ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2013

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 180

Flow and Compression ofGranulated Powders

The Accuracy of Discrete Element Simulationsand Assessment of Tablet Microstructure

ANN-SOFIE PERSSON

ISSN 1651-6192ISBN 978-91-554-8769-0urn:nbn:se:uu:diva-208808

Dissertation presented at Uppsala University to be publicly examined in B42, BMC,Husargatan 3, Uppsala, Friday, November 22, 2013 at 09:15 for the degree of Doctor ofPhilosophy (Faculty of Pharmacy). The examination will be conducted in Swedish.

AbstractPersson, A.-S. 2013. Flow and Compression of Granulated Powders: The Accuracy ofDiscrete Element Simulations and Assessment of Tablet Microstructure. Acta UniversitatisUpsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty ofPharmacy 180. 65 pp. Uppsala. ISBN 978-91-554-8769-0.

Simulations are powerful and important tools for gaining insight into powder processes.Ultimately, simulations have the potential to replace experiments. Thus, accurate models andinsight into the essential factors for descriptions of powder behaviour are required. In this thesis,discrete element method (DEM) simulations of granule flow and compression were evaluatedto deduce parameters and potential models essential for the experimental and numericalcorrespondence. In addition, the evolution in tablet microstructure during compression wasstudied using mercury porosimetry.

Granule flow was measured using angle of repose, discharge rate, and shear. The granular flowdepended primarily on particle shape and surface texture due to the mutual influence of thesetwo parameters on the inter-particle forces. Rolling friction stabilised both the heap formationand promoted shear in the elastic quasi-static flow regime. Thus, rolling friction was establishedto be an essential simulation parameter for the correspondence to experiments.

Current compression models often neglect the elastic compact deformation during particleloading. In this thesis, two fundamentally different models were evaluated with focus ofincluding the elastic deformation. The first model comprised a maximal particle overlap, whereelastic deformation commences. The second model accounted for the contact dependence andimpingement at high relative densities. This model was based on a truncated-sphere followedby a Voronoi extension. The validity of the models was demonstrated by the elastic qualitativecorrespondence to experimental compressions for ductile materials.

In tablets, the void (inter-granular pore) diameter was dependent on the degree ofcompression. Thus, the degree of compression provides an indication of the tabletmicrostructure. The microstructure was subsequently observed to be related to the tablet tensilestrength as inferred from a percolation threshold required for formation of coherent tablets.

In summary, this thesis has shed light onto the potential of simulating flow and compressionof granulated pharmaceutical powders using DEM. Continuous work in the area are required tofurther improve the models to increase the experimental and numerical correspondence.

Keywords: Discrete Element Method, Granule, Flow, Angle of Repose, Discharge Rate,Shear, Rolling friction, Compression, Elastic deformation, Microstructure, Degree ofcompression, Tensile strength

Ann-Sofie Persson, Uppsala University, Department of Pharmacy, Box 580,SE-751 23 Uppsala, Sweden.

© Ann-Sofie Persson 2013

ISSN 1651-6192ISBN 978-91-554-8769-0urn:nbn:se:uu:diva-208808 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-208808)

Till mamma och pappa

Never, never, never give up~Winston Churchill

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Persson, A.-S., Alderborn, G., Frenning, G. Flowability of sur-

face modified pharmaceutical granules: A comparative experi-mental and numerical study, European Journal of Pharmaceuti-cal Sciences, 42 (2011) 199-209.

II Persson, A.-S., Frenning, G. The influence of rolling friction on the shear behaviour of non-cohesive pharmaceutical granules – An experimental and numerical investigation, European Journal of Pharmaceutical Sciences, 49 (2013) 241-250.

III Persson, A.-S., Frenning, G. An experimental evaluation of the accuracy to simulate granule bed compression using the dis-crete element method, Powder Technology, 219 (2012) 249-256.

IV Persson, A.-S., Frenning, G. On the role of bulk modulus and granule hardness on the simulation accuracy of confined bulk granule compression, Manuscript.

V Nordström, J., Persson, A.-S., Lazorova, L., Frenning, G., Alderborn, G. The degree of compression of spherical granular solids controls the evolution of microstructure and bond proba-bility during compaction, International Journal of Pharmaceu-tics, 442(1-2) (2013) 3-12.

Reprints were made with permission from the respective publishers.

I was involved in the appended papers as follows: Papers I-IV: I was highly involved in the experimental parts, the data analy-sis and interpretation, and the paper writing in conjunction with my co-authors. I did not perform any of the simulations.

Paper V: I was involved in the mercury porosimetry measurements, parts of the data analysis, and paper writing.

Contents

1. Introduction .............................................................................................. 11

2. Characteristics of particles and powders ................................................. 13 2.1 Primary and secondary particles ..................................................... 13

2.1.1 Granule properties .................................................................... 13 2.2 Powders ........................................................................................... 16

2.2.1 Powder properties ..................................................................... 17

3. Numerical methods for particle simulations ............................................ 20 3.1 Numerical simulations .................................................................... 20 3.2 The discrete element method (DEM) .............................................. 20

3.2.1 Force-displacement contact laws .............................................. 22 3.2.2 Models and parameters used in the thesis ................................ 25

4. Aims ......................................................................................................... 27

5. Experimental methods ............................................................................. 28 5.1 Particle characterisation .................................................................. 28

5.1.1 Size ........................................................................................... 28 5.1.2 External volume-specific surface area ...................................... 28 5.1.3 Density and intra-granular porosity .......................................... 29 5.1.4 Mechanical characteristics ....................................................... 29

5.2 Characterisation of powders ............................................................ 30 5.2.1 Flowability ............................................................................... 30 5.2.2 Mathematical relations for bulk compression .......................... 32

6. Results and discussion ............................................................................. 34 6.1 Granule characteristics .................................................................... 34

6.1.1 Shape, size, density and porosity .............................................. 34 6.1.2 Granule surface sliding friction coefficients ............................ 36 6.1.3 Mechanical properties .............................................................. 36

6.2 Experimental evaluations of granule flow simulations (Papers I and II) ....................................................................................................... 38

6.2.1 The effect of rolling friction and cohesion on the angle of repose and discharge rate ..................................................................... 39 6.2.2 The effect of rolling friction on granular shear behaviour ....... 40

6.3 Evaluation of bulk granule compression simulations (Papers III and IV) ..................................................................................................... 42

6.3.1 Inclusion of a maximal plastic overlap in the truncated Hertzian contact model ........................................................................ 43 6.3.2 The accuracy of a truncated-sphere contact model with a Voronoi extension ................................................................................ 45

6.4 Correlation of degree of compression to tablet microstructure and tensile strength (Paper V) ......................................................................... 46

7. Conclusions .............................................................................................. 49

8. Future perspective .................................................................................... 50

9. Populärvetenskaplig sammanfattning: Flöde och komprimering av sammansatta partiklar – experimentell utvärdering av datorsimuleringar .... 51

9.1 Pulver och tabletter ......................................................................... 51 9.2 Datorsimuleringar ........................................................................... 52 9.3 Utvärdering av datorsimuleringar ................................................... 52 9.4 Studie av partikelpositioner i tabletter ............................................ 53

Acknowledgements ....................................................................................... 54

References ..................................................................................................... 57

Abbreviations

Kawakita parameter Heckel parameter

Effective-medium parameter Kawakita parameter

Granular bond number Degree of compression

Maximal degree of compression Time-step constant Normal damping coefficient

Tangential damping coefficient CAR κ-carrageenan

Pore diameter Median particle diameter

DEM Discrete element method Young’s modulus ∗ Effective Young’s modulus Cohesion force Gravitational force Force exerted on particle i Normal force Tangential force Force at yield

FEM Finite element method FE/DE Finite/discrete element method ∗ Reduced shear modulus

Particle hardness ℎ Particle bed height ℎ Initial particle bed height HP High porosity MCC granules

Moment of inertia of particle i Heckel parameter

Normal particle stiffness Tangential particle stiffness

LAC Lactose LP Low porosity MCC granules

Mass of particle i

MCC Microcrystalline cellulose Pressure Yield pressure

PEG Polyethylene glycol PVP Polyvinylpyrrolidone

Particle radius ∗ Effective particle radius Cut-off distance

Time Time-step

Critical time-step Torque exerted on particle i Rolling friction torque Mercury volume Velocity of particle i Normal particle velocity Tangential particle velocity

Greek letters

Angle of repose Shear rate

Maximal plastic overlap Normal particle overlap

Tangential particle overlap Particle overlap at yield

Particle solid fraction Bulk modulus Internal bulk friction coefficient Rolling friction coefficient Sliding friction coefficient

Poisson’s ratio Bulk density

Effective particle density Relative density

Normal stress and tensile strength

Maximal tensile strength Yield stress

Shear stress Angular velocity of particle i

Filling fraction of granule bed

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1. Introduction

The drug development process is an extended procedure ranging from screening for active ingredients to large-scale manufacture by the pharma-ceutical industry. Drug formulation is an integral part of the process. It be-comes essential after selection of the drug candidate and thereafter remains important during the entire development process [1]. The science of formula-tion is termed pharmaceutics or galenical pharmacy after the Greek physi-cian Galenos [2]. Pharmaceutics involves the encapsulation of a drug into a suitable vehicle that preserves the chemical and physical stability of the compound and optimises its delivery to achieve the ideal drug effect [3].

Tablets are currently the most used drug vehicle, primarily due to their ease of administration. The relatively cheap manufacturing cost additionally increases the benefits of the tablet as a dosage form [4, 5]. The complexity of tablet formulation, however, is seldom reflected upon. During manufacture, the particle and powder properties greatly influence the finished product. The optimal combination of drug, excipients, and formulation factors ena-bles manufacture of tablets with suitable tensile strength that are indisposed of capping, and lamination [6, 7]. A further complication is the intricate tab-leting process. This involves numerous stages (Figure 1), which require var-ious unit operations including e.g. mixing, milling and compression [8, 9]. Hence, to produce high-quality tablets, each of the unit operations entails optimisation for every specific formulation. Moreover, the ambient envi-ronment may contribute supplementary complexity to the tableting process [10].

