One of the long term barriers to advanced and accurate modelling of particulates is the lack of a suitable set of test particles that can be used to validate particle models. Generally the approach has been to take a specific, simplified particle system, measure the mechanical and surface properties as accurately as possible, and input these parameters into a model. The model is then used to estimate a property of the agglomerate – for instance agglomerate strength – and compared to experimental measurements on the simplified particle system. Whilst some of these approaches have produced some elegant simulation results, they often fail to produce an accurate prediction of the full distribution of behaviour of the simple particle system, let alone the behaviour of far more complex industrial powders.
There are two key limitations with the existing approach. Firstly, we collapse our experimental data to an average particle shape, average roughness, average surface energy etc. and eliminate the complexity of real particles very early in the process. The final model becomes "an average of averages", and the important effects of the structure, interactions and distributions are lost. Secondly, the destructive experimental tests can only ever test a single agglomerate in a single test condition and a single (usually unknown) orientation. The structural details of the agglomerate and the test conditions (particularly orientation) are never precisely modelled and the experimental test can never be replicated with an identical particle under identical conditions. Thus we are never sure if the model is insufficient to describe the behaviour, or if the model was accurate but the number of experimental testing replicates was insufficient to statistically converge to the average behaviour predicted by the model.
Real agglomerates produced by spray fluidised beds and high shear mixers in industrial processes have complex structures and irregular shapes which are difficult to study directly. At a basic level, general terms such as porosity or its complementary solid fraction are used to define the structure of the agglomerates [1-3]. These terms can also be related to variables such as coordination number or envelope density [4-6]. However, more advanced and useful analytic tools, such as X-ray microtomography technique, are recently available to study the structure of the agglomerates. Farber et al. [7] used X-ray microtomography to characterise pharmaceutical granules. Total porosity, pore size distribution and geometric structure were obtained by this technique. Rahmanian et al. [8] have also used X-ray microtomography to characterise the granule structure evolved in a high shear granulator. Due to complexity of the agglomerate breakage analysis in some cases, such as characterisation of internal stresses by experimental work, numerical simulation using Distinct Element Method (DEM) has been widely used by different researchers to provide a basis for sensitivity analysis of different factors affecting the agglomerate structure, and hence the breakage of agglomerates [9-11]. Golchert et al. [12, 13] for the first time studied the failure of the agglomerates with their structures characterised by X-ray micro-tomography, and their strength analysed by DEM models. The 3D spatial locations of particles of real agglomerates were obtained and implemented into the simulation code to generate simulated agglomerates. The effects of agglomerate shape and structure on breakage patterns during compression were analysed. A similar piece of work was carried out byMoreno-Atanasio et al. [14]. More recently, Dadkhah et al. [15, 16] characterised the internal morphology of agglomerates produced by a spray fluidised bed using X-ray micro-tomography. The 3D volume images of agglomerates were analysed in terms of porosity, coordination number, coordination angle. For the first time, they separated the solidified binder morphology of these agglomerates using this imaging technology. Although structural details of agglomerates can be obtained by X-ray micro-
Karen Hapgood ARR67-02 Page 4
tomography, the destructive breakage tests can only be carried out on a single sample under a single orientation.
The effect of structure details has hardly been investigated and the breakage test can never be replicated under identical conditions. The complexity of the agglomerate structure, arising from different parameters such as primary particle size distribution, void fraction, inter-particle bond characteristics and material properties of both primary particles and bonds, makes it difficult to establish a full map of agglomerate breakage regimes. Overall, the agglomerates can break in different patterns, depending on their properties and loading conditions leading to various failure modes. Several pieces of work have been done on classification of patterns of agglomerate breakage [17, 18]. Subero and Ghadiri [17] made agglomerates using glass ballotini as primary particles bonded together by bisphenol-based epoxy resin. In order to explore the effect of agglomerate structure on agglomerate impact strength, the agglomerates were made with different levels of porosity by making different number and size of the macro-voids. The particles were impacted at different impact velocities and angles. In order to elucidate the fracture patterns, the shapes of the fragments were observed. They reported different patterns of breakage for agglomerate impact breakage obtained in their work, such as localised damage, fragmentation, multiple fragmentations with localised damage and disintegration. In order to study the effects of structure on agglomerate breakage, it is desirable to produce multiple identical test agglomerates with controlled structures, and then study their breakage behaviour in detail with the aid of mathematical models and experimental instruments.
In this project, 3D printer-Objet Connex 500 is used to print multiple customised agglomerates. The Objet 500 is an eight jet "PolyJet" printer which can print multiple materials simultaneously in a single print run, including rigid or rubber-like flexible materials with well-defined mechanical properties. Liquid photopolymer is printed on a build tray to form the object and cured with UV light. It can also print a removable support gel to support overhangs and/or complicated geometry. PolyJet prints simultaneously different materials with varied mechanical properties to represent the particles and/or dried liquid bridges between the particles. There are five broad material classes available, some with sub-variations: rigid opaque materials (2 variations); rubber-like materials (3 variations); transparent materials (2 variations); a polypropylene-like material and a high temperature material. The properties of each material are well defined and detailed datasheets are available [19], specifying density, hardness, tensile strength, elongation at break, elastic modulus, water adsorption and glass transition temperature Tg (where relevant), and other properties as well as the ASTM test method used to measure each of these properties. This permits a broad spectrum of agglomerates to be produced with "tuneable" physical properties.
In year one, quasi-static compression tests and drop weight impact tests were carried out using a spherical symmetrical agglomerate to investigate the agglomerate breakage behaviour at different strain rates. Preliminary experiments to determine the influence of agglomerate orientation, bond properties and strain rates were conducted to demonstrate "proof of principle" for the approach. An updated description of this work is included in this report, and the first "proof of principle" paper has recently been published in Powder Technology in late 2016. In year two, two different agglomerates were designed (cube shaped tetrahedral agglomerate, and a spherical shaped randomly structured agglomerate) and both breakage tests and DEM modelling were conducted. This report summarises the progress to date and the remaining work for year 3.