenomenon of band formation. Location of the axial bands remains the same for heavy and light particles in both systems. We have also reestablished that an inhomogeneous particle configuration in the radial plane induces growing instabilities in the axial plane which amplify to form particle bands similar to monodisperse suspensions.

Forced axial segregation in axially inhomogeneous rotating systems

Controlling segregation is both a practical and a theoretical challenge. Using a novel drum design comprising concave and convex geometry, we explore, through the application of both discrete particle simulations and positron emission particle tracking, a means by which radial size segregation may be used to drive axial segregation, resulting in an order of magnitude increase in the rate of separation. The inhomogeneous drum geometry explored also allows the direction of axial segregation within a binary granular bed to be controlled, with a stable, two-band segregation pattern being reliably and reproducibly imposed on the bed for a variety of differing system parameters. This strong banding is observed to persist even in systems that are highly constrained in the axial direction, where such segregation would not normally occur. These findings, and the explanations provided of their underlying mechanisms, could lead to radical new designs for a broad range of particle processing applications but also may potentially prove useful for medical and microflow applications.

Shear-induced segregation of particles by material density

Recently, shear rate gradients and associated gradients in velocity fluctuations (e.g., granular temperatures or kinetic stresses) have been shown to drive segregation of different-sized particles in a manner that reverses at relatively high solids fractions (〈f〉>0.50). Here we investigate these effects in mixtures of particles differing in material density through computational and theoretical studies of particles sheared in a vertical chute where we vary the solids fraction from 〈f〉=0.2 to 0.6. We find that in sparse flows, 〈f〉=0.2 to 0.4, the heavier (denser) particles segregate to lower shear rates similarly to the heavier (larger) particles in mixtures of particles differing only in size. However, there is no segregation reversal at high f in mixtures of particles differing in density. At all solids fractions, heavier (denser) particles segregate to regions of lower shear rates and lower granular temperatures, in contrast with segregation of different-sized particles at high f, where the heavier (larger) particles segregate to the region of higher shear rates. Kinetic theory predicts well the segregation for both types of systems at low f but breaks down at higher f's. Our recently proposed mixture theory for high f granular mixtures captures the segregation trends well via the independent partitioning of kinetic and contact stresses between the two species. In light of these results, we discuss possible directions forward for a model framework that encompasses segregation effects more broadly in these systems.

Density-driven spontaneous streak segregation patterns in a thin rotating drum

Granular mixtures may segregate because of external driving forces, which play an important role in industry and geophysics. We investigate experimentally the mechanism of density-driven spontaneous streak segregation patterns in a thin rotating drum. We find that a spontaneous streak segregation pattern can occur in such a system, which we call a D-system. A phase diagram identifies three segregation pattern regimes in this study: the mixing regime, the core segregation regime, and the streak segregation regime.

Suppression and emergence of granular segregation under cyclic shear

While convective flows are implicated in many granular segregation processes, the associated particle-scale rearrangements are not well understood. A three-dimensional bidisperse mixture segregates under steady shear, but the cyclically driven system either remains mixed or segregates slowly. Individual grain motion shows no signs of particle-scale segregation dynamics that precede bulk segregation. Instead, we find that the transition from nonsegregating to segregating flow is accompanied by significantly less reversible particle trajectories and the emergence of a convective flow field.

Ringlike spin segregation of binary mixtures in a high-velocity rotating drum

This study presents molecular dynamics simulations on the segregation of binary mixtures in a high-velocity rotating drum. Depending on the ratio between the particle radius and density, similarities to the Brazil-nut effect and its reverse form are shown in the ringlike spin segregation patterns in radial direction. The smaller and heavier particles accumulated toward the drum wall, whereas the bigger and lighter particles accumulated toward the drum center. The effects of particle radius and density on the segregation states were quantified and the phase diagram of segregation in the ρ(b)/ρ(s) - r(b)/r(s) space was plotted. The observed phenomena can be explained by the combined percolation and the buoyancy effects.