To produce high-quality solid dosage forms, there is a need for deeper understanding of the unit operations involved during tableting [8, 11]. After the FDA (Food and Drug Administration) initiated the concept of PAT (Pro-cess Analytical Technology) [12] and QbD (Quality by Design) [9], focus has been directed towards improved formulations by direct incorporation of quality into the product [13, 14]. Numerical simulations are in this circum-stance an important tool for increasing the requisite process knowledge. With the aid of simulations, the effect of various parameters such as friction and cohesion can be systematically investigated without material losses. Additionally, it is possible to obtain an early understanding of the powder behaviour during handling.

To replace physical experiments with simulations, the existing models for describing particle behaviour need improvement and experimental evalua-

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tion. At present relatively few simulations are experimentally evaluated, and even fewer are performed with pharmaceutically relevant materials.

The aim of this thesis was to investigate the utility of the Discrete Ele-ment Method (DEM) as a simulation tool for describing flow and compre-ssion for granulated pharmaceutical materials, in particular those based on the common excipient microcrystalline cellulose (MCC). Simulations were evaluated experimentally where the simulation parameters were, to the ex-tent possible, matched to the experimental conditions. Moreover, the micro-structure of tablets composed of MCC granules was investigated and related to the degree of compression and tablet tensile strength.

Figure 1. Overview of some unit operations in the tableting process. The green col-orations display the focus of the thesis.

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2. Characteristics of particles and powders

2.1 Primary and secondary particles Particles may be defined as single solid units and they are commonly classi-fied as primary and secondary particles. Secondary particles are agglomer-ates composed of a number of primary particles often randomly oriented within the agglomerate [15, 16]. The agglomerates are often termed granules or pellets, depending on their shape and surface texture. In general, granules are non-spherical irregular particles, whereas pellets are characterised by a spherical shape [17]. The primary particles are often cohered through wet granulation where a liquid and a binder are added to form the granules [15]. The process can also be accomplished under dry conditions i.e., by dry gran-ulation [18]. The shape characteristics of the pellets are often obtained by extrusion followed by spheronisation of the wet granule mass [19, 20]. The experimental work in this thesis was conducted using spherical secondary particles prepared by wet granulation, hereafter referred to as granules.

2.1.1 Granule properties Porosity The random primary particle orientation in granules contributes to an intra-granular porosity, whose magnitude depends on the drying mechanism of the granules [21-23]. The drying mechanism may, in turn, be altered by various drying techniques [23, 24] or by the volatility of the granulation liquid used during the granulation process. Volatile liquids such as ethanol are known to enhance the drying rate and generate high intra-granular porosity, see e.g. [25-27]. The porosity [21, 23, 28] and the orientation [29] of the primary particles generate large variations within and between batches, and greatly influence the granule mechanics.

Mechanics Particles typically possess various mechanical properties, which largely de-pend on the material characteristics [15]. The mechanics can be thought of in terms of the particle behaviour under compressive, shear, and tensile stresses [30]. These properties are generally categorised into elastic and plastic de-formations, in addition to brittle fracture (Figure 2) [31].

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Elastic deformation is a reversible process causing non-persistent altera-tions of the particle shape and occurs in numerous pharmaceutical materials [32]. The elastic material properties are usually defined by the Young’s modulus (also termed elastic modulus ( )) [33], and the Poisson’s ratio ( ) [34]. These quantities are measures of the elastic stiffness and the lateral expansion, respectively of the material during load. The Young’s modulus is defined as the ratio between the applied normal stress and the corresponding strain; thus it does not depict the elastic volume change. To describe this property the elastic bulk modulus ( ) is preferable.

Plastic deformation is an irreversible process causing permanent altera-tions of the particle shape. It depends on the motion of the intra-granular particles and is often denoted the plastic flow. Hence, plastic properties de-pend on the ease by which the primary particles flow in the granule and thus provide an indication of the particle strength [30]. Inherent plastic material deformation is characterised by particle yield stress ( ), which is the stress required to induce plastic flow [32]. Local disorders, such as intra-granular porosity, may alter the material strength [30]. A high deformation propensity is often correlated with a high intra-granular porosity due to the large availa-ble space for plastic flow [28]. Closely related to the particle plasticity is particle hardness i.e., the resistance to particle indentation [30, 33]. Hardness is, in addition, influenced by the elastic particle properties due to the elastic particle deformation surrounding the plastic zone.

Figure 2. Schematic illustration of the various modes of mechanical behaviour often encountered during compression. is the normal force.

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Repulsive forces The contact point between two particles generally experiences a repulsive force. In addition there are repulsive forces that originate from the contact between a particle and a container wall or equivalent. These repulsive forces limit the proximity that is possible for two particles. An elastic spring of a certain stiffness is usually used to represent contact repulsion. The spring may also be combined with a dashpot to generate damping effects. During loading the spring stiffness is considered as the determinant factor of the particle deformation propensity [35].

Cohesive forces Cohesion is a measure of the attractive forces between similar surfaces. In solid particle systems the cohesion is dominated by van der Waals forces [36-38]. In addition, capillary forces and electrostatic forces may be present depending on the ambient conditions [37]. Cohesive forces are of long-range order and are generated from induced dipoles by polarisation [37, 39]. The polarisability is dependent on the material characteristics and described by the Hamaker constant [40]. The strength of the cohesion forces is a function of the distance between the particles and is typically stated to be proportional to the reciprocal of the squared inter-particle distance for the interaction between two spheres [39]. Hence, cohesive strength decreases rapidly with inter-particle distance. In dry particulate systems, the cohesive forces are most prominent between micro-sized particles due to the cohesive domi-nance over the gravitational force (Figure 3a), as defined by the cohesive granular bond number ( ) [37].

Frictional forces Frictional forces appear in response to particle motion. They cause energy dissipation resulting in prohibition of particle motion [39]. Hence, when a tangential or rotational particle motion is initiated, the inter-particle friction-al forces will greatly influence the particle behaviour. Depending on the motion, two types of frictional forces are necessary to evaluate.

Sliding friction In general, inter-particle sliding can only occur if the particle bed dilates through the application of a tangential force. The resistance against sliding is commonly divided into two components – one which is load dependent and another which is adhesion dependent. Both must be surmounted to allow particle bed dilation. The load-dependent component is dependent on the sliding friction coefficient ( , Figure 3b) between the surfaces and is thus related to the particle surface structure and morphology. The adhesion-dependent component is due to intermolecular attractions and may thus be assumed to be negligible in coarse-granular systems. It is generally accepted that the sliding friction coefficient between irregular surfaces is high due to

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the extensive dilation required to induce sliding [39]. Moreover, a pro-nounced surface roughness may increase the sliding friction coefficient be-cause particles of similar hardness presumably interlock during sliding [41-43].

Sliding friction coefficients can be further categorised into static and ki-netic/dynamic sliding friction coefficients. The former refers to the re-sistance to induce motion and the latter to the resistance to maintain motion [39, 43].

Rolling friction Rotational motions are commonly described using torque ( , Figure 3c), which is dependent on the rolling friction coefficient ( ). Like the sliding friction coefficient, the rolling friction coefficient opposes rolling motion and particle bed dilation is necessary to induce particle rolling. Rolling re-sistance is often considered to be a shape parameter as the particle shape is the determinant factor for the rolling behaviour [44]. Generally, rolling is promoted for spheres due to the small contact area. In addition, rolling fric-tion may occur as a result of contact deformation [39, 44] although this is most prominent for soft materials.

Figure 3. Schematic illustration of a) cohesion force ( ), b) tangential force ( ), and c) torque ( ). is the gravitational force, is the normal force, and and are the sliding and rolling friction coefficients, respectively.

2.2 Powders A powder is defined as a collection of particles, typically ranging in size between one micrometre and one millimetre [45]. The properties of a pow-der depend largely on the characteristics of the comprising particles. How-ever, the particles can behave differently in the bulk state and they can be affected by the ambient conditions. Powder materials are therefore very complex to understand and also to handle. During tablet manufacturing, the

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powder characteristics strongly influence the quality of the product. Two of the most essential properties of the powder are its flowability and compress-ibility. The former is important during the mixing and both characteristics affect the compression procedure. These properties are described in detail below.

2.2.1 Powder properties Flowability Definition The flowability of a powder is defined as the ease with which it flows through specified equipment [46]. A free-flowing powder is recognised by its ability to flow under the influence of the gravitational force in the absence of externally applied stresses [38]. Free-flowing powders enable uniform blends, continuous and reproducible material discharge from the hopper into the die, and the possibility of rearrangement in-die during tableting. It should be noted, however, that free-flowing powders have a higher tendency to segregate during handling [38]. Nevertheless, solid oral dosage forms of high uniformity of content and mass are usually prepared from free-flowing powders.

Determinant factors The flowability of a powder can be inferred from the particle packing, where particles in free-flowing powders generally form a close arrangement upon pouring i.e., they form a powder bed of low porosity. This behaviour is re-flected by the inter-particle forces present in the powder, where small inter-particle forces promote powder flow. Hence, particle size, shape, and surface texture strongly influence the powder flowability. The presence of moisture in the granule bed may also increase the inter-particle cohesion and thereby decrease flowability [38]. Particle size enlargement, through granulation, is commonly used to decrease the influence of the cohesive forces, and thus improve the flowability of powders [16].

