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Publications - MacroPac

The following papers describe work that was done using various versions of MacroPac. The most recent papers are at the top.

Role of pellet size, shape, and filling method in achieving fill weight uniformity for encapsulated pelletized systems: A comparison of experiment and computer simulation, A M Ali, M de Matas, P York, R C Rowe, J Pharm Sci 99, 1299-1308 (2010)

Abstract

Correlations between experimental filling and computer simulation for real pelletized systems were evaluated in this study. Simulations were successful in predicting the fill weight variability of a variety of pellet sizes and shapes and demonstrated similar values and trends to those observed experimentally. Simulation also helped identifying the critical variables affecting filling consistency such as pellet attributes and filling methods. Unit filling and automatic filling were found to be more comparable to simulation whilst manual flood filling appeared to lack reproducibility. Computer simulation can therefore be used as a method for predicting fill weight variability for different pellet fractions filled using different filling methods, which can facilitate process control and assurance of product quality.

Investigating the effect of shape on particle segregation using a Monte Carlo simulation, S J Roskilly, E A Colbourn, O Alli, D Williams, K A Paul, E H Welfare and P A Trusty, Powder Technology 203 211-222 (2010)

Abstract

A Monte Carlo simulation has been used to investigate the segregation potential of a range of particulate systems under conditions in which the particles undergo high amplitude low frequency shaking. These systems involve a wide range of binary powder mixtures in which complex particle shapes have been investigated, including plates and rods which represent the real world materials encountered in pharmaceutical systems such as those which include crystalline components. Previous simulations on the segregation propensity of systems with different shapes were limited to spheres and spherocylinders, with relatively low vibrational amplitude drops. A commercial computer application for particle packing—called MacroPac—has been successfully employed here, as it has been able to model systems that are more complex where the shape variation is much wider. These simulations apply to the case of macroscopic particles, in the absence of air resistance and inter-particle forces. For non-spherical shapes, an ‘effective size’ which relates to the radius of gyration of the particles is determined. Our studies indicate that with high amplitude low frequency shaking, in a mixture of particles with different shapes but with equal volumes, the particles with the larger ‘effective size’, which tend to have a lower packing fraction, segregate to the top.

Computational analysis of transitional air flow through packed columns of spheres using the finite volume technique, M J Baker and G R Tabor, Computers and Chemical Engineering 34 878-885 (2010)

Abstract

We compare computational simulations of the flow of air through a packed column containing spherical particles with experimental and theoretical results for equivalent beds. The column contained 160 spherical particles at an aspect ratio N=7.14, and the experiments and simulations were carried out at particle Reynolds numbers of (Re_dP=700−5000). Experimental measurements were taken of the pressure drop across the column and compared with the correlation of Reichelt (1972) using the fitted coefficients of Eisfeld and Schnitzlein (2001). An equivalent computational domain was prepared using Monte Carlo packing, from which computational meshes were generated and analysed in detail. Computational fluid dynamics calculations of the air flow through the simulated bed was then performed using the finite volume technique. Results for pressure drop across the column were found to correlate strongly with the experimental data and the literature correlation. The flow structure through the bed was also analysed in detail.

Influence of pellet aggregate populations on the variability of pellet filling into hard shell capsules: A comparison of experiment and computer simulation, Ahmed M. Ali, Marcel de Matas, Peter York, Ray C. Rowe, European Journal of Pharmaceutical Sciences 38 197-205 (2009)

Abstract

Variations in pellet filling into hard shell capsules and other cavities are attributed to many factors including fluctuations in pellet size, shape polydispersity, presence of aggregates and electrostatic charge. The influence of pellet aggregation has not previously been investigated, and therefore modelling of the filling behaviour of pellet populations with different levels of twin, triplet and tetrahedral aggregates was evaluated in this study. Pellet/aggregate mixtures were also filled experimentally alongside simulation. The experimental and simulation results for fill weight variability showed that predictions of the trends and values of the percentage coefficient of weight variation (% CV) for mixtures containing twin aggregates up to a level of 20% (w/w) could be achieved. The filling behaviour for triplet and tetrahedral aggregates could not however be simulated effectively due to pellet segregation.

