Powder Flow

Executive Summary

Many particulate products are manufactured through powder compaction, in which die filling is a critical process stage as the die filling performance will determine the process efficiency and product quality. For aerated powders, the interaction between particle and the surrounding air could play an important role during die filling. Although die filling has attracted increasing attention over the last two decades, our understanding on die filling of aerated powders is still limited. In particular, how the system design will affect the die filling performance, how significant the presence of air will affect die filling behavior, and whether powders can segregate during die filling are still not well understood. To address these questions, both experimental and numerical investigation were carried out on this project, and this report summarise the key findings on these three aspects. This report contains 5 chapters: the first two chapters examine the effect of system design (die shape, size and orientation) with experimental work reported in Chapter 1, and numerical study in Chapter 2. The effect of air presence on die filling behavior was presented in Chapter 3 and Chapter 4, with chapter 3 focusing on theoretical modeling and Chapter 4 on measuring air pressure buildup in the die. Chapter 5 reports the size-induced segregation during die filling.

We would like to acknowledge IFPRI for financially supporting this project. We also would like to thank Michele Marigo and Tim Freeman for constructive discussions throughout this project.

Executive summary.

This reports presents the results of a series of experiments aimed at studying the factors affecting the amount of charge in dispersed and bulk powders, for how long the charge remains in the bulk powder before dissipating into the environment and the effect of the electric charge on the solid fraction of a bulk powder. The powders used in this study cover a range of particle sizes from 3 μm to roughly 1000 μm, although not all powders were used in all the experiments.

Experiment 1

In the first experiment presented in this report, particles are dispersed in a gas stream and charge due to collisions with a tribocharger. It is found that the main factor affecting the maximum amount of charge per particle is the particle size, since the charge is limited by the electric field on the surface of the particles and for the same charge on a particle, the electric field on its surface scales with the square of the diameter. In practical applications the particles may not experience enough number of collisions with solid surfaces to charge up to their maximum level, but the results presented in this report indicate than, on equal conditions, it is still the particle size the main parameter affecting the particle charge.

Experiment 2

In the second experiment we measure the charge distribution of the particles that come out of the tribocharger. We have found that the particle charge has a very wide distribution spanning both polarities. This finding may be explained if the charge transfer from the tribocharger to the dispersed particles causes a shift in a pre-existent charge distribution in the direction of the transferred charge. In consequence, the particles in a neutral bulk powder may carry electric charge, but on some of the particles the charge is positive and on the others is negative.

Experiment 3

In the third experiment we have measured the charge in a bulk powder formed by sedimentation of highly charged particles. We have found that while particle settles, the layer of bulk powder formed losses its charge. We propose a model that qualitatively describes the decay of the charge in the bulk powder based on the assumptions that the charge in the bulk powder has some mobility and that charge is dissipated on the surfaces of the bulk powder by neutralization with ions existing in the surrounding gas in order to keep the electric field on the surface of the powder at a value equal or below the breakdown field in the gas. The amount of charge in a bulk powder results from an equilibrium between charge dissipation into the surroundings and the accretion of new charge from the incoming particles and according to the model, depends on the charge on the particles that sediment, the mass flow rate at which they arrive and the effective electrical conductivity of the powder.

The effective electrical conductivity can be estimated from the typical time for charge dissipation, which is of the order of minutes, yielding a value of the effective electrical conductivity of the bulk powder of the order of nS/m.

Experiment 4

In the fourth set-up we measure directly the effective electrical conductivity of some powders as a function of consolidation and ambient humidity. The effective conductivity is found to be in the order of nS/m and it is highly dependent on humidity and to a lesser extend, on particle size. The strong dependence on humidity, specially for smaller particle sizes, may explain why the charge on bulk powders seem to be highly unpredictable in environments in which humidity is not controlled.

Experiment 5

In the fifth and last set-up, we measure the poured and tapped densities of charged and uncharged powders in order to determine if there is an effect of electric charge on the solid fraction, but within the accuracy of our experiment, we have found none.

Executive Summary

Segregation model development holds promise for translation of academic research into industrial practice. Two significant issues that hamper the applicability of models in industry, however, are (1) the inherent difficulty in measuring segregation rates (especially in an experimental setting) for validation purposes and (2) the significant dearth of validated scale-up studies for these models.