Granule shear flow Granule shear flow is commonly categorised by the elastic and inertial flow regimes [47]. The elastic flow regime is characterised by force chains sup-porting the granule bed and is subcategorised into the elastic quasi-static and the elastic-inertial regimes. The elastic quasi-static regime is evident at low shear rates in combination with high-filling fraction. It is therefore common-ly encountered in regular granular shear. In this regime, formation of the force chains is proportional to shear-rate and breakage is proportional to the reciprocal shear-rate. Thus, the total force chain formation is shear-rate in-dependent. However, the lifetime of the force chain decreases with increased

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shear-rate, which thus decreases the coordination number [47, 48]. The elas-tic quasi-static regime can further be apparent in granule beds of intermedi-ate-filling fractions in presence of sliding friction. The elastic-inertial regime is shear-rate dependent because the inertial forces accelerate and decelerate the particles to the force chain. This regime is evident at both low- and high-filling fractions in combination with exceptionally high shear rates; thus it is seldom encountered in reality.

The inertial regimes – inertial non-collisional and inertial-collisional – are found in dilute granular systems. The dilute character promotes particle coll-isions, similar to a gas-like behaviour. The collisions constitute either large particle clusters as in the inertial non-collisional regime, or binary particles as in the inertial-collisional regime. In the inertial regimes, the collision freq-uency increases with shear rate. Thus, in contrast to the elastic quasi-static regime, the coordination number here increases [47, 48].

Transitions between flow regimes are enabled by changes in shear rate or filling fraction and may be followed in flow regime maps for constant vol-ume [47] or constant applied stress [49]. However, the maps appear similar to each other because shear stresses scale similarly with shear-rate for both constant volume and constant stress [50].

Compressibility Definition Compressibility is defined as the ability of a powder to reduce in volume upon stressing [7]. Stressing is often induced by simple tapping, vibration or by mechanic compression. In addition, compressibility is commonly linked to flowability through the Hausner ratio [51] and the Carr’s compressibility index [52]; a highly compressible powder flows poorly [38].

Compression stages During confined compression i.e., compression in-die, of non-fragmenting particles several compression stages are often mentioned [7, 53-56]. In gen-eral, rearrangement of the powder particles occurs initially at low pressure until a constrained state with permanent particle positions is obtained (stage one in Figure 4). At this stage the particles may also experience some elastic deformation before reaching the yield point i.e., the point where the plastic particle deformation commences. As long as free volume is available (free in terms of intra- and inter-granular pores), plastic deformation is enabled (stage two in Figure 4). As pressure increases, the free volume decreases until there is only a limited space available for further volume changes. At this stage the plastic deformation becomes negligible and only elastic com-pact deformation is possible at increasing pressures (stage three in Figure 4). The last stage of the confined compression is initiated at unloading, where an

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elastic recovery of the compact is apparent (stage four in Figure 4). The stages may occur sequentially but often occur in parallel with each other.

Figure 4. The stages during confined compression include: 1) particle rearrangement and elastic particle deformation, 2) plastic particle deformation, 3) elastic compact deformation, and 4) elastic recovery of the compact.

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3. Numerical methods for particle simulations

3.1 Numerical simulations In the past few decades, numerical simulations have increasingly received attention in various fields of science. In pharmaceutics, simulations are espe-cially suitable when a limited amount of sample material is available, or at an early stage of formulation development when information is needed. Par-ticle simulations are typically performed at three levels: the continuum, the particulate (discrete), and the combined continuum-discrete.

The finite element method (FEM) implements simulations at the continu-um level. It is typically suitable for micro-sized powders where a small vol-ume includes a large number of particles and thus reflects a macroscopic phase [57]. The FEM is in particular appropriate for compaction simulations, from which density and stress distributions may be obtained [57-59].

Simulations at the particulate level are performed with the discrete ele-ment method (DEM) [60]. DEM enables detection of inter-particle accelera-tions, forces, and positions in the powder bed. DEM simulations can obtain information that is not otherwise possible to obtain experimentally. The dis-crete character makes DEM applicable to various unit operations especially blending and flow. Due to the comprehensive calculations with DEM, simu-lations comprising a few thousands particles are generally preferable in order to save computational time.

The most thorough simulations may be performed using the combined FE/DE method, where a discrete particle is simultaneously considered as a continuum. The FE/DE method is superior for simulations of realistic parti-cle systems, but requires extensive computational time and is, hence, unreal-istic for systems corresponding to experimental conditions.

The experimentally evaluated simulations in this thesis were performed using the DEM, as described below.

3.2 The discrete element method (DEM) The DEM with the soft-particle approach [60] is most commonly used for simulations of dense granular behaviour where numerous persistent particle contacts are present [35]. For simplicity, the contacts are modelled to be a function of the particle overlap ( ), assuming independent contacts. With

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the DEM a simulation sequence (Figure 5) is repeated continuously during the entire simulation run. First, the sequence includes contact detection and calculation of the contact force using an appropriate contact model. Thereaf-ter, Newton’s second law is used to calculate the translational (linear) (Eq. 1) and the rotational (angular) motion (Eq. 2), = , Eq. 1

= , Eq. 2

where and are the force and torque exerted on particle , respectively.

, and represent the mass, velocity, and time whereas and denote the moment of inertia and angular velocity for spherical particles. By inte-gration of the equations of motion, information regarding particle accelera-tion, velocity, position and rotations are obtained. The simulation sequence is referred to as time-step, during which the particle system is considered to be static. Hence, the simulated time-step must be small enough for the as-sumption to be valid. To maintain stability of the simulation, it is necessary that the selected time-step constitute a fraction of the critical time-step [60]. The critical time-step was originally suggested to be ∆ = 2 / where m and k are the particle mass and stiffness, respectively [60]. However, other suggestions have been proposed in the literature e.g., by Tsuji et al. [61], where the critical time-step is assumed to be ∆ = 2 / . Nowadays however, it is common to calculate the time-step according to ∆ ≤/ , where Ct is a constant, see [62] and references therein.

Figure 5. Flow sheet representing the simulation sequence of a single time-step.

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3.2.1 Force-displacement contact laws In general, contact forces during the simulation are determined from the particle displacement that is expressed as the particle overlap using an ap-propriate contact model. The contact forces are commonly decomposed into normal ( ) and tangential( ) forces and, depending on the characteristics of the model, the correlation between the forces and particle overlap varies. Contact models often reported in the literature include the linear spring- dashpot (often seen in flow simulations, see e.g., [47, 48, 63]), and the non-linear Hertzian correlation (commonly used in compression simulations, see e.g., [64, 65]). The correlation of force to particle overlap for the two models is described below. Furthermore, the novel truncated-sphere contact model [66] is described.

Linear spring-dashpot In the linear spring-dashpot model [60] a linear spring is used to model the repulsive contact forces (Figure 6). The model assumes that elastic inter-particle contact forces are linearly dependent on the particle overlap accord-ing to: = −( + ), Eq. 3 = −( + ), Eq. 4

where and are the particle stiffness and overlap, respectively and the subscripts and denote the normal and tangential direction. Moreover, a dashpot is included for energy dissipation. This is described by the latter part of Eqs. 3 and 4 where and represents the damping coefficients and the velocities, respectively. In this thesis the linear spring-dashpot model was used in Paper I and II.

Figure 6. Schematic illustration of the linear spring-dashpot contact model.

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Non-linear Hertzian correlation and truncated extension In contrast to the former contact model, the Hertzian correlation assumes a non-linear relationship between the normal force and the normal particle overlap [67],

= ∗ ∗ , Eq. 5

where ∗ and ∗ are the effective Young’s modulus and particle radius, re-spectively.

During simulations of particle compression, the onset of plastic defor-mation and the following plastic deformation must be stated in the model. The truncated Hertzian model proposed by Thornton and Ning [68] suggests the initiation of plastic deformation at the normal overlap, , according to Eq. 6,

= ∗ ∗, Eq. 6

where is the yield pressure. Thereafter, the Hertzian distribution is trun-cated at yield pressure i.e., the contact pressure cannot exceed the pressure at yield. Consequently, a linear increase in force with overlap is apparent ac-cording to Eq. 7, = + ∗ − , Eq. 7

where is the normal force at yield. The truncated Hertzian model is com-monly used in the literature [65, 69] and was used in Paper III of this thesis, where it is referred to as the original contact model.

In Paper III, the tangential force originates from the Mindlin-Deresiewicz model modified by Di Renzo and Di Maio [70] as:

= ∗ ∗ , Eq. 8

where ∗ is the reduced shear modulus.

Truncated-sphere model with Voronoi extension During confined compression, at large strains, the assumption of contact independence ceases to be valid [71, 72] and the problem of contact im-

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pingement becomes apparent. A recently developed analytical model [66], hereafter referred to as the truncated-sphere model, indicates the potential for simulating small to moderate strains. The model describes the plastic contact deformation as a truncation of a spherical particle. Moreover, an assumption of particle volume preservation during compression implies that the sphere radius increments with increasing pressure. At large strains, when contact impingement is initiated, an extension of the model is necessary for calcula-tions of particle volume. The inclusion of Voronoi cells (Figure 7) provides satisfactory descriptions of the particle volume in DEM compressions [73]. Compared to the modified contact model previously described, this model is more refined as it takes into account the contact dependence and impinge-ment. This model is used in Paper IV.

Figure 7. Schematic illustration of a Voronoi cell.

Additional parameters incorporated in the contact models In order to numerically describe a solid particle system in terms of flow and compression, additional parameters should be included in the above men-tioned contact models. These parameters include inter-particle friction forces and cohesion forces.

Friction forces As mentioned in the previous section, particle sliding induces tangential forces. Hence, simulations of particle flow and compression necessitate the incorporation of a sliding friction coefficient ( ) as: ≤ , Eq. 9

to explain that the tangential force is regulated by the presence of the sliding friction.

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Sligthly more uncommon is the inclusion of a rolling friction coefficient ( ). The parameter, however, is important for the reduction of particle roll-ing. The may be expressed as described according to Zhou et al. [74], as, = − , Eq. 10

where is the rolling friction torque and is a unit vector describing the angular velocity. Note that the may be converted into a dimensionless parameter by incorporation of the particle radius ( ) as = − .