A discrete finite element modelling and measurements for powder compaction, J L Choi and D R Gethin, Modelling Simul. Mater. Sci. Eng. 17 035005 (22pp); doi: 10.1088/0965-0393/17/3/035005 (2009)

Abstract

An experimental investigation into friction between powder and a target surface together with numerical modelling of compaction and friction processes at a micro-scale are presented in this paper.

The experimental work explores friction mechanisms by using an extended sliding plate apparatus operating at low load while sliding over a long distance. Tests were conducted for copper and 316 steel with variation in loads, surface finish and its orientation. The behaviours of the static and dynamic friction were identified highlighting the important influence of particle size, particle shape, material response and surface topography. The results also highlighted that under light loading the friction coefficient remains at a level lower than that derived from experiments on equipment having a wider dynamic range and this is attributed to the enhanced sensitivity of the measurement equipment. The results also suggest that friction variation with sliding distance is a consequence of damage, rather than presentation of an uncontaminated target sliding surface.

The complete experimental cycle was modelled numerically using a combined discrete and finite element scheme enabling exploration of mechanisms that are defined at the particle level. Using compaction as the starting point, a number of simulation factors and process parameters were investigated. Comparisons were made with previously published work, showing reasonable agreement and the simulations were then used to explore the process response to the range of particle scale factors. Models comprising regular packing of round particles exhibited stiff response with high initial density. Models with random packing were explored and were found to reflect trends that are more closely aligned with experimental observation, including rearrangement, followed by compaction under a regime of elastic then plastic deformation.

Numerical modelling of the compaction stage was extended to account for the shearing stage of the extended sliding plate experiment. This allowed micro-scale simulations of the friction mechanisms seen within the experimental programme. The frictional response with similar stress level in the normal direction as reported for the experiment was first emulated and explored and qualitative agreement was achieved showing a similar pattern. The factors identified from the experiments were investigated on smooth and rough surfaces highlighting each effect. It was confirmed that the rough surface clearly leads to higher friction coefficient since it accounts for both plain friction and topographical effects and the average stress distribution increased against the restraining die wall when the rough surface was introduced for the model with round regular packing of particles. Random packed models again showed a better reflection of the experimental conditions. A wider distribution of stress was observed because of the further rearrangements. Interlocking was observed for the models with irregularly shaped particles on a rough surface, which led to an increase in normal stress on the top punch. This would lead to dilation in the case where a punch was force level controlled as for the experiment.

Geometrical percolation of hard-core ellipsoids of revolution in the continuum, S Akagawa and T Odagaki, Phys Rev E 76 051402 (2007)

Abstract

The percolation threshold of hard prolate ellipsoids of revolution dispersed in a continuum is obtained as a function of the aspect ratio. First random close packing of ellipsoids is produced by a dropping-and-shaking protocol. Two ellipsoids are regarded as connected when the come sufficiently close. Then a given fraction of ellipsoids selected randomly is removed and percolation of remaining ellipsoids is investigated as the fraction of remaining ellipsoids is varied. It is shown that the critical volume fraction of the coloured ellipsoids is a decreasing function of the aspect ratio and that the aspect ratio dependence is well fitted by the inverse of the interaction range determined by the surface area and the radius of gyration of the ellipsoid surface.

The influence of pellet size, shape and distribution on capsule filling - A preliminary evaluation of three-dimensional computer simulation using a Monte Carlo technique, R C Rowe, P York, E A Colbourn and S J Roskilly, International Journal of Pharmaceutics, 300 32-37 (2005)

Abstract

A computer simulation based on a Monte Carlo technique has been developed and used to investigate the influence of pellet size, dispersity, shape and aggregation on the filling of hard shell capsules. The simulations are in general agreement with experimental observations previously reported. The results also confirm recent findings that filling is a function of pellet shape and that above an aspect ratio value of 1.2 filling reproducibility is reduced. The methodology is simple and rapid in execution allowing many computer-based experiments to be performed with minimum effort.

Note: This was performed using a modified pre-release version of MacroPac that allows rounded bottoms on a cylindrical vessel. See a picture, of a simulation of a capsule containing spherical pellets with a range of particle sizes, here.