In this project, we seek to alleviate these two shortcomings of segregation research through a combined theoretical, computational, and experimental program. One unique aspect of our work is that we use flow perturbations to establish an “equilibrium” between segregation and mixing in free surface granular flows in order to alter the steady-state distribution of particles. By achieving this balance between the rate of segregation and the perturbation rate, we can combine the model expressions that we are interested in testing with dramatically simplified experiments to ultimately deduce the segregation rate (and validate the expressions). Moreover, by exploring a novel view of the interplay between granular rheology and segregation, we aim to introduce a new way of structuring segregation rate models that will make them inherently more scalable than any models previously reported. As the project progresses, we expect to yield – either via adoption from the literature or through new theoretical development – (experimentally) validated segregation models that can be incorporated into device-level transport equations in order to supply quantitative prediction of segregation at process scale.

Executive Summary

The ball indentation method has been applied to a range of sizes of silanised glass beads, pea protein, maize starch, titania and alumina. The penetration depth range which provides a stable hardness measurement is determined for each material, which is identical for most materials. Ball indentation and shear cell measurements at moderate stresses allow the constraint factor to be determined. The value of constraint factor varies for different materials, but remains independent of consolidation stress in the range tested for all materials except pea protein, where a larger error is observed in the ball indentation measurements, and alumina. For silanised glass beads the constraint factor increases slightly as particle size is reduced. Comparison of the materials tested in this work and those by (Zafar, 2013) indicates that constraint factor varies between 1.7 – 4.8, and for most materials the value is below 3. All tested materials except titania, alumina and durcal 15 exhibit a notable deviation in flow behaviour at low stresses, with a rapid reduction in the yield stress inferred by ball indentation.

Future work will experimentally investigate the influences of size distribution, surface energy, density and shape on the constraint factor, with DEM also used to investigate the shape effect. DEM will investigate the variation of constraint factor in the low stress range that cannot be reached experimentally. Finally the reliable penetration depth range at higher strain rates will be determined using the freefall ball indentation method.

EXECUTIVE SUMMARY

Currently, there is no first-principles, general theory of intermediate dry granular flow that predicts its rheological response as a function of particle size, shape, and friction (even leaving aside adhesion, which is more challenging still). It is an open question what constitutive equations best describe such flows. Therefore, there is a need for experimental data which tests these theories, and thereby provides an improved understanding of how particle properties control the rheology of granular materials, independent of the flow geometry. Rather than using empirical relations fit to bulk data for a particular flow geometry and particles, we aim to connect grain-scale parameters to macroscale behaviors.

In this initial year of effort, we have focused on testing the Kamrin nonlocal theory [Kamrin and Koval 2012] in experiments. Our apparatus is a modification of a 2D annular shear apparatus capable of providing much better measurements of local boundary forces than has previously been possible, in addition to providing conventional particle-tracking. A key upgrade to the apparatus was the development of a circle of leaf springs as the outer wall. We have calibrated these to provide measurements of both normal and tangential forces at the outer boundary; torque values at the inner boundary are known from an in-line torque sensor. We have run the experiment under continuous shear, allowing us to obtain high-quality measurements of the velocity profile, the internal stress field, and the fluidity field. These experiments were done with a 60-40 mix of circular and elliptical disks at four rotation rates and two packing fractions. We find that there is a single set of parameters (similar to those found by Kamrin) which provide good agreement with the model and do not need to be adjusted in order to cover wide range of shear rates and packing fractions.

By analyzing the positions of the leaf springs, we have successfully observed fluctuations in the boundary forces which arise due to the buckling of force chains. Importantly, this new technique will allow for measuring shear forces even for non-photoelastic particles. We have also installed a polariscope within the apparatus, allowing for future work on internal forces using photoelastic particles.

Segregation model development holds promise for translation of academic research into industrial

practice. One significant hindrance to model development, however, is the inherent difficulty

in measuring segregation rates (especially in an experimental setting). In this project, we seek

to establish an “equilibrium” between segregation and flow perturbation in free surface granular

flows in order to overcome this experimental hurdle. That is, by using periodic flow inversions,

we hope to alter the steady-state distribution of particles whereby there exists a balance between

the rate of segregation and the perturbation rate. In this way, we can combine the segregation

rate expressions that we are interested in testing with our previously developed segregation control

framework such that knowing the perturbation rate, we can deduce the segregation rate (much

like knowing an equilibrium concentration, along with a reverse reaction rate, one can deduce the

rate of the forward reaction). In our first year, we examined binary segregation rate models, both

computationally and experimentally, that are appropriate for free surface flows of granular materials.

We started with well established models for both size segregation and density segregation and

compare these to new and proposed models. We tested these models, both computationally and

experimentally, using an industrially-relevant device – a tumbler-type mixer – by introducing an

axially-located baffle that periodically perturbs the flow. This flow perturbation allows us to modify

the expected segregation “equilibrium” such that varying flow properties (like rotation rate) as

well as material properties (like size or density ratio) will lead to results that collapse onto a “master

curve” when using an accurate segregation model. As the project progresses, (experimentally)

validated segregation models can be incorporated into device-level transport equations in order to

yield quantitative prediction of segregation at process scale.

Measurements of Unconfined Yield Stress

Measurements of unconfined yield stress at low stresses are often inconsistent, or do not correlate with observed process behaviour. Over the last decade or so a number flowability measurement techniques operable at low stresses have been introduced, or become more prominent. A few of these devices are also capable of flowability measurements at strain rates beyond the quasi-static regime. One such technique is ball indentation, which directly measures hardness; the resistance of the bed to plastic deformation. The unconfined yield stress is directly related to the hardness by the constraint factor, which is dependent on particle properties, although the constraint factor cannot yet be determined a priori.

Flowability Measurement Techniques

• The flowability of titania is measured here using ball indentation and a Schulze ring shear tester.
• In contradiction to previous research on ball indentation, the bed hardness is found to be approximately constant at dimensionless penetration depths of 0.1 – 0.3, yet increases beyond this range.
• This could suggest that the suitable penetration depth range is not only dependent on indenter size, but particle size also.
• The bed hardness is found to increase approximately linearly with consolidation stress, and correlates with unconfined yield stress measurements from a shear cell at normal stresses of 3 – 15 kPa.
• The constraint factor is found to be approximately constant at higher stresses, but increases slightly at lower stresses.
• Inferred yield stress values at low stresses are greater than those extrapolated from shear cell measurements, again in contradiction to previous findings on other powders.

Future Work

Future work will utilize DEM to explore the variation of constraint factor at lower stresses and for varying particle properties. The flowability of silanised glass beads of a range of surface energy values will be characterised by ball indentation at quasi-static and dynamic conditions, along with non-spherical particles, such as calcium carbonate and limestone.

This technique further benefits from the requirement of only a small powder quantity.

This report summarizes the work performed during the last 12 month primarily by the project student, Mr. El Hebieshy. It covers the following three topics:

1) The effect of die shape and orientation on flow behavior of aerated powders during die filling.

This is a natural continuation of the DEM work reported in our first IFPRI report, in which a systematic numerical analysis of the effect of die shape and orientation was presented. In order to validate the DEM results and provide physical insights into the effect of die shape and orientation on die filling behavior, we performed an extensive experimental investigation using 10 powders of distinctive powder characteristics and various shaped dies as used in our DEM simulations reported last year. We found that powder flow during die filling was mainly determined by two primary powder characteristics: the true density and the median particle size (d50), which could adequately distinguish die filling behavior of most powders considered in this study. In addition, for non-axis-symmetrical dies (e.g. oval and rectangular), the die orientation affects the die filling performance, which also depends on the aspect ratio of the die openings. It was shown that the effect of die shape on die filling performance was not significant.

2) Theoretical modeling of die filling of aerated powders.

A theoretical model was developed to predict the mass flow rate during die filling with various powders considered in this study. In order to validate the theoretical model, two sets of experiments were performed: i) the open die experiments in which the effect of entrapped air is eliminated, and ii) the closed die experiments in which the entrapped air could have a significant impact on the flow behavior of air sensitive powders. It was found that the developed theoretical model was capable of predicting the mass flow rate and the critical filling speed, and could capture the influence of air sensitivity of the powders during die filling.

3) Size-induced segregation during die filling.

A preliminary experimental study was performed using a mixture of two powders with similar density but different particle sizes. Segregation tendency at various filling speeds was examined and it was found that the segregation tendency decreased with an increase in filling speed.

Based upon current research and the tasks proposed in the original IFPRI proposal, the following future project plan is proposed:

• Segregation during die filling. A systematic study on segregation induced by density and size difference (i.e. density- and size-induced segregation) will be performed, as well as airflow induced segregation.

• Modelling die filling with aerated powders. The theoretical model developed recently will be extended to analyse die filling with aerated powders, especially by considering build up of air pressures inside the die during die filling. A thorough experimental study on pressure gradient induced by the entrapped air will also be carried out, for which an instrumented die with air pressure measurement during die filling processes will be designed. The experimental study will be used to validate and refine the model.

• Flow behavior of aerated powders during rotary die filling. Most die filling studies focused on translational motion of the shoe or the die, while in practical tableting processes, die filling was performed in a rotary tableting machine. To mimic the real die filling process, we plan to design and build a rotary die filling system. Using this system, how rotational angular speed and powder characteristics on die filling performance of aerated powders will be experimentally explored for the first time.

Executive Summary

Various shaped dies have been used to manufacturing particulate products of distinctive shapes in a number of industries (e.g. pharmaceutical, agrichemicals, ceramics). Although the formulations and manufacturing systems used are similar, the powder behavior during die filling could be affected by the orientations of dies when non-axisymetric dies are used. However, there is little understanding of the effect of system set-up on die filling behavior. Therefore, a systematic study on the effect of the shape and orientation of dies on powder flow behavior was performed numerically. Using the inhouse DEM-CFD code, a methodology was developed to model complex die geometries, for which triangular meshes were employed to discretized the complex boundaries. Using the developed methodology, various die shapes, including circle, square, ellipse and rectangle, were modeled and the effect of orientation for non-axisymetric dies on die filling were explored and presented in Section 1. It is found that the dies with larger aspect ratio and parallel orientation (to the filling direction) lead to smaller mass flow rates and lower critical velocities. In addition, the dies with elliptic openings can generally give higher critical velocities than those with rectangular shapes. These results indicate that for die filling with non-axisymetric dies the system set up, especially the orientation, can have a significant impact on the powder flow behavior during die filling. An experimental apparatus was also developed and some preliminary study using this mode die filling system was performed and reported in Section 2. Further improvement of the measurement robustness is on-going.

Planned Tasks

It is hence planned that, in the 2nd year of this project, the following tasks will be performed (details are given in Section 3):

• Experimental study of the effect of system design on die filling of aerated powders (Task 2c of the IFPRI proposal).
• Experimental study on segregation during die filling with mixtures of aerated powders (Task 2b of the IFPRI proposal).
• DEM-CFD analysis of segregation during die filling with aerated powders (Task 1b of the IFPRI proposal).

Particle Scale Simulation of Industrial Particle Flows

Particle scale simulation of industrial particle flows using DEM (Discrete Element Method) offers the opportunity for better understanding of the flow dynamics leading to improvements in equipment design and operation. These can potentially lead to large increases in equipment and process efficiency, throughput and/or product quality. Industrial applications can be characterized as large, involving complex particulate behaviour in typically complex geometries.

Importance of Particle Shape

The critical importance of particle shape on the behaviour of granular systems is demonstrated. Shape needs to be adequately represented in order to obtain quantitative predictive accuracy for these systems.

Exploration of Industrial Applications

We explore the breadth of industrial applications that are now possible with a series of case studies. The inclusion of cohesion, coupling to other physics such fluids, and its use in bubbly and reacting flow are becoming increasingly viable.

Challenges in Model Development

Challenges remain in developing models that balance the depth of the physics required with the computational expense that is affordable, and in the development of measurement and characterization processes to provide the expanding array of input data required.

Advancements in Computer Power

Steadily increasing computer power has seen model sizes grow from thousands of particles to many millions over the last decade which steadily increases the range of applications that can be modelled and the complexity of the physics that can be well represented.