Cohesion In Paper I, cohesion forces were included in the model as a function of their granular Bond number ( ) [75]. Bond number is defined as the ratio be-tween the cohesive force ( ) and the gravitational force ( ). The cohesive force is dependent upon the normal and cohesive particle stiffness in addi-tion to the spatial extent i.e., the cut-off distance ( ).

3.2.2 Models and parameters used in the thesis Different contact models were used for the simulations in Papers I-IV (Table 1). In addition, various inter-particle forces were used and systematically altered in Papers I and II. It should be noted, the friction coefficients in Ta-ble 1 is used for particle-particle (p-p) interactions and not particle-wall (p-w) interactions. These were typically similar (Paper I) or lower (Paper II-IV) than the p-p friction coefficients. Similar p-p and p-w friction coefficients were used because of the slightly rough funnel surface in Paper I. In the oth-er Papers the wall surfaces were smooth; thus lower p-w than p-p frictions were used.

Table 1. Contact models and inter-particle parameters used in the simulations.

Paper Contact model a b c

I Linear spring-dashpot 0.4-0.8 0-10 µm 0-10 II Linear spring-dashpot 0.1-0.9 0-0.2 -

III Hertz and truncated Hertz 0.5 1 µm - IV Truncated sphere with Voronoi extension 0.2 - - a particle-particle sliding friction coefficient. b particle-particle rolling friction coefficient. c granular bond number. In Paper III, shear was simulated with two types of boundary conditions: standard, and Lees-Edwards periodic boundary conditions [76]. The standard boundary conditions were employed in two directions, x and y. Hence, parti-cles were reinserted from the front and from the side of the simulation do-main. The Lees-Edwards periodic boundary conditions enable particles to

26

also be inserted from below or above of the domain i.e., in the z direction. This type of boundary conditions also accounts for the motion of the domain. Hence, particle velocity, and position are accounted for.

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4. Aims

The overall aim of this thesis was to experimentally investigate to what ex-tent the discrete element method is a suitable numerical tool for simulations of granule flow and compression. Furthermore, the contributing papers aimed to investigate:

The influence of rolling friction and cohesion on the granule dis-

charge rate and angle of repose. The influence of rolling friction and cohesion on the experimental

and numerical correspondence for the discharge rate and angle of repose.

The effect of rolling friction on the shear flow regimes. The influence of system size and boundary conditions on the shear

behaviour. The influence of rolling friction on the experimental and numerical

shear correspondence. The capacity of the truncated Hertzian contact model to simulate

the various compression stages. The impact of a maximal plastic overlap in the truncated Hertzian

model on the elastic compact deformation. The accuracy of the truncated-sphere contact model with Voronoi

extension for simulations of the elastic compact deformation. The accuracy of bulk modulus and granule hardness as simulation

parameters during compression. The pore structure of tablets composed of high- and low-porosity

granules.

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5. Experimental methods

This section gives a general overview of the methods available and those used for the major experimental work in the thesis. For details about the used methodologies, the reader is referred to the method sections of the attached papers.

5.1 Particle characterisation 5.1.1 Size The size of an irregular particle is often determined in terms of its equivalent particle diameter. The equivalent diameter is defined as the diameter of a sphere with e.g., equal area, volume or sedimentation velocity as the irregu-larly shaped particle. In addition, the equivalent particle diameter is related to the size characterisation method, and is commonly designated in accord-ance with the analysis technique [77]. The projected particle diameter is one of the most commonly used particle diameters, and is easily assessed with microscopy techniques [77, 78]. This diameter is based on the area of a two-dimensional projection of the particle. The projection is prepared for parti-cles placed in their most stable orientation, often resulting in a slight overes-timation of the particle diameter [77].

5.1.2 External volume-specific surface area The external surface area may be considered as the area available for bond formation during tableting [79], i.e., the area of the open pores is excluded. The external surface area may be determined with permeametry in a transi-ent mode with the Blaine apparatus (for primary particles) [80] or the steady-state configuration (for granules) [81]. Both setups measure the resistance to air-flow through the particle bed. The pressure difference is used for calcula-tions of the volume specific surface area for granules with the Kozeny-Carman equation [82], and for fine particle materials with the Kozeny-Carman equation corrected for slip flow [83].

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5.1.3 Density and intra-granular porosity The density of a particle is commonly categorised into the apparent particle density and the effective particle density. The apparent particle density is a good estimate of the true density of powder materials and is traditionally determined using helium pycnometry [84]. The displaced helium volume, during measurement, is used for assessment of the particle volume. The ap-parent particle density is thereafter calculated from the mass and volume of the solid material [85]. Helium pycnometry is preferentially used for meas-urements of primary particles due to the inaccessible pore system of second-ary particles. For granules comprising two or more materials, the apparent particle density is preferably calculated from the proportions and apparent particle densities of the composites [86].

The effective particle density is the particle density including both open and closed pores. It is assessed with mercury pycnometry where mercury encloses the granule material that enables calculation of the granule volume [87].

The effective and apparent densities may be used in conjunction for cal-culations of the intra-granular porosity [88]. Additionally, the pore size and pore volume distribution can be assessed through mercury porosimetry [89, 90]. This technique is based on intrusion of mercury into open pores down to sizes of 3 nm [91]. The pore size is calculated from the relationship of pore diameter to applied pressure as stated in the Washburn equation, assuming cylindrical pores [92].

5.1.4 Mechanical characteristics Measurements of mechanical characteristics of particles are often conducted using the force-displacement relationship obtained during single particle compressions [25, 69, 93]. For pharmaceutical materials, which often display an elastic-perfectly plastic behaviour, an initial non-linear elastic region fol-lowed by a plastic linear region is evident. By fitting of the elastic region to the Hertzian correlation [67] and the plastic region to the elastic-perfectly plastic correlation [68], the effective Young’s modulus ( ∗)and the yield pressure, respectively, may be estimated [69]. It should be emphasised how-ever that the yield pressure is not equivalent to the yield stress, which is an inherent material property. Moreover, the yield stress is related to particle hardness ( ) as ≈ 3 [33]. The hardness is typically larger than the yield stress due to the surrounding elastic constraint as reflected by the con-straint factor [30] (usually three for pharmaceutical materials [33]). The hardness parameter can be estimated from the plastic region of the force-displacement curve using the relationship proposed by Abbott and Firestone and described by Jackson and Green [94] and Yap et al., [93] or from inden-tation tests [33]. The elastic Poisson’s ratio parameter is often collected from

30

the literature and a value of 0.3 [34] is commonly used for pharmaceutical materials [95, 96].

For compacts, the elastic and plastic parameters are determined by other methodologies. Three-point bending tests are commonly used for determina-tion of Young’s modulus [33, 97] and compaction studies are often used for analysis of particle yield stress with e.g., the Heckel correlation [33, 98].

5.2 Characterisation of powders 5.2.1 Flowability There are numerous techniques available for characterisation of powder flowability [99]. According to the European Pharmacopoeia, flowability is most commonly analysed through measurements of angle of repose, com-pressibility index/Hausner ratio, flow rate through an orifice, and shear [100]. The techniques are often categorised as direct or indirect methods depending on the applicability of the results. In addition, the flow is com-monly reflected by the methodology, requiring a thorough selection and description of the methodology to extract usable data.

Angle of repose The angle of repose is defined as the powder inclination angle ( ) that in-duces powder flow (Figure 8a). Flowability characteristics are usually de-fined by the magnitude of the angle, where large angles are indicative of poorly flowing powders [52]. Several setups for measurements of the angle of repose are available including the fixed funnel with free standing plate (Figure 8a) and the revolving cylinder [101, 102]. The available methodolo-gies are suitable for various powders, e.g., the fixed funnel is suitable for frictional powders whereas the revolving cylinder is suitable for cohesive powders [102]. Hence, the various setups provide non-equivalent angle of reposes and thus require careful data interpretation.

Hopper discharge rate The rate at which a powder is discharged from a hopper provides a simple, direct method for determination of flowability [103]. Concerning flow from hoppers unequipped with feeding devices, i.e., flow under gravity, the parti-cle properties size and shape, in addition to hopper width, inclination angle, and orifice diameter must be considered [38]. The hopper discharge rate may be measured simultaneously during the angle of repose measurement using the setup illustrated in Figure 8a.

For coarse non-cohesive particles the discharge from flat-bottom cylindri-cal hoppers is often described with the Beverloo equation [104]. In this equa-tion the hopper discharge rate is related to the effective orifice diameter ex-

31

cluding dead space to the power of 5/2. Various hopper geometries may be considered if a correction factor is included [105].

Shear Flowability testing by shearing provides comprehensive knowledge of the powder behaviour. Shearing may be conducted using a number of various shear testers such as the traditional translational Jenike shear tester and rota-tional ring shear testers [38, 99]. In Paper II, shearing was conducted in a rotational manner using a powder rheometer, with the setup illustrated in Figure 8b. The different shear testers operate on the same premises i.e., first the powder is prepared by overconsolidation followed by pre-shear to reach a steady-state. Secondly, the point of powder failure at various applied loads (lower than pre-shear) is measured [38, 99, 106]. The slope of the yield lo-cus, i.e., the shear stress vs. normal stress curve, is regarded as the internal bulk friction coefficient and provides knowledge about the frictional forces present in the powder [38, 106]. For cohesive powders, the intercept of the slope provides an estimation of the cohesiveness of the powder [106]. Fur-thermore, applying Mohr’s stress circles to the yield locus gives an estimate of the stress planes present in the powder bed [38, 106]. Tangent to the Mohr circle and intersecting the origin, the effective yield locus provides infor-mation about the powder in a non-cohesive state [106]. The effective yield locus is used especially in silo designs [38].