The effect of relative particle size and deformation behaviour on the consolidation of binary powder mixtures,R C Gibb, R C Rowe, P York and P W Stott, Journal of Pharmacy and Pharmacology 57(Supplement) S63 (2005)

Abstract

Research has shown that although general rules can be applied when powders are mixed and compressed into tablets, interactions can be complex and depend on physical properties such as particle size, shape, deformation behaviour and strain rate. This study is an attempt to understand the consolidation behaviour of powder mixtures. MacroPac v4 was used to generate packing simulations of binary powders to show percolation behaviour.

See a picture of a simulation of the packing of Avicel PH101 (75 vol%) and Calipharm D (25 vol%) here.

Download a copy of the poster, presented at the British Pharmaceutical Conference in Manchester in September 2005. This is nearly 4MB.

A combined finite-discrete element method for simulating pharmaceutical powder tableting, R. W. Lewis, D. T. Gethin, X. S. Yang and R. C. Rowe, International Journal for Numerical Methods in Engineering, 62 835-869 (2005)

Abstract

The pharmaceutical powder and tableting process is simulated using a combined finite-discrete element method and contact dynamics for irregular-shaped particles. The particle-scale formulation and two-stage contact detection algorithm which has been developed for the proposed method enhances the overall calculation efficiency for particle interaction characteristics. The irregular particle shapes and random sizes are represented as a pseudo-particle assembly having a scaled up geometry but based on the variations of real powder particles. Our simulations show that particle size, shapes and material properties have a significant influence on the behaviour of compaction and deformation.

See a picture of a simulation here. This shows the packing of plates and spheres in a tablet die, already meshed prior to the application of a compaction force.

Heat transfer through die coatings in the aluminium die casting process, W Griffiths and K Kawai, Foundry Practice, 2419-14 (2004)

Abstract

The aim of this work was to model the interfacial heat transfer mechanisms in the die casting process and in this way to obtain an estimate of the heat transfer coefficient. Its focus was to determine an equation that could be used to estimate the interfacial heat transfer coefficient in oder to provide values for use in the simulatio of casting solidification and which cold be appllied to a range fo alloys in a range of conditions. MacroPac was used to model the coating surface roughness. Good agreement was found between measured surface roughness parameters and values obtained by modelling the coating formation in this way.

Interface and bulk properties in films of phase separated dispersion particles, S Kirsch, A Pfau, E Haedicke and J Leuninger, Progress in Organic Coatings 43 193-204 (2002)

Abstract

Structured latex particles are of high interest as tailor made dispersion binders to meet contradictory requirements in different fields of applications. Aqueous dispersions, e.g. used as binders in solvent-free, low pigmented paint formulations, have to cope with the challenge to guarantee an excellent film forming ability at room temperature as well as a low tack.

In this work, the synthesis and characterizations of hemisphere-like particles with different chemical constitutions are described. The single particles were placed onto various types of substrates. The particle-surface interface was then investigated by atomic force microscopy (AFM). Characteristic differences were found as a function of the polarity of both polymer and substrate. Including these findings, AFM was used to determine the impact of the interface structure on the bulk properties of the final dispersion films. The results are compared to computer simulations of the packing of the particulate materials.

A correlation of microscopic interface structure to macroscopic application properties of the corresponding disperson films is presented. The results are compared to sets of blends with identical chemical composition and equivalent volume fraction and the corresponding statistical copolymers.

The packing of thick fibres, K E Evans and M D Ferrar, J Phys D Appl. Phys 22 354-360 (1988)

Abstract
Computer simulations have been performed for the close packing of thick fibres with aspect ratios between 1 and 30. Results are presented for a range of fibre orientations including 3D random, in-plane random and aligned. It is shown that a small degree of out-of-place randomness enhances packing compared with both in-plane and 3D random orientation distributions. Thickness effects are found to be significant in determining the maximum packing fractions for aspect ratios <20. Local ordering is also a significant feature in the close packing of fibres which are otherwise random over length scales greater than the fibre length.

Note: This paper outlines the original concepts that underpin MacroPac.