Dependencies between internal structure and mechanical properties of spray dried granules – Experimental study and DEM simulation

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Contents lists available at ScienceDirect

Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt

2

Original Research Paper

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Dependencies between internal structure and mechanical properties of spray dried granules – Experimental study and DEM simulation

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S. Eckhard a,⇑, M. Fries a, S. Antonyuk b, S. Heinrich c

9 10 11 13 12 14 1 2 6 9 17 18 19 20 21 22 23 24 25 26 27 28

a

Fraunhofer Institute for Ceramic Technologies and Systems IKTS, Dresden, Germany Chair of Particle Process Engineering, University of Kaiserslautern, Kaiserslautern, Germany c Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Hamburg, Germany b

a r t i c l e

i n f o

Article history: Received 18 January 2016 Received in revised form 21 June 2016 Accepted 25 September 2016 Available online xxxx Keywords: Granule structure Spray drying DEM Compression strength Porosity

a b s t r a c t The mechanical properties of spray dried granules are decisive with regard to further applications and can be modified via internal granule structure. To obtain the correlations between structural and mechanical properties, necessary experiments are often time and resource consuming. The simulation of varied granule structures and their effect on resulting mechanical properties seems to be a promising approach. In this paper, a model of the particulate internal structure of a spray dried granule was generated with the Discrete Element Method (DEM) based on real structure parameters. The model considers real primary particle number, particle size distribution and radial granule inhomogeneity, what results in the implementation of granule shell thickness and macro void. The internal structure of simulated granules showed significant influence on their mechanical properties. An increase of granule shell thickness and packing density of the primary particles within the shell results in fracture strength increase accompanied by decreasing fracture strain. The simulated reduction of the solid bridge bond size between the primary particles representing the decreasing binder amount leads to decreasing fracture strength and strain as previously determined experimentally (Eckhard et al., 2014). Consequently, the DEM is appropriate for evaluating the effect of changed real internal structure parameters on resulting mechanical granule properties. Ó 2016 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan.

30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

49 50

1. Introduction

51

The mechanical properties of spray dried granules, like fracture strength and strain, have a significant influence on the processing of the whole granule batch. Depending on the applications the granules have to meet specific requirements: For the generation of homogeneous green compacts during die pressing low fracture strengths of the spray dried granules are desired to guarantee a complete destruction of the granules during compression step. Parallel a sufficient granule strength is needed to survive previous handling, transport and dosage possesses without breakage as destroyed granules would influence the flow behavior of the batch negatively and may cause inhomogeneities within the compact structures [2]. If the spray dried granules shall be used, e.g. as catalyst carrier structures, high fracture strengths are needed to achieve a high stability for surviving handling and regeneration cycles. The granules have to be stable to guarantee a constant flow

52 53 54 55 56 57 58 59 60 61 62 63 64 65

⇑ Corresponding author at: Winterbergstraße 28, 01277 Dresden, Germany. E-mail address: [email protected] (S. Eckhard).

velocity of gas through the catalyst bulk. For an optimized reaction efficiency a high granule surface and porosity is desired [3]. The relation between internal structure and mechanical properties of spray dried granules is still a field of research. The mechanical granule properties can be tailored by the specific selection of type and amount of additives to the suspensions previous to spray drying or by the modification of the internal granule structure itself [1,4–6]. Rumpf [7] and Kendall [8,9] described the agglomerate strength as function of porosity, size and properties of the primary particles as well as of the applied additive system. Binder additives increase granule fracture strength [10–12]. At the same time the internal structure is changed but the structural impact on the mechanical properties is overlaid by additive influence [13]. Especially if the required additives are expensive or the suitable additive selection is limited because of further processing steps or applications, a desired change of the mechanical granule properties can only be achieved via internal granule structure modification. For particular agglomerates Subero et al. and others showed an increasing fracture strength with decreasing porosity [10,14–16]. Also the reduction of the primary particle size leads

http://dx.doi.org/10.1016/j.apt.2016.09.008 0921-8831/Ó 2016 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan.