Figure 8. Schematic illustration of a) angle of repose ( ), and b) rotational shear for determination of granule flowability. ℎ is the particle bed height.

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5.2.2 Mathematical relations for bulk compression As mentioned above, compression may be induced through various stressing conditions. Bulk compression through simple tapping can be analysed by relating the bulk and tap densities through the Hausner ratio [51] or Carr’s compressibility index [52]. In this section, the focus will be towards analysis of bulk compressions in-die i.e., compression induced by a mechanically applied stress. Bulk compressions are commonly analysed by various empir-ically derived equations that relate the particle bed porosity to the applied pressure [98, 107]. For pharmaceutical materials, the Heckel [108] and Kaw-akita [109] relationships are traditionally used [110-112]. Recently derived compression equations include the analytical effective-medium relation, which is based on single particle properties [113]. This equation displays potential in describing the plastic particle deformation during compression and the parameter has been found analogous to the Heckel 1/ pa-rameter [110]. The effective-medium equation will not be further reflected upon in the context of this thesis.

Heckel correlation The Heckel equation was originally proposed for metal powders [108]. The equation describes the decrease in powder bed porosity (1 − ) as a func-tion of applied pressure ( ), ln = + , (Eq. 11)

where is a constant, often referred to as the Heckel parameter. Its recipro-cal is termed the yield pressure of the powder material and is obtained from the intercept of the linear Heckel plot and is often considered to repre-sent particle rearrangement.

Kawakita correlation The Kawakita model was developed for soft and porous powders, and is hence suitable for pharmaceutical materials. The Kawakita equation de-scribes the volume-pressure relationship according to [109]:

= = , (Eq.12)

or when expressed in linear form,

33

= + , (Eq.13)

where is the degree of compression (engineering strain), and ℎ and ℎ are the initial and final powder bed heights, respectively. The constants, and , commonly referred to as the Kawakita parameters, describe the material properties. represents the maximal degree of compression ( ) and is a measure of the intitial porosity of the powder bed. The pressure required to reach /2 is usually referred to as the reciprocal of .

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6. Results and discussion

6.1 Granule characteristics This section will give a brief overview of the characteristics of the model systems used in the experimental work. The work was conducted with granulated powders either prepared commercially or in-house.

To the extent that was possible, the evaluated simulations were matched to the experiments, especially with regard to size (assuming mono-disperse particle size distributions), effective granule density, and mechanical proper-ties. 6.1.1 Shape, size, density and porosity Due to their spherical shape, granules constitute an excellent experimental system for comparison to simulations. Simulations of spheres are frequently performed [35] as they permit the use of simple contact models that typically reduce the computational complexity. However, efforts in simulating non-spherical particles have been made recently [114, 115]. A simple way to alter spherical shape is to include a rolling friction parameter to an otherwise idealised spherical system to prevent the rolling behaviour [116].

The commercial granules (Figure 9a) were based on MCC and are hence-forth referred to by their particle size (Table 2). The granules were nearly perfectly spherical with a shape coefficient of ~6.8 and had comparable in-tra-granular porosities. Although a slight trend in increasing bulk density with increased particle size was evident (Table 2), the particles packed close-ly upon pouring with a minor increase in density after tapping. The polymer coatings in Paper I yielded slightly irregularly shaped particles with smooth surfaces (Figure 9b) compared to the uncoated granules in Figure 9a. The commercial granules were also used in Papers II and III.

Table 2. Characteristics of the commercial granules in Papers I-III.

Granule d50 (µm)a ρeff (g/cm3)b ρbulk (g/cm3)d Porosity (%)

C100 170.1 1.45 (0.01) 0.78 (0.01) 7.9 (0.37) C200 317.2 1.46 (0.03) 0.82 (0.01) 7.3 (1.85)

C350 442.8 1.45 (0.00) 0.84 (0.02) 7.8 (0.29) C500 641.3 1.44 (0.00) 0.89 (0.00) 8.5 (0.05) Standard deviations are given in parentheses. a Median particle diameter. b Effective granule density. c Poured bulk density.

35

Figure 9. Micrographs of granules used in the thesis. LP and HP are the low and high porosity granules, respectively.

The in-house granules were based on MCC and κ-carrageenan (CAR). Addi-tion of polyethylene glycol (PEG, a softening agent [117]), lactose (LAC, a brittle-ductile material [118]) and ethanol (a granulation liquid) extended the property range of the granules (Table 3). The granules were classified into three groups on the basis of their intra-granular porosity – low (~10 %, Fig-ure 9c), intermediate (~18-22 %, Figure 9e and f), and high (~32 %, Figure 9d). In general, the granules were of similar size and provided similar pack-ing properties (Table 3). It should be noted that some of the in-house gran-ules were slightly elongated, with shape coefficients up to ~7.8 (for details see Paper IV).

Table 3. Characteristics of the in-house granules in Papers IV-V.

Granule d50 (µm)c ρeff (g/cm3)d ρbulk (g/cm3)e Porosity (%)

MCC 938.0 1.41 (0.00) 0.85 (0.01) 10.5 (0.24)

MCC 2.5% PEG 917.4 1.38 (0.01) 0.81 (0.00) 11.7 (0.37)

MCC 5% PEG 980.5 1.37 (0.00) 0.82 (0.00) 11.8 (0.16)

MCC LAC 1043.4 1.27 (0.00) 0.74 (0.01) 17.9 (0.18)

CAR LAC 1023.0 1.29 (0.01) 0.77 (0.01) 17.9 (0.34)

CAR LAC 5% PEG 940.7 1.21 (0.01) 0.73 (0.01) 22.1 (0.47)

LPa ** 1.42 (0.01) 0.80 (0.01) 10.5 (0.62)

HPb ** 1.08 (0.02) 0.55 (0.01) 31.8 (1.32)

Standard deviations are given in parentheses. **Sieve size: 800-900 µm. a Low-porosity granules. b High-porosity granules. c Median particle diameter. d Effective granule density. e Poured bulk density.

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6.1.2 Granule surface sliding friction coefficients In Paper I, sliding friction coefficients were estimated for uncoated, polymer coated, and lubricated granules. The estimates were based on sliding be-tween granules and both a smooth (MCC tablet) and a rough (paper) surface. This type of sliding can also be used to estimate the inter-particle sliding friction due to a small contact area, similar as the point contact between two particles [119]. Sliding friction coefficients ranging between 0.2 and 0.9 were obtained; the lowest friction was between the granule-tablet surfaces and the highest between the granule-paper surfaces. The validity of the setup is confirmed by sliding between glass and steel beads. Previously, sliding friction coefficients in the lower range or somewhat below is found for glass, and steel beads [119]. Due to the lower deformation propensity of these, the sliding friction of MCC was considered valid. In the simulations, the select-ed sliding friction coefficients were in the same range as the experimentally determined coefficients. In Paper II however, the range was somewhat ex-tended with a lower sliding friction coefficient.

6.1.3 Mechanical properties Both the plastic and the elastic properties were assessed from the force-displacement relationship for single granules. The force-displacement curve generally displayed small, non-linear regions at low force, followed by ex-tended linear regions at increasing force until particle breakage (Figure 10).

Figure 10. Typical examples of force-displacement curves for single granules.

The plastic properties were evaluated in terms of yield pressure and stiff-ness-based hardness. For the commercial granules, the yield pressure ( ) decreased (p<0.05) with increasing particle size (Table 4) i.e., the defor-mation resistance was more prominent for small granules. The in-house granules were divided into two mechanically different groups depending on the type of additives: ductile and ductile-brittle. The ductile group constitut-

37

ed the MCC and MCC PEG containing granules, whereas the MCC LAC, CAR LAC, and CAR LAC PEG granules were classified as ductile-brittle. A general trend of decreasing particle hardness with inclusion of a softening agent or a brittle material was as expected apparent for the granules (Table 4). The calculated yield stresses (obtained through the relation between the hardness and yield stress, = 3 [33]) ranged from 15-20 MPa. Hence, the plastic flow of the particles was initiated relatively early during the bulk compression process. Moreover, estimations of particle plasticity can be influenced by the instrumental setup and loading condition. The unconfined plastic properties are presumably lower than plastic properties determined in a confined manner [30].

Table 4. Plastic characteristics of the granules.

Granule Py (MPa)a H (MPa)b

C200 214.01 (36.38) -

C350 199.65 (26.80) -

C500 170.40 (18.31) -

MCC - 63.1 (6.51)

MCC 2.5% PEG - 61.8 (6.60)

MCC 5% PEG - 52.1 (7.76)

MCC LAC - 44.7 (12.15)

CAR LAC - 55.1 (7.11)

CAR LAC 5% PEG - 50.1 (6.33)

Standard deviations are given in parenthesis. a Yield pressure. b Stiffness-based hardness.

The elastic properties were characterised with measures of the effective Young’s modulus and the bulk modulus. The commercial granules displayed similar elastic resistance as indicated by the ∗ (Table 5). Similar bulk mod-uli were also evident for the in-house granules (Table 5). Both elastic param-eters, however, displayed large standard deviations and the values should therefore be regarded as rough estimations rather than absolute. Comparison of the two elastic parameters clearly displays that the initiation of elastic deformation is reached earlier in the volume mode (bulk modulus) than the lateral one (Young’s modulus). It should be noted that the estimates of ∗ and were obtained for porous particles. Hence, the values were lower than would have been expected for non-porous particles. For non-porous MCC particles, values of Young’s modulus of 7-10 GPa have been reported [33]. Ultimately, this corresponds to bulk moduli between 5.8 to 8.3 GPa i.e., up to ten times greater than for the porous particles.

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Table 5. Elastic properties of the granules.

Granule ∗(GPa)a κ (MPa)b

C200 2.31 (0.33) - C350 2.56 (0.49) - C500 2.45 (0.31) - MCC - 843.7 (92.0) MCC 2.5% PEG - 817.2 (86.4) MCC 5% PEG - 699.5 (115.2) MCC LAC - 664.0 (137.6) CAR LAC - 769.2 (97.4) CAR LAC 5% PEG - 698.5 (92.9) Standard deviations are given in parentheses. a Effective Young’s modulus. b Bulk modulus.

6.2 Experimental evaluations of granule flow simulations (Papers I and II)

The simulations in Paper I clearly displayed that non-cohesive and cohesive granules have fundamentally different flow behaviours (Figure 11). For non-cohesive granules the flow behaviour is presumably influenced by a rota-tional particle motion that generates a continuous flow of discrete particles. This was confirmed by the experiments. For cohesive granules, flow of clus-ters was instead visible due to the attractive inter-particle forces that generate large particle assemblies [37]. In this thesis, Paper I investigated simulations of both non-cohesive and cohesive, whereas only non-cohesive granules were investigated in Paper II.

Figure 11. Simulations of non-cohesive and cohesive granule discharge.

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6.2.1 The effect of rolling friction and cohesion on the angle of repose and discharge rate

Influence of sliding and rolling friction The angle of repose and discharge rate of uncoated, polymer-coated and lubricated granules in Paper I were found to depend especially on granule shape and surface texture. The shape was altered by polymer coatings con-taining various amounts of polyethylene glycol (PEG) and polyvinylpyrroli-done (PVP). PEG/PVP are known to increase the tackiness of surfaces [120] and were hence expected to alter particle cohesiveness. However, the poly-mer coatings influenced the friction coefficients rather than particle cohe-siveness. Moreover, no clear concentration dependency on the flow behav-iour was evident. Surprisingly, granules coated with PEG/PVP 90/10 formed more stable heaps and were discharged slower than granules coated with PEG/PVP 50/50, for which the coating had only a minor influence on parti-cle shape. Lubrication prohibited heap formation and increased the discharge rate, thereby promoting granule flow. It should be noted, the ranking of the granule-paper sliding friction coefficients were satisfactorily reflected by the angles of repose and discharge rates. In addition, a correlation between the experimental discharge rates and those calculated with the Beverloo equation confirmed the non-cohesive nature of the granules studied [121].

The inclusion of rolling friction in the numerical model altered both the angle of repose and discharge rate (Figure 12). At low sliding friction coef-ficient ( = 0.4), a rolling friction threshold was evident in the generation of stable heaps. At intermediate ( = 0.6) and high ( = 0.8) sliding fric-tion coefficients, the angle of repose increased in a virtually linear manner with the rolling friction coefficient. For the discharge rate, a linear decrease was observed with increased rolling friction, independent on the magnitude of the sliding friction coefficient.

Figure 12. The effect of rolling friction on a) discharge rate, and b) angle of repose at three sliding friction coefficients ( ) for non-cohesive granules.

40

Previously, the potential of DEM simulations of angle of repose [119, 122] and discharge rate [121] for glass and steel materials has been demonstrated. Here, the quantitative experimental and numerical correspondence (Figure 13a) displays that DEM can accurately simulate the angle of repose and dis-charge rate for non-cohesive pharmaceutical materials. It should be noted, that the best correspondence was for the intermediate- and high-sliding fric-tion coefficients.

Influence of cohesion As inferred from the simulations, increased cohesion forces, at a cut-off dis-tance of = 1 µm, influenced the flow behaviour (data not shown). The discharge rate decreased and the angle of repose increased i.e., similar as for the rolling friction coefficient. Moreover, increasing the sliding friction coef-ficient increased the resistance to flow.

In contrast to the non-cohesive systems, the simulations here overestimat-ed the angle of repose (Figure 13b). Thus, the cohesion generated more sta-ble heaps than what were generated experimentally, despite the tacky poly-mer coatings. These results suggest that for the granular systems used in Paper I, the inclusion of cohesion as a simulation parameter was not suitable.

Figure 13. Comparison of experimental and simulated angles of repose and dis-charge rates at varying sliding friction coefficients (µs) for a) non-cohesive granules, and b) cohesive granules.

6.2.2 The effect of rolling friction on granular shear behaviour The experimentally sheared granules had similar shear characteristics. How-ever, an unexpected size dependence was evident where the resistance to shear appeared to increase with particle size (Figure 14a). This is presuma-bly explained by irregular shear planes caused by the large particles, result-ing in particle interlocking [41].

41

Figure 14. Average yield loci obtained from a) experiments and b) simulations. Notice that the simulations are scaled with respect to particle size (d) and stiffness (k) and are performed at two shear rates, = 0.01 ms-1 (open symbols) and = 0.1 ms-1 (closed symbols). is the shear stress, is the normal stress, and is the roll-ing friction coefficient.

The simulated yield loci clearly displayed both a rolling friction and a shear rate dependence. The shear resistance increased similarly in presence of rolling friction or at increased shear rate. In addition, the effect was more pronounced in presence of rolling friction in combination with increased shear rate (Figure 14b). The influence of the two parameters was especially evident at low sliding friction (compare Figure 15a and b). At low shear rate ( = 0.01 ms-1) small effects of rolling friction on the internal bulk friction ( ) were evident. At high shear rate ( = 0.1 ms-1) large effects were ob-served at low sliding friction. The rolling friction appeared to cause a transi-tion from the inertial non-collisional flow regime to the elastic quasi-static one already at = 0.3 (Figure 15b). This transition is explained by the rolling friction coefficient combined with high shear rate. These parameters enhanced the particle overlap and thereby created stronger and more persis-tent inter-particle contacts that presumably facilitated force-chain formation. In a similar manner, the elastic quasi-static range is extended in presence of sliding friction for elliptic particles [114]. These may be considered compa-rable to spheres in presence of rolling friction [116].

Similar shear stresses were obtained from simulations with standard boundary conditions, and Lees-Edwards periodic boundary conditions (data not shown). However, to form force chains of similar length it was necessary to take the system size into consideration. The simulations with standard boundaries required larger systems (8000 particles) than the simulations with periodic boundaries (2000 particles).

The experimental and simulated shear stresses both increased in a nearly linear manner with normal stresses (Figure 14). The internal bulk friction coefficients deviated, however, where the experimental values were consid-

42

Figure 15. The influence of rolling friction coefficients on the flow regime transition at two different shear rates: a) = 0.01 ms-1, and b) = 0.1 ms-1.

erably larger than the simulated ones. For the C350 granules, an internal friction coefficient (derived from the average yield locus) of 0.53 was ob-tained. For the simulated granules, internal friction coefficients were in the range 0.25-0.37. The highest internal friction coefficient was apparent for granules sheared at the high shear rate, and in presence of high inter-particle sliding ( = 0.9) and rolling ( = 0.1) friction. Despite the inclusion of a rolling friction coefficient, the particle shape is presumably the determinant factor for the deviation between the experimental and numerical values. Hence, the sphere assumption is not valid and inclusion of accurate particle shape to the model is necessary to improve the correspondence between simulated and experimental values. However, the simulated internal bulk friction coefficients clearly displayed that sliding friction, rolling friction, and shear rate were important for the correspondence to experiments. More-over, rolling friction, and shear rate promoted the elastic quasi-static regime, which (as mentioned above) occurs in real granular flows.

6.3 Evaluation of bulk granule compression simulations (Papers III and IV)

As stated earlier, several stages are apparent during compression, which renders bulk compression simulation a challenging process. This is due to the high relative density ( > 0.8) at high applied load, where the assump-tion of contact independency becomes invalid [71, 72, 123]. In simulations, it is therefore common to neglect the last stage of compression i.e., the elas-tic compact deformation. Thus, after yield the plastic deformation is as-sumed to continue indefinitely. In order to perform realistic simulations comparable to experiments, this stage is nevertheless necessary to include. In

43

this thesis, experimental evaluations were performed for simulations using two different approaches for inclusion of the elastic compact deformation.

6.3.1 Inclusion of a maximal plastic overlap in the truncated Hertzian contact model

The simulations were initially conducted with the classical Hertz correlation [67], and the subsequent plastic deformation was simulated with the truncat-ed Hertzian analysis (original contact model) [68]. Subsequently, the simula-tions were either terminated with particle unloading or extended with the modified contact model prior to unloading. In the modified contact model, the elastic deformation was assumed to commence at a maximal plastic over-lap after which the plastic deformation henceforth was ignored. The maximal plastic overlap ( ) between a spherical particle and a confining surface was calculated as:

1 − = , (Eq. 14)

where is the particle radius, is the solid fraction of the particle, and is the filling fraction of the granule bed. Typically, simple cubic-lattice ( ≈ 0.52) systems were simulated. Note that, contact dependence was not considered in the model.

Compression simulations with the modified contact model satisfactorily corresponded to experimental compressions for C200 and C350 granules (Figure 16a and b). However, there was an underestimation at the start and an overestimation at the end of the asymptotic region. The latter deviation was confirmed by the Kawakita parameter (data not shown). The model overestimated, however, the degree of compression considerably for the C500 granules (Figure 16c). Moreover, there was a slightly increased initial-compression propensity for these granules, presumably due to the low yield pressure (Table 4). The overestimation may be further explained by the de-creased coordination number as evident for the C500. Hence, a larger pro-portion of the particles in-die is located at the edges where the particles are less confined.

The different compression stages are clearly depicted in the experimental curve in Figure 17 (solid line). A comparison with the original contact mod-el (dashed line in Figure 17) revealed accurate simulations of the rearrange-ment and the subsequent plastic deformation of the granules. Furthermore, the elastic recovery was also satisfactorily reflected. In addition, inclusion of the modified contact model (dotted line in Figure 17) managed to incorpo-rate the elastic deformation of the compact. The elastic deformation was initiated at a granule bed height of approximately four millimeters i.e., con-

44

Figure 16. Experimental and numerical degree of compression (C) as a function of pressure for: a) C200, b) C350, and c) C500 granules.

sistent with the experiments. The elastic response, however, was greater and more rapid in the experimental system.

