ARR - Annual Report

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.

Milling is commonly deployed in many industrial sectors for intended 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 centrifugal impact pin mill has been selected as the first mill to be studied for this project, in collaboration with Hosokawa Micron Ltd. The work performed in Year 3 of the project is summarized as below.

• UPZ100 pin mill experiments were conducted with the effect of rotary speed and feed rate examined.
• Conceptual design of instrumented pin was trialed in laboratory and its mechanical response was explored in both static and dynamic loading.
• An inverse analysis scheme has been developed and validated for determining force and angles from strain measurement on an instrumented steel pin.
• With the finding of the significance of tangential component of impact velocity, a new breakage model was proposed based on a mechanistic approach assuming that lateral crack accounts for the chipping mechanism.
• The new model was then assessed and compared with other breakage models which demonstrates that the new model is superior in predicting both normal and oblique impact regimes for the range of velocities studied.
• DEM simulations of single particle breakage were conducted to study the damage ratio arising from the velocity regimes pertaining to an impact mill.
• A recently developed new DEM bond contact model was utilized considering axial, shear and bending behaviour of bond.

The breakage pattern of chipping and fragmentation under low and high impact velocity was successfully reproduced in DEM.

One of the long term barriers in understanding granule breakage is the lack of a universally accepted test method or test granules to systematically evaluate agglomerate breakage propensity and mechanism. Computer simulations are often used but are limited by the lack of identical, controlled agglomerates to test and validate simple models, let alone replicate the complex structure of real industrial agglomerates.

This report summarises progress to date on a new 3D printing production method of test agglomerates with defined and "tuneable" properties. Agglomerates were designed using Solidworks 2014 software and printed by an Objet500 Connex 3D printer. Materials with different mechanical properties were used to print the particles and the inter-particle bonds, allowing combinations of bond strength, particle strength and agglomerate structure to be tested. Compression and impact tests were performed to investigate the breakage behaviour of printed agglomerates in terms of agglomerate orientations, bond properties and strain rates.

The compression and impact results reveal different agglomerate breakage characteristics. For compression tests under low strain rate, breakage occurs at the bond between primary particles, and the compressive strength is influenced by the bond strength significantly. In future, it is worth to further relate the microscopic particle-particle and particle-bond interactions to the macroscopic compressive strength. For impact tests with high strain rate, the agglomerates with flexible bond show rebound behaviour, while the agglomerates with rigid bond fracture. Under the same impact conditions, the rubber materials have high fracture toughness and the rigid materials behave in a more brittle manner that can fracture easily. For the fractured agglomerates, clear fracture planes can be observed with low impact energy. At high impact energy, a large amount of small debris occurs, and the breakage extent increases accordingly.

Now that proof of principle for the approach has been established, the next stage of the project is to conduct systematic studies of agglomerate strengths varying structure, material properties, under various breakage forces, orientations and strain rates.

This report covers the results obtained in the second year of this project. At the end of the first year, we have developed an experimental set-up capable of dispersing a sample of about 10 g of powder in a gas stream, charging it by tribocharging, collecting the sample inside a Farday cage and measuring the charge in the collected sample. During this year, we have improved the set-up by building two tribochargers: a nylon cyclone tribocharger and a steel tube tribocharger. With this new set-up we are able to measure both the charge acquired by the particles in dispersion (but only when the steel tribocharger is used) and the ccharge remaining in the powder when collected.

We have run experiments with a set of seven materials stored at different humidities and dispersed using air and dry N2. From the results we have obtained we can conclude that in dispersion particles become electrically charged up to the maximum given by the electric field that would cause a corona discharge. However, when settled, the particle must lose most of their charge to keep the field created by the settled sample below the limit imposed by corona discharge. The remaining amount of charge on the settled powder depends on the sample mass and as a result, the specific charge of the collected sample tends to decrease when the collected mass is increased. A quantitative model for a simplified sample geometry has been developed.

We have found that the charge in the collected sample decays in a relatively short time, of the order of some minutes. We have decided to measure poured and tapped densities to evaluate the effect of charge on the packing as these experiments can be performed during the time span that powder remains charged. However, the results obtained are in conclusive. Possible explanations for the lack of a clear trend in the effect of specific charge and storage conditions on the solid fraction are given in the text.

During the Annual General Meeting, we were requested to move to smaller particle sizes (below 10 μm), storage humidites (below 10% RH) and dispersion gas humidities (dry nitrogen). The upgrades done in the tribocharging set-up to meet this condition are presented in the test, as well as some preliminary results.

Work has also continued in the other experiments planned in the project: individual particle size and charge distribution determination with particle tracking velocimetry (PTV) and scanning probe microscopy (SPM) experiments. However, no new significant results have been obtained and for these reason this report will focus on the results of the specific charge obtained with the tribocharging set-up. The state of the PTV and SPM experiments is discussed at the end of the 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.