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Nomenclature A APB d F break FC FD F grav F PB F tot H J k kPB m MC M homo M hollow

86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127

area (image analysis) [m2] solid bridge bond area (DEM) [m2] diameter or respectively size [m] granule fracture force [N] contact force (DEM) [N] damping force (DEM) [N] gravitational force (DEM) [N] solid bridge bond force (DEM) [N] total contact force (DEM) [N] granule classification parameter (image analysis) [–] moment of inertia (DEM) [kg/m2] contact stiffness (DEM) [N/m] solid bridge bond stiffness (DEM) [N/m3] mass [kg] contact moment (DEM) [N m] amount of homogeneous granules per batch (image analysis) [%] amount of hollow granules per batch (image analysis) [%]

to increasing fracture strength because of increased contact numbers and packing density. To have a more detailed look on the effect of different internal structure parameters of spray dried granules on fracture strength and strain, a new method for structure preparation and quantification was developed [17,18]. In our previous study granules with increased shell thickness (macro structural change) as well as reduced micro porosity (micro structural change) showed an increased fracture strength [1]. Moreover the fracture strain can be decreased reducing the micro porosity and vice versa. Both effects, micro and macro structural change, can overlay each other and result in higher pronunciation or neutralization of the influencing structure changes. For the investigated granules, a dominating influence of the micro structure on the resulting mechanical properties was identified [1,19]. For the verification and expansion of the experimentally derived correlations regarding the specific change of mechanical properties via internal granule structure parameters more experimental investigation and systematic structure modifications are necessary. As the experimental possibilities are limited and very time consuming, the development of a simulation tool is a promising technique to review and expand the experimentally derived correlations. For the actual study a simulation model based on DEM is chosen. The suitability of the discrete element method for the realization of tasks concerning the mechanical properties of particular systems during compression or impact is already described by several authors [20–28]. The compression of agglomerate structures using DEM was performed e.g. by Thornton et al., Antonyuk et al. and others [29–33]. State of the art is the simulation of porous systems as homogeneous particular structures over the whole system (granule) volume as done e.g. by Müller [34,35], Antonyuk [21,22], Khanal [36] and others [32,37–39]. The particles forming the agglomerate are hold together by adhesion forces or implemented bonds [22,32,33]. These studies did not focus on real internal spray dried granule structures. For the aspired DEM investigation of the effect of changed internal granule structures with regard to micro and macro structure variations, the established structure simulation has to be improved. Radial structure differences have to be implemented into the DEM granule structure model to be able to simulate the effect of changed structure composition and therewith porosity distribution within the granule on resulting mechanical properties.

M PB M tot Sgran T t crit U

ebreak emicro emacro

kPB

g l rPB rbreak m

resulting moment from applied solid bridge bond (DEM) [N m] total applied moment at a contact (DEM) [N m] shell thickness of a single granule (image analysis) [%] temperature [°C] critical time step (DEM) [s] overlap between two contacting entities (DEM) [m] granule fracture strain [%] micro porosity (image analysis) [%] macro porosity (image analysis) [%] solid bridge bond size radius multiplier (DEM) [–] damping coefficient (DEM) [kg/s] friction coefficient (DEM) [–] solid bridge bond strength (DEM) [N/m2] granule fracture strength [MPa] contact velocity (DEM) [m/s]

Aim of this study is the reproduction of real internal structures of porous spray dried granules with defined internal macro void and shell thickness and the appropriate simulation of the deformation behavior using DEM simulation. For this actual study of the uniaxial compression test of single spray dried granules the PFC3D simulation code by Itasca is used.

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2. Contact model for the simulation with the discrete element method

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Basis of the DEM simulation is a discrete numerical model firstly introduced by Cundall and Strack [40] describing the mechanical behavior of solid disks or spheres. Therewith the behavior of a complex system consisting of a defined amount of single objects can be modeled. Single objects represent rigid and non-deformable primary particles moving independently from each other only interacting at contact points. Particle elements can be modeled as spheres or as random combination of spherical components. Besides particle elements wall elements, representing machine equipment or surrounding boundaries, can be modeled. Wall elements interact with the particles but not with each other. Forces developing from contacts between individual particles and walls only influence the behavior of each particle object. To model a complex system behavior, as it is the case for the particular granule structures of this study, single particles within the simulation can be bonded together at contact points representing solid bridges. Besides shear and compression forces, solid bridge bond elements are able to transmit tensile forces, which are calculated according to linear-elastic beam theory (Euler–Bernoulli beam), as introduced into DEM by Potyondy and Cundall [41]. For the actual studied effect of changed internal granule structure on resulting mechanical granule properties, the DEM software PFC3D (Itasca Consulting Group) was used. By applying a suitable contact model with specific particle and solid bridge bond properties a realistic system behavior can be modeled. As the system behavior is an effect of forces between contacting entities and resulting movement acting on the objects, one calculation cycle contains the repeated quasi simultaneous application of ‘Newton’s Second Law’ of motion for every particle as well as the application of the ‘Force Displacement Law’ at every contact. The ‘Force Displacement Law’ within one calculation cycle connects the relative displacement of two contacting elements