It should be noted that the loading stage in the simulations was terminated once a bed height corresponding to the experiments was reached, thus ex-plaining the low applied pressures.

Figure 17. The compression process reflected by the pressure as a function of the granule bed height for experimental and simulated C350 granules.

The modified model displayed a relatively simple and straightforward ap-proach for inclusion of the elastic compact deformation during loading. Sev-eral changes could be incorporated to enhance the experimental correspond-ence. It would be reasonable to include an improved description of the parti-cle volume changes during compression and to include the contact depend-ence during high pressure compression.

45

6.3.2 The accuracy of a truncated-sphere contact model with a Voronoi extension

Granules of ductile and ductile-brittle character were simulated using the truncated-sphere contact model [66] at low pressures. At high pressures the Voronoi extension [73] was used to describe the contact area. The plastic stiffness-based hardness (Table 4) and elastic bulk modulus (Table 5) were used as simulation parameters.

For the ductile granules a satisfactory qualitative correspondence was ev-ident for the experiments and simulations (Figure 18). The quantitative dif-ference seemed to be due to a higher compression propensity of the simulat-ed granules. It appears that the simulated granules rearranged themselves to a greater extent than the experimental granules, thus explaining the higher compression propensity. Presumably, the extensive particle rearrangement depends on the simulated spherical shape and the slightly low sliding friction coefficient ( = 0.2) included in the model. However, the discrepancy bet-ween the experimental and simulated curves was somewhat less for the MCC PEG granules (Figure 18b and c) than for the MCC granules (Figure 18a).

Figure 18. Pressure as a function of granule bed height for experimental and simu-lated granule compressions: a) MCC, b) MCC 2.5% PEG, and c) MCC 5% PEG.

For the ductile-brittle granules the shape of the experimental and simulated curves differed extensively (Figure 19). In general, the experiments dis-played a more rapid decrease in granule bed height than did the simulations. This is presumably due to some particle fragmentation causing a pronounced particle rearrangement and thereby volume reduction; this fragmentation was not included in the numerical model. Moreover, the model did not account for the intra-granular porosity (and hence densification during compression) of the experimental granules. Hence, this may explain further the experi-mental and numerical deviation for both the ductile and the ductile-brittle granules.

The truncated-sphere contact model with the Voronoi extension satisfac-torily described the compression process of ductile particles. To increase the

46

Figure 19. Pressure as a function of granule bed height for experimental and simu-lated granule compressions: a) MCC LAC, b) CAR LAC, and c) CAR LAC 5% PEG.

quantitative correspondence with the experimental data it is essential to in-clude a higher sliding friction coefficient in addition to a rolling friction coe-fficient in the model. Moreover, refinement of the model to enable simula-tions of fragmenting materials is necessary.

6.4 Correlation of degree of compression to tablet microstructure and tensile strength (Paper V)

Due to the preservation of granule structure during compression [28], tablets composed of granules display often a bimodal pore size distribution as con-firmed in Figure 20. The bimodal character of the pore system originates from the distribution of air within or between granules i.e., the pores can be intra-granular or inter-granular (commonly referred to as voids). However, the relative distribution of the pores was dependent on the properties of the original granules. For the tablets constituting high-porosity (HP) granules, the air was mainly located intra-granularly. For the tablets compressed from low-porosity (LP) granules, the air was evenly distributed intra-granularly and in voids (Figure 20). In addition, as also stated by Johansson et al. [54], the HP granules had a higher tendency to reduce in porosity upon compres-sion than the LP granules. Furthermore, the pore size of the HP tablets de-creased to a high extent during compression whereas only a slight decrease was apparent for the LP tablets (Figure 20). Thus, the relative granule posi-tions were suggested to be related to the void diameter, which hence can be used as a descriptor of the tablet microstructure.

Porosity is related to the degree of compression and tablet tensile strength [28, 54], both of which appear to increase with the original granule porosity i.e., the plastic deformation propensity. As the evolution in tablet microstruc-ture of the HP tablets was significantly affected, it suggests that the micro-structure is controlled by the granule plasticity. A nearly linear relationship between the void mode diameter and the degree of compression indicated

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Figure 20. Pore size distribution of tablets composed of a) high porosity (HP), and b) low porosity (LP) granules. represents the volume mercury intruded in mL/g sample and represents the pore diameter in µm.

that the degree of compression is the determinant factor for the microstruc-ture (Figure 21a).

Regarding the tablet tensile strength, HP tablets displayed higher tensile strength than the LP tablets despite a similar total tablet porosity (Figure 21b). Thus, the total tablet porosity was not a suitable indicator of tablet tensile strength as the original granule porosity varied. However, the tensile strength can also be considered as an inter-particle bond network. In that case, a percolation theory (which states the minimum number of bonds es-sential for formation of coherent tablets) can be applied. A linear relation-ship between the bond probability (scaled tensile strength) and the degree of compression was obtained with a critical threshold value of 0.33 (Figure 21c). Hence, formation of coherent tablets is only possible above this critical threshold.

Figure 21. Influence of: a) degree of compression on the void mode diameter, b) tablet porosity on the tablet tensile strength, and c) degree of compression on bond probability (( / ) / ) for high (HP) and low (LP) porosity tablets.

In summary, the tablet microstructure was successfully described by the void diameter, which subsequently was controlled by the degree of compression.

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In addition, a critical degree of compression required for formation of coher-ent tables was identified.

49

7. Conclusions

This thesis investigated the potential of using DEM for simulations of flow and compression of granulated pharmaceutical powders. Rolling friction and cohesion were both found to prohibit the granule flow, as inferred from the angle of repose and discharge rate. However, the friction-containing systems proved a quantitative experimental correspondence, whereas the simulations overestimated the flow for the cohesive systems. Rolling friction was demonstrated to be an essential parameter for stabilising granule shear, and thereby promoting shear in the elastic quasi-static flow regime. Although rolling friction improved the experimental correspondence, a shape parame-ter is required to achieve a quantitative agreement. Furthermore, the simulat-ed shear appeared independent of the boundary conditions used, provided that the system size was taken into account.

These studies demonstrate two promising models for simulating the chal-lenging compression process. The first approach of including a maximal plastic overlap to the truncated Hertzian contact model satisfactorily incor-porated the elastic compact deformation stage, although the magnitude was not completely comparable to experiments. The second approach was the truncated-sphere model with a Voronoi extension, which is a refined model considering the contact dependence and impingement at high relative densi-ty. This model was accurate for ductile materials, whereas inclusion of frag-mentation in the model would be necessary for ductile-brittle materials.

Finally, the void diameter of tablets was found to be a suitable descriptor of tablet microstructure. The void diameter was controlled by the degree of compression, which subsequently controlled the bond probability i.e., the tablet tensile strength.

To summarise, this thesis has demonstrated the suitability of DEM for simulating granule flow and compression. Moreover, it describes parameters found to be essential for accurate descriptions of the unit operations. Addi-tionally, it has contributed to an increased understanding of the correlation between the degree of compression and tensile strength.

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8. Future perspective

Advances in the numerical field of pharmaceutical technology have been evident during several years. This thesis has contributed with knowledge of the effect of rolling friction on the flow behaviour and displayed promising contact models for granule compression. However, lots of unanswered ques-tions still remain.

The importance of rolling friction on the flow behaviour requires further attention. To some extent, rolling friction may account for a slight spherical deviation but, as inferred from the shear, it incompletely reflects non-spherical particles. Further simulations on the flow of non-spherical particles are required for adequate investigations of real powder systems. The effect of rolling friction should also be studied for non-spherical particles which, despite their non-spherical shape, can still induce a rolling motion.

The truncated-sphere model with a Voronoi extension appears highly promising for further studies on the inclusion of elastic deformation due to the consideration of contact dependence and impingement during compres-sion. As inferred from the results, the experimental and numerical deviation for ductile materials appeared to depend on an extensive particle rearrange-ment for the simulated granules. The inclusion of a rolling friction coeffi-cient might hinder the flow and decrease the rearrangement propensity and thus increase the experimental and numerical correspondence. Inclusion of a critical stress intensity factor may incorporate brittle characteristics in the model and thus enable simulations of fragmenting materials.

Finally, one of the most crucial things in simulations is to select appropri-ate parameters. In order to perform unbiased comparisons to experiments, the simulation parameters must accurately reflect the studied systems. De-velopment of sensitive equipment capable of analysing single particle prop-erties, including e.g., inter-particle friction and damping coefficients, and elastic properties of non-porous solid materials, is required. Moreover, there is a necessity to widen the applicability of DEM to micro-sized particles in order to predict behaviour of various powder systems, and not solely gran-ules. This requires, however, extensive computational capacity.

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9. Populärvetenskaplig sammanfattning: Flöde och komprimering av sammansatta partiklar – experimentell utvärdering av datorsimuleringar

9.1 Pulver och tabletter Formulering av läkemedel benämns i vetenskapliga samband som galenisk farmaci och utgör en mycket viktig del i läkemedelsutvecklingen. Bered-ningsformen ska garantera läkemedlets hållbarhet och frisättning för att ge en säker och önskvärd effekt i kroppen.

Tabletter är idag den vanligaste formen av ett läkemedel och de flesta av oss har med största säkerhet någon gång svalt en tablett. Få har däremot re-flekterat över tablettens komplexitet. Tabletter är populära då de både är enkla att inta och billiga att tillverka. Tabletter tillverkas av läkemedelssub-stans och hjälpämnen, som huvudsakligen är i pulverform.