Isolating segregation mechanisms in a split-bottom cell

We study the segregation of mixtures of particles in a split-bottom cell to isolate three possible driving mechanisms for segregation of densely sheared granular mixtures: gravity, porosity, and velocity gradients. We find that gravity alone does not drive segregation associated with particle size without a sufficiently large porosity or porosity gradient. A velocity gradient, however, appears to be capable of driving segregation associated with both particle size and material density. In all cases, the final segregation state is approached exponentially.

Kinematics of densely flowing granular mixtures

We measure the kinematics of segregating granular mixtures in dense free-surface boundary-layer flow in a rotated drum. We find that in a segregating mixture, the different components move with roughly the same velocities, except for a relatively small segregation velocity perpendicular to the direction of flow. On the other hand, the mean variance of the velocities--often associated with a granular temperature--may differ for the two components. In the majority of the high-density boundary layer, the difference is driven by relative particle size and may be understood considering a geometrically motivated model. In the low-density region at the top of the boundary layer, the difference is driven by relative particle mass, similar to observations in more energetic systems.

Eliminating segregation in free-surface flows of particles

By introducing periodic flow inversions, we show both experimentally and computationally that forcing with a value above a critical frequency can effectively eliminate both density and size segregation. The critical frequency is related to the inverse of the characteristic time of segregation and is shown to scale with the shear rate of the particle flow. This observation could lead to new designs for a vast array of particle processing applications and suggests a new way for researchers to think about segregation problems.

Effects of fluid viscosity on band segregation dynamics in bidisperse granular slurries

Parallel experiments in long, axially rotated cylinders are used to study the influence of interstitial fluid viscosity on particle segregation in bidisperse granular slurries. A uniformly mixed initial state segregates into surface bands, which alternate between regions of large particles and regions composed of a mixture of small and large particles. As the tumbler rotates, the relative area of the mixed particle bands increases and saturates, while the number of bands reaches a peak and then decreases logarithmically in time for all viscosities studied. With increasing interstitial fluid viscosity, the asymptotic mixed band area increases proportionally, the time for bands to appear at the surface decreases, and the peak number of bands goes through a maximum at a viscosity of approximately 3 cP . Extrapolation to the low-viscosity limit matches the data for dry granular systems; at the high-end viscosity there is a value beyond which no axial banding occurs. A heuristic mechanism based on the coexistence of pure and mixed particle phases and their dependence on viscosity is presented to rationalize key aspects of the results.

Capturing patterns and symmetries in chaotic granular flow

Segregation patterns formed by time-periodic flow of polydisperse granular material (varying in particle size) in quasi-two-dimensional (quasi-2D) tumblers capture the symmetries of Poincaré sections, stroboscopic maps of the underlying flow, derived from a continuum model which contains no information about particle properties. We study this phenomenon experimentally by varying the concentration of small particles in a bidisperse mixture in quasi-2D tumblers with square and pentagonal cross sections. By coupling experiments with an analysis of periodic points, we explain the connection between the segregation patterns and the dynamics of the underlying flow. Analysis of the eigenvectors and unstable manifolds of hyperbolic points shows that lobes of segregated small particles stretch from hyperbolic points toward corners of the tumbler, demonstrating the connection between regions of chaotic flow and the shape of the segregation patterns. Furthermore, unstable manifolds map the shape of lobes of segregated particles. The techniques developed here can also be applied to nonpolygonal tumblers such as elliptical tumblers, as well as to circular tumblers with time-periodic forcing.

Dynamics of axial segregation in granular slurries: parallel experiments and influence of aspect ratio and periodic tilting

An efficient technique for conducting rotating tumbler experiments in parallel is introduced and used to study the effect of tumbler length and periodic tilting of the tumbler on axial segregation. When rotated, bidisperse granular slurries segregate into what appear at the surface to be alternating bands of larger and smaller particles. The number of bands increases linearly with tumbler length while the fractional area occupied by each type of band is constant. Periodic tilting of the rotation axis induces a periodic axial flow of particles in the flowing layer. For the range of tilt angle amplitudes investigated (0 degrees -3.5 degrees), the number of bands decreases with increasing angle, but the rate of merging and the fractional area of bands rich in smaller particles are unaffected.