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with the resulting contact force. Displacements are calculated using ‘Newton’s Second Law’ that are necessary for the generation and loss of contacts within the modeled system. Based on the new positions and therewith actualized contact numbers actual forces and moments are recalculated. The calculation cycle is repeated until a previously defined final state, e.g. target time, is achieved. The total force applied on a contact ~ F tot can consist of gravitational force ~ F grav , contact force ~ F C and solid bridge bond force ~ F PB . ~ F C and ~ F PB can be separated in a normal and a shear component, where ~ n and ~ s are the unit vectors in normal and shear direction, ~ tot consists of the contact respectively. The total applied moment M ~ C as well as the moment resulting from applied solid moment M ~ PB . bridge bonds M Decisive for the contact force ~ F C is the applied contact model: The contact model consists of the classical models for friction, damping and elastic contact law in normal and shear direction, what is schematically visualized in Fig. 1. The resulting contact force in normal direction ~ F n is a combinaC

tion of the contact force between two contacting entities A and B, ~ F n . The damping term with damping F n , and the damping force, ~ D

C;AB

coefficients gnAB or gsAB and contact velocity tnAB represents the irreversible energy dissipation during the contact deformation behavior. Both terms act in parallel. The easiest case is the linearity between contact force ~ F n and determined overlap U n between C;AB

AB

193

the two contacting entities, as it is applied for the actual model (Kelvin-Voigt model)

196


n  ~ F nC ¼ ~ F nC;AB þ ~ F nD ¼ kAB U nAB þ gnAB v nAB ~ nAB :

192

194

ð1Þ

199

In addition to the energy dissipation because of viscous deformation (damping), friction can occur. In shear direction an additional friction term acts in series

202

~ F sC ¼

197 198

200



s kAB U sAB

þg

s AB

v

s AB

  tAB : ; lAB F nC;AB ~

ð2Þ

204

The friction term contains the friction coefficient l [–]. From l and the force acting in normal direction ~ F n the maximum shear

205

contact force ~ F sC;max can be calculated

208

~ F sC;max ¼ l~ Fn:

203

206

ð3Þ

212

If the applied shear contact force equals or is larger than the calculated maximum shear contact force, sliding occurs and the actual shear contact force is reduced to the calculated maximum shear contact force:

215

if ~ F sC > ~ F sC;max

209 210 211

213

Fn: then ~ F sC ¼ ~ F sC;max ¼ l~

ð4Þ

Via integration of material bonds into the simulation, the realistic behavior of a multi component systems can be simulated – a solid bridge bond force becomes active: The force in the solid bridge bond acts in parallel with the contact bond. Because of the relative motion of particles to each other forces and moments raise within the solid bridge bond. These moments and forces depend on the bond properties (bond cross sectional area APB , normal and shear stiffness kPB , normal and shear strength rPB ). The cross sectional solid bridge bond area APB is calculated using the implemented radius multiplier kPB . The absolute solid bride bond radius equals this multiplier times the minimum radius of the two bonded particles. A material bond can be irreversibly destroyed, if the critical strength of the material is reached

rPB;max ¼ rPB;crit :

ð5Þ

The resulting force due to bonds ~ F PB;AB can be separated in a normal and shear part, whereas term APB represents the cross sectional area of the bond:

216 217 218 219 220 221 222 223 224 225 226 227 228

229 231 232 233 234

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~ F PB;AB ¼ ~ F nPB;AB þ ~ F sPB;AB ;

ð6Þ

  n ~ F nPB;AB ¼ kPB;AB APB DU nAB ~ nAB ;

ð7Þ

s ~ ~s : F sPB;AB ¼ kPB;AB APB DU

ð8Þ

243

For the simulation of the dynamic behavior of a complex system a time step needs to be repeatedly calculated at the beginning of each calculation cycle. The time step needs to fulfill the criterion that within one calculation step interferences can only be transmitted from one element to one direct neighbor and should be as high as possible for a sufficient computing time. The base is the determined critical time step that can be calculated for transla-

244

238 240 241

trans

tional movement using translational stiffness k rot

movement using rotational stiffness k

tcrit

237

and rotational

of the particles:

rffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffi m m J ¼ ¼ trans ¼ rot : k k k

245 246 247 248 249 250 251 252

253

ð9Þ

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3. Reference granules for DEM simulation

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3.1. Spray drying

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For the reproduction of real internal structures within the DEM model as well as the validation of the DEM simulation ceramic granules were spray dried from aqueous suspensions. The used primary particles were a-alumina particles (NO 731-10 MF, Nabaltec)

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Fig. 1. Systematic visualization of implemented contact models in normal and shear (tangential) direction.