Ett pulver är en ansamling av små separata partiklar. Dessa kan i sin tur sättas samman till större partiklar, även kallade granulat. Under tillverkning-en av tabletter genomgår pulvret vanligen flera olika processer så som blandning, malning och pressning. Resultatet av processerna t.ex. bland-ningskvalitet och tabletthållfasthet återspeglas av pulvrets beteende så som rinnförmåga (flöde) och benägenheten att minska i volym (komprimerbar-het). Flödet och komprimerbarheten påverkas i sin tur av de enskilda partik-larnas egenskaper så som storlek, form och ytstruktur. Partikelegenskaperna styr bl.a. motståndet (friktionen) mot glidning och rullning mellan partiklar-na och är en mycket viktig faktor under pulverflöden.

Trots mångårig verksamhet och erfarenhet med tablettillverkning finns fortfarande en begränsad processförståelse vilket orsakar skiftningar i pro-duktkvalitet. För att öka kvaliteten och undvika kassering av stora mängder tabletter försöker man numera att ”bygga in” kvalitet i produkten under till-verkning. Detta kräver dock en djup förståelse för processerna och faktorer som påverkar dessa. Ett viktigt verktyg i sammanhanget är datorsimulering-ar.

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9.2 Datorsimuleringar Med hjälp av datorn och olika modeller, som beskriver hur partiklar beter sig i förhållande till varandra, kan olika pulverbeteenden simuleras. Simulering-arna möjliggör en noggrann undersökning av olika faktorer (motstånd, stor-lek, deformationsegenskaper, m.fl.), som kan ha inverkan på pulverbeteen-det. För att i framtiden kunna ersätta experiment med datorsimuleringar måste modellerna utvärderas experimentellt för att kontrollera precisionen av simuleringen. Den övergripande målsättningen med avhandlingen har varit att experimentellt utvärdera simuleringar med inriktning mot flöde och kom-primering av sammansatta partiklar.

9.3 Utvärdering av datorsimuleringar Flödet av sammansatta partiklar studerades experimentellt och med simule-ringar dels genom mätningar av förmågan att bilda en hög och dels genom mätningar av partiklarnas flödeshastigheter. I det förra fallet mättes rasvin-keln i den bildade högen och i det senare den tid som krävdes för en mängd partiklar att passera genom en trattformad konstruktion. För dessa mätningar påvisades en mycket god överensstämmelse mellan experiment och simule-ringar. För flödesbestämningen genom mätningar av skjuvmotstånd erhölls en någon sämre överensstämmelse mellan experiment och simuleringar. Samtliga flödesstudier påvisade däremot tydliga indikationer gällande vikten av att inkludera rullmotstånd i modellen för att öka överensstämmelsen.

Komprimering har även studerats med målet att utvärdera två simule-ringsmodeller för att beskriva hela komprimeringsförfarandet. Komprime-ringsprocessen anses i regel bestå av fyra steg, omförflyttning av partiklar, permanent deformation, icke-permanent deformation och slutligen avlast-ning. I komprimeringssimuleringar anses oftast den icke-permanenta de-formationen som försumbar. För att på ett tillfredsställande sätt beskriva komprimering av partiklar måste dock hänsyn tas till den icke-permanenta deformationen. I avhandlingen utvärderades två principiellt olika perspektiv. I den första modellen behandlades partikelkontakterna separat, medan kon-takternas inbördes påverkan vid höga komprimeringstryck inkluderades i den andra modellen. Båda modellerna visade en acceptabel överensstäm-melse mellan experiment och simuleringar.

Sammanfattningsvis, har potentialen att simulera flöde och komprimering av sammansatta partiklar visats. Studierna har även gett en ökad förståelse för faktorer viktiga för överensstämmelsen mellan experiment och simule-ringar. Två lovande simuleringsmodeller har utvärderats där stor potential föreligger för ytterligare förändringar som kan förbättra överensstämmelsen mellan experiment och simuleringar.

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9.4 Studie av partikelpositioner i tabletter Den femte och sista studien utfördes med avsikt att studera positionen av de sammansatta partiklarna i tabletter och avviker därmed något från de övriga studierna. I studien visades graden av volymminskning hos partikelbädden reglera partikelpositionerna i tabletten samt styra tablettens hållfasthet. Alltså, graden av volymminskning är en viktig faktor som kan användas till att förutse kvaliteten av tabletter formade från sammansatta partiklar.

54

Acknowledgements

The work was carried out at the Department of Pharmacy, Faculty of Phar-macy, Uppsala University, Sweden. The work was financially supported by the Swedish Research Council.

IF:s stiftelse, Anna-Maria Lundins stipendiefond and Lettersteds resestipen-dium are greatfully acknowledged for travel grants that enabled participation at various conferences.

Stort tack till alla på institutionen för farmaci som bidragit till ytterligare fem härliga år på BMC. Jag vill särskilt tacka:

Docent Göran F, min tålmodige handledare. Tack för att du vågade släppa in mig i den spännande, roliga och svårbegripliga modellvärlden trots att jag inte hade riktigt rätt bakgrund. Jag uppskattar särskilt att du alltid haft dörren öppen och jag fått komma med frågor närhelst jag behövt. Tack också för att du orkat svara på frågorna om och om igen!

Professor Göran A, min biträdande handledare. Att lyssna på dig får mig alltid inspirerad till forskning och en stark önskan till att lära mig mer.

Dr Josefina och Dr Lucia, för ett mycket givande samarbete i porstrukturs-projektet! Jag hade aldrig trott att jag skulle tycka det var så roligt att jobba med kvicksilver. Josefina – tack även för att du alltid är så uppmuntrande. Lucia, gruppens solstråle, för att du alltid tänker på alla och ställer upp trots att du är upptagen.

Stort tack till alla (både förr och nu) i pulvergruppen som på olika sätt bi-dragit till trivseln i gruppen och för att ni gör så spännande forskning. Jag vill särskilt uppmärksamma:

Camilla, tack för all hjälp och stöd under den första delen av min dokto-randtid. Christin, tack för all rolig undervisning du gett mig. Jag uppskattar speci-ellt att jag fått vara salvtant tillsammans med dig!

55

Dr Denny, för att du alltid pushar för fikabröd på gruppfikat! Dr Foad, thanks for all nice discussions and for annoying me with your singing on the other side of the wall. You have given me many memor-able laughs! Dr Gråsjö, tack för allt uppmuntrande och för att du tog dig tid att kom-mentera på avhandlingen, jag har uppskattat det mycket. Henrik, jag måste säga att jag är lite avundsjuk på hur kul du kommer att ha det under de närmsta åren. Lycka till! Dr Ingvild, tack för att du en gång berättade varför pulverforskning var så roligt. Jag delar din åsikt! Joel, stort tack för att du tog hand om mig när jag var ny på institutionen. Tack även för alla roliga samtal och att jag haft dig som stöd under de läskurser vi genomlidit. Samaneh, min rumbo och vän, du är den största anledningen till att jag tycker det är roligt att åka till jobbet på morgonen! Jag vet att vi kanske snackar lite för mycket om både forskning och livet ibland, men i slutän-dan har det varit gynnande för min effektivitet.

Birgitta, Eva L. J., Eva N. A., Lotta och Ulla, stort tack för all hjälp och för alla trevliga samtal.

Alla nuvarande och tidigare doktorandkollegor som gör institutionen till den roligaste arbetsplatsen. Det är till stor del ni som gjort att det varit värt att hänga på BMC i några år till! ~ Jag vill även tacka min familj, släkt och vänner i den ”riktiga världen” för att ni alltid finns där och uppmuntrar till jobbet och livet. Jag vill speciellt tacka:

Mogens, du övertalade mig att fortsätta doktorera när jag tvekade och jag har inte ångrat det en sekund. Stort tack för din villkorslösa uppmuntran under åren och att du fanns där när livet var som jobbigast.

Dr Tomas, för all doktorandpepp och roliga sammankomster.

Rodina, for talking me into starting belly dancing!

56

André, för att du ofrivilligt står ut med mig och för att du fräschar upp mina gymnasiekunskaper.

Linda, jag önskar att jag vore lika spontan och smågalen som du!

Apotekargänget Alma, Elin, Emma, Linnea, Louise, Malin och Maria för att ni åtminstone försöker tycka det är intressant när jag pratar pulver. Tack för allt roligt vi gjort tillsammans, jag minns särskilt roliga citat, otaliga fester, kryssningar och resorna till Valencia, NY, Japan, London och Shanghai (Elin, jag skrattar fortfarande så jag får ont i magen när jag tänker tillbaka). Jag ser fram emot fler roliga tillställningar!

Oskar, du har gett mig ett nytt perspektiv på livet. Tack för att du drar med mig på en massa skoj och för att du alltid gör mig glad!

Fina mormor Karin, för all omtänksamhet och att du gjort mig till ett kak-monster med ditt trugande ”Ta en kaka till”. Jag önskar du vore här!

Min syster Dr Sus, för att du har visat vägen. Tack för att du delar min dåliga humor och skrattar med mig när ingen annan gör det. Moster Affens charm-troll Livia, för ditt envisa frågande som alltid får mig på bra humör. Erik, tack för att du tog fotot till baksidan.

Mamma Siv-Britt och pappa Allan, för att ni är de bästa föräldrarna jag kan ha! Jag uppskattar att ni gjort mig till en självständig person som inte är rädd för att jobba hårt när det behövs. Tack för att ni finns och för allt ni gör för mig!

Min fina Kenth, för att du coachar mig till mina beslut, att du fick mig att våga bli sambo och att du envist släpar med mig runt löpspåret. Du gör att solen skiner varje dag!

Ann-Sofie

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Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 180

Editor: The Dean of the Faculty of Pharmacy

A doctoral dissertation from the Faculty of Pharmacy, UppsalaUniversity, is usually a summary of a number of papers. A fewcopies of the complete dissertation are kept at major Swedishresearch libraries, while the summary alone is distributedinternationally through the series Digital ComprehensiveSummaries of Uppsala Dissertations from the Faculty ofPharmacy.

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