ARR - Annual Report

The stability of gels of attractive colloidal particles determines the shelf life of products across many sectors. Our project is concerned with coming to a deeper understanding of why and how such gels may collapse under gravity using experiments supported by simulations.

State Diagram Mapping

In our first year, we mapped out the state diagram of a model colloid-polymer mixture of this kind consisting of sterically-stabilized polymethylmethacrylate (PMMA) spheres in which a short-range interparticle attraction was induced by linear polystyrene dispersed in hydrocarbon solvents. Exclusion of polymer in the space between two nearby particles results in a net osmotic pressure pushing the particles together, giving a ‘depletion attraction’ whose range and depth are controlled by the size (i.e., molecular weight) and concentration of the polymer respectively. We showed that the equilibrium phase behavior of this experimental model system could be mapped onto a ‘universal phase diagram’, which we obtained using simulations, via an ‘extended law of corresponding states’. This then permitted us to show that gelation in our model system was due to arrested spinodal decomposition, in which the denser part of a coarsening bicontinuous texture underwent dynamical arrest into metastable gel states.

Collapse Mechanisms

We found that these gels could collapse under gravity in two qualitatively distinct ways. After an initial period of stability, gels at moderate colloid concentrations sedimented very rapidly with a constant meniscus speed after a ‘delay time’, before switching abruptly to a stretched-exponential compaction mode, finally arresting suddenly when the sediment reached a volume fraction of f 0:55. At higher colloid volume fractions, however, gels collapsed in a stretched-exponential fashion, asymptotically reaching the limit of random close packing, frcp 0:64. BD simulations never reproduced the rapid collapse regime; we concluded that hydrodynamics are essential in this phenomenon.

Current Research

This year, we have concentrated on elucidating the mechanism of the rapid collapse. Work with the magnetic resonance imaging (MRI) group of Prof Lynn Gladden in Cambridge show that when the gel slowly separates from the top meniscus, dense material gathers at the top. We observe the rapid sinking of this material through the body of a gel just before the onset of macroscopic rapid collapse. Calculations provide support for the idea that rapid collapse is initiated when the gel structure is no longer able to support the weight of these dense clusters. Presumably, at high enough f, the gels are always strong enough to support the weight of such ‘debris’ at the top, so that the gel collapses as a compacting poroelastic continuum (known to follow a stretched-exponential law, as indeed observed in our system). Interestingly, further calculations starting from this insight were able to account for the difference between observed and simulated gel boundaries, as well as the effect of particle size (the latter via comparison with literature data).

Solvent Mixture Experiments

Using a mixture of solvents, we were able to overmatch the density of the particles, creating a system in which gravitational instability consisted of ‘creaming’ upwards rather than sedimentation. This has allowed us to collect preliminary single-particle resolution 3D data of the ‘top’ part of a collapsing gel. Dramatic movies of ‘volcanos’ erupting at the gel-supernatant interface have been obtained.

Finite-Element Analysis

Finally, comparison of finite-element analysis of gels as elastic continua with previous, macroscopic dark-field optical imaging suggests that ‘fault lines’ in the gel correspond to stress concentrations of an elastic body hanging from the walls of the sample container. These ‘fault lines’ are presumably where heavy ‘debris’ first sink through the gel, and/or polymer rich solvent flows to the surface through ‘vents’ for the observed ‘volcanic eruptions’. Detailed working along these lines next year should provide further insights.

During the third year of this project we focused on the following activities:

• We have completed the study of the force displacement law for high densities which was also part of a parallel leveraging project funded by Abbvie. This work has demonstrated that the utilization of DEM to high relative density compaction problems requires a completely different approach to the force displacement law than traditional DEM. The contact response between particle was found to depend on the overall triaxiality of the contact deformations on of the particle. A new deformation fabric tensor was proposed based on the deformation and direction of all contacts on a particle. These results form the basis for more appropriate force-displacement laws at contacts that can be implemented in discrete element simulations for high density problems.

• A detailed study was conducted on the contact problem between dissimilar spheres (different radii and different materials cases). This problem is central in the cases of powder mixture compaction. New results are presented in the report.

• An experimental study was conducted in the NaCl-Starch system – a binary system with peculiar behavior in terms of the strength of mixtures. We have first repeated the experimental results to verify them. We have identified a different method of milling that produces completely opposite trends. Our analysis of results indicates that there is a strong coupling between the milling process and the microstructure of the compacts. The milling process results in essentially a change of the particle size that depends on the materials of the mixture.

Ongoing work focuses on (a) the introduction of failure models in DEM, (b) the extension of the large relative density approach for DEM for multi material systems, (c) understanding the role of shear motions in multi material systems, (d) parametric studies for powder mixtures (d) model validation.

In previous years the experimental set-up was about granules composed of only two phases, a particle phase and a binder phase. The particle phase consisted of insoluble limestone particles with different particle size distributions. The particle size distribution was varied systematically by changing the ratio of coarse to fine primary particles. It was found that the composition of primary particles plays an important role for the granule properties, especially the amount and distribution of coarse primary particles.

The aim of this years project

was to amplify the knowledge about structure - functionality correlation. Therefore a set of experiments with two different primary particle phases was investigated. The materials were chosen to have a soluble and an insoluble particle phase. As soluble particle phase sodium chloride was chosen because it allows the measurement of conductivity during dissolution. The insoluble particle phase was again chosen to be limestone. Also the binder was hold constant to be polyethylene glycol but it was now used in a melted state and not in concentrated solution as before.

Granulation method

Additionally the granulation method was changed into a two step method involving casting and milling. This step was necessary because it was aimed to generate a random close structure of primary particles in binder. In more detail a mixture of primary particles was mixed with melted binder and casted on a plate for cooling. The amount of binder was adapted to generate a saturated system without porosity. Afterwards the hardened plate was milled down to the desired granule size between 250 and 710m.

Investigation of granules

The granules were investigated in two ways as done in previous work. The structure was determined from X-ray micro-tomography images calculating structure measures like chord length distribution, covariance function and star volume of different phases. The granule properties were determined by different measurements including single particle crushing and dissolution behavior.

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.

During this initial year of the project we have worked in developing a setup to charge a sample of powder. Ideally, this set-up must achieve a reproducible specific charge for a sample weighting several grams, to allow the charged sample to be used in packing experiments. We completed work on an initial design based on dry powder inhalers. The sample weight delivered each time in this initial design was up to 15 mg. We measured the specific charge by means of a Faraday cup, and the particle charge distribution by particle tracking image analysis. For this design we found them to be compatible within the accuracy of the experiments. Since a sample weight of 15 mg was placed manually in the powder dispenser, this setup is not practical to make packing experiments.

We moved to a setup based on venturi injection of the powder sample in a gas stream. This new setup can charge larger samples (several grams in a continuous way), and it is suitable for packing experiments. We are currently testing that the charge acquired by the particles is homogeneously distributed in the final packing. To this aim, we have resorted to the same procedures of measuring the specific charge and charge distribution that we used for the inhaler-like tribocharger. The measurement of the charge distribution has been improved to discriminate the sign of the charge of each particle. We have also set controlled humidity enclosures to keep the samples in order to investigate the effect of humidity on the charge and particle aggregation.

However, at the moment of writing the present report, we have not been able to reconcile the results of these two types of measurements for this new tribocharger (venturi based). The reasons for the discrepancy are that most of the sample comes out of the venturi tribocharger with larger velocities and with a larger total charge than in the inhaler-like tribocharger. This fact implies that: a) the particle charge distribution is made from a small subset of the whole sample, i.e. those particles at the final part of the injected sample that move at smaller speeds, and may not be representative of the powder, and b) a sample weighing some milligrams, although much smaller than the weight that we can pass through the tribocharger, saturates the electrometer measuring the total charge of the sample in the Faraday cup setup. Work is currently in progress to overcome these difficulties.

We have also started experiments to measure the charge distribution on the surface of particles. We have used Kelvin Force Micros copy (KFM) as we have found than it is easier to interpret than Electrostatic Force Microscopy, which was proposed for the initial stages of the project. We have developed a procedure to fix the particles for Atomic Force Microscopy imaging. We have been able to measure both the topography of a particle and its contact potential with a conductive AFM's cantilever. Further analysis is now in progress to separate the different contributions to the contact potential measured by the microscope in order to determine the charge distribution and its polarity on the particle's surface.

In the next pages, we describe in detail the techniques used as well as the evolution of experiments as setups and analysis were improved. We discuss the results obtained with the tested materials. Finally, in the conclusion we summarize the main findings.

Executive Summary

Milling is commonly deployed in many industrial sectors for particle size reduction. In this project, we aim to develop a robust methodology to link material grindability with particle dynamics in a mill in order to provide an innovative step--‐change in mill fingerprinting and optimization. This involves characterizing the stressing events that prevail in a milling operation and establishing material grindability in the context of the stressing events. The material grindability will require a detailed study of the fundamental fracture and breakage mechanisms of individual particles under different loading regimes, and how they relate to the mechanical properties and the final size distribution. This will provide the fundamental scientific basis for developing appropriate grindability tests capable of analyzing particle breakage subjected to particle impact, compression, shear and abrasion etc. pertaining to a milling process, which in turn will provide the basis for an improved particle breakage model calibrated against defined grindability. The IFPRI Grindability Project commenced on January 2013 and is planned for 6 years. The centrifugal impact pin mill has been selected as the first mill to be studied for this project, in collaboration with Hosokawa Micron Ltd. In the first year, the work focused on developing a computer model and conducting the discrete element modelling of pin mill to examine the particle dynamics during the milling process. This provided a better understanding of the comminution process such as the local stressing events and spatial distribution of impacts etc. under different operating conditions. This report summarizes the work performed within the second year of the project. Two materials, zeolite and alumina, have been chosen as the test particles with semi--‐brittle and brittle failure behaviour respectively. The compressive test of single particle coupled with X--‐ray microcomputed tomography (XìCT) was carried out to give a better understanding of particle breakage from the micro--‐scale standpoint. The 3D volume of particle was visualized and the 3D object was segmented to characterize the inherent crack in the particle by specifying thresholding value in Avizo Fire™. The spatial orientation of particle during projection was investigated and this problem was solved using a linear interpolation algorithm. By using 3D Digital Image Correlation (DIC), with a pair of images taken before and after an inherent crack propagates, full field displacement can be observed and the extent of crack development can be quantified to some extent. The presented results show that the combined use of XCT and DIC is an enhanced tool to study the breakage mechanism of individual particles under compression. Single impact test has been conducted to investigate the particle behaviour under dynamic impact. The breakage event was captured using a high--‐speed camera and the breakage pattern under high impact velocity was observed. The effect of impact velocity and incidence angle on particle breakage has been examined. The breakage rate increases with the increase of impact velocity, with chipping being the main breakage type at low impact velocities whereas fragmentation dominates at high impact velocities. Whilst the normal velocity component plays an important role in particle breakage, one key finding is that the tangential component of the velocity becomes increasingly important as impact velocity increases. Preliminary results of pin mill test for both zeolite and alumina were presented and compared with the predictions from the most common particle breakage models in the literature. The model fitting with the impact test data suggests that current models is deficient in predicting the breakage behavior of particle under impact comminution. IFPRI has funded a further collaboration project between Edinburgh and Dr Colin Hare of the University of Leeds to supplement the characterisation of these test particles using the well established facilities at Leeds to provide further measurements deploying the impact and nano--‐indentation techniques. The results from the collaboration are reported separately. Over the next 12 months, the project will focus on: particle breakage model development, which will consider the measured mechanical properties and loading conditions. Then breakage comparison with the newly developed model will be made with the final set of milling experiments to be conducted. Further investigation will be done in terms of in--‐situ loading single particle compression under simultaneous X--‐ray ìCT. The numerical work will continue to compute particle dynamics in real--‐geometry pin mill based on the first year’s numerical work. The new understanding will form the basis for developing the grindability test(s) capable of characterising particle breakage subjected to the dominant loading events identified within a milling operation.

Executive Summary

During the second year of this project we focused on the following activities:

• A detailed study of the force displacement for high densities was conducted as part of a parallel leveraging project funded by Abbvie. The project looks at the fundamentals of DEM simulations for single particle compacts. A paper was submitted to the Journal of Solids and Structures and is under review. The material presented here is directly from that paper that has not been published yet.
• A detailed study was conducted on the contact problem between dissimilar spheres (different radii and different materials cases). This problem is central in the cases of powder mixture compaction. Some results are presented in the report. A paper is being prepared for submission.
• An experimental study was conducted in the NaCl-Starch system – a binary system with peculiar behavior in terms of the strength of mixtures. Literature results that showed decreased strength of mixtures compared with the individual constituents have been duplicated. Ball milling of the mixture before compaction resulted in unusual high strength and ductility. Results from this work are being analyzed. A paper is expected to be submitted by early 2015.
• An x-ray transparent die has been designed for experiments within an x-ray tomography machine. The die was designed to withstand 150MPa.

Ongoing work focuses on (a) the importance of the elastic unloading behavior in DEM which may be related to residual stresses present in mixtures. (b) the introduction of failure models in DEM, (c) understanding the difficulties associated with material properties selection in DEM – primarily related to friction coefficient(s).

1. Introduction

The earlier parts of the project were focused on the implementation of structure descriptors and determination of physical parameters of model granules and their correlation to structure parameters. The first results were intensified and finding checked for correctness.

Model granules were generated containing different size distributions of primary particles to achieve different internal structures. A series of bimodal particles size distribution of fine and coarse limestone particles were granulated with polyethylene glycol binder. Three dimensional X-ray micro tomography images of the model granules were recorded and used for further calculations of structure descriptors. The structure descriptors that were evaluated include volume and surface fraction, star volume, chord length distribu- tion and covariance function.

For the determination of physical properties the techniques established last year were applied. Mechanical strength is measured by single particle crushing and the dissolution or disintegration behaviour by conductivity measurements and online particle sizing respectively. The structural as well as the physical parameters provide results that are suitable to distinguish between differently structured granules.

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).