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S. Eckhard et al. / Advanced Powder Technology xxx (2016) xxx–xxx

with a primary particle size of dPP,50,0 = 1.1 lm (dPP,10,0 = 0.7 lm, dPP,90,0 = 2.1 lm). The mean primary particle size dPP,50,0 and primary particle size distribution values were determined using laser diffraction analysis (Mastersizer 2000, Malvern). For the size characterization three measurements were performed, whereas the standard deviation of these measurements was below 1%. The particles were suspended in water by stirring followed by the addition of a binder polymer PVA (polyvinyl alcohol ‘Mowiol 4-88’, Clariant). After additional stirring for 1 h the suspensions were dried using spray driers with fountain spray system. For spray drying of batches G1 and G3 (Table 1) a pilot scale spray dryer Production Minor (GEA Niro A/S) was chosen. For spray drying of batch G2 a lab scale spray dryer Mobil Minor (GEA Niro A/S) was used. The spray drying parameters were adapted to achieve comparable granule size distributions and thermal spray drying conditions (Tin and Tout). As within this study the relation between quantified internal structures and resulting mechanical properties of a defined granule size fraction is studied experimentally and using DEM, the spray drying process of the granules itself showed only subordinated importance. The drying medium was air in all cases and the suspension was atomized using a two fluid nozzle. Spray drying conditions as well as resulting granule sizes are concluded in Table 1. Based on our previous study the formulations of the suspensions were modified for the investigation of the effect of changed granule structures on resulting mechanical properties [1]: For the spray drying of the granule batch G1 for calibration of the simulation model a solid content of 40 wt% primary particles in the suspension was chosen. The amount of added binder PVA was 3 wt %. For DEM model validation two further batches were spray dried: Batch G2 was spray dried from a suspension with increased primary particle number. The solid content was raised to 68 wt%, the additive amount was kept constant at 3 wt% PVA. The granules of batch G3 were spray dried from a 40 wt% solid content suspension with reduced binder amount of 1 wt% PVA.

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3.2. Internal granule structure

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The internal structures of the spray dried granules were characterized using image analysis of FESEM images. The necessary images were taken of granule cross sections. The cross sections were prepared following a method published by Höhn et al. [17,18]. A granule size fraction of 45–63 lm was used, embedded in epoxy resin and polished mechanically. The preparation of a narrow size fraction is essential for the desired granule structure quantification close to the center plane of the granules. For the preparation of smooth surfaces without inhomogeneities a polishing step using ion beam preparation was added (BIB RES 101, BALTEC). The internal granule structures were visualized using a field emission scanning electron microscope (FESEM NVision, Zeiss). Images were taken at two magnifications to analyze internal granule macro structure (150 magnification) and micro structure (approx. 20,000 magnification) (Fig. 2). The structure quantifica-

299 300 301 302 303 304 305 306 307 308 309 310 311 312

tion was done using a commercially available image analysis tool (AnalySIS FIVE, Olympus). For the characterization of the granule macro structure the parameters average shell thickness Sgran [%], average macro porosity emacro [%] and batch composition of hollow (M hollow [%]) and homogeneous granules (M homo [%]) were determined. To separate the granules into two different granule types (hollow and homogeneous) a ratio H [–] of the internal void area Amacro [lm2] to the total granule area Agran [lm2] was determined as

Amacro H¼ : Agran

ð10Þ

The calculation of H is necessary for the classification of hollow and homogeneous granules within a batch. If the void area is larger than 10% ðH > 0:1Þ of the total granule area, the granule is classified as hollow. Assuming an ideal spherical shape of the granule and the internal void, the granule diameter dIA;gran [lm] and internal void diameter dIA;macro [lm] can be calculated. These values were used to determine an average shell thickness Sgran [%] as well as the macro porosity emacro [%]:

Sgran

ð11Þ

315 316 317 318 319 320 321

322 324 325 326 327 328 329 330 331 332

335 336

3

emacro ¼

dIA;macro  100 3

dIA;gran

:

ð12Þ

The macro structure characterization was done analyzing 20 images per sample. The number of evaluated granules per sample lies between 810 and 1268 granules. The micro structure of the granules was characterized with the parameter micro porosity emicro [%] as the void amount between the primary particles within the shell. This parameter was determined using image analysis (AnalySIS FIVE, Olympus). For each analyzed 2D SEM image of the micro structure the particle and void area were detected using gray scale differences. From these two determined parameters per image (particle area AIA;micro;part and void area AIA;micro;v oid ), the amount of void area is determined as a percentage

emicro ¼

AIA;micro;v oid  100 : AIA;micro;v oid þ AIA;micro;part

ð13Þ

For the characterization of the average micro porosity of each sample 20 images are analyzed and averaged. From both porosities a total porosity etotal is calculated

etotal ¼ emacro þ

emicro  ð100  emacro Þ 100

338 339 340 341 342 343 344 345 346 347 348 349

350 352 353 354 355

356

:

ð14Þ

The granules for calibration (G1) and verification (G2 and G3) of the DEM model were evaluated regarding the described internal structure parameters. As the applied primary particle material is comparable for all three investigated batches the simulated primary particle sizes for all samples G1–G3 are handled comparable.

G1

G2

G3

wt% wt%

40 3

68 3

40 1

Spray drying conditions Inlet temperature Tin Outlet temperature Tout

°C °C

190 87

185 95

190 88

Granule properties Granule size d10/d50/d90

lm

30/58/111

28/57/117

29/55/99

Suspension formulation Solids content (primary particles) Additive (Mowiol PVA 4-88)

314

333

ðdIA;gran  dIA;macro Þ  100 ¼ ; dIA;gran

Table 1 Suspension properties and spray drying conditions of samples G1–G3. Granule sample

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Fig. 2. Visualization of determined internal structure parameters on micro and macro level.

G2

G1

G3

Fig. 3. Example images of internal structures of batches G1 (left), G2 (middle) and G3 (right).

365

Example images are presented in Fig. 3. The resulting properties are concluded in Table 2.

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3.3. Mechanical granule properties

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The mechanical granule properties were characterized by the measurement of granule fracture strength rbreak [MPa] and granule fracture strain ebreak [%]. The parameters were determined using uniaxial compression tests of single granules between two plates (GFP, Etewe) what is a common method to characterize mechanical

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granule properties [22,30,42]. The experimental setup of compression of the granule between two flat punches also serves as a model for the DEM simulation. Experimental compression tests were carried out with strain control (constant stressing velocity of 10 lm/s). The fracture strength was calculated from measured fracture force F break assuming an ideal spherical shape of the granule with experimental obtained diameter dgran

F break

rbreak ¼ p 4

2

dgran

:

ð15Þ

Table 2 Internal structure properties of samples G1–G3. Granule sample

G1

G2

G3

Structure properties – image analysis Amount of homogeneous granules Amount of hollow granules Shell thickness (with regard to granule radius) Macro porosity Micro porosity Total porosity

% % % % % %

79.9 20.1 81.9 ± 2.6 2.8 ± 0.9 48.7 ± 1.7 50.1

96.3 3.7 91.1 ± 1.6 0.7 ± 0.7 46.5 ± 2.2 46.9

82.0 18.0 74.5 ± 2.3 2.8 ± 1.0 43.1 ± 3.3 44.7

Structure properties – laser diffraction dPP,10,0 dPP,50,0 dPP,90,0

lm lm lm

0.7 1.1 2.1

0.7 1.1 2.1

0.7 1.1 2.1

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4. DEM simulation – structure generation and calibration

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4.1. Internal structure generation

394

The internal granule DEM structure model was generated using the experimental data of sample G1. For the following calibration process of the mechanical granule properties, one single measurement M1 from the 30 determined stress-strain diagrams is selected. This specific stress-strain diagram is used for the calibration and the implementation of a defined granule size dgran;M1 into the DEM simulation. Therefor the single measured stress-strain diagram was determined, that fitted the closest to the average stress-strain diagram of sample G1. Furthermore the determined mechanical properties of the single measurement M1 should be as close as possible to the average mechanical properties of sample G1. The selection is done following the least square method - the graph between beginning of stressing (zero deformation, e = 0%) and a deformation that equals three times the fracture strain (e = 3 ⁄ ebreak) is tested regarding least differences. The stress-strain diagram M1 within Fig. 4 representing the batch G1 is the target stress-strain diagram and therewith used for calibration of the DEM model. From the selected measurement M1 the input parameter granule size dgran;M1 for the simulation is derived (Table 4). Assuming an ideal spherical granule shape, the solid phase amount within the granule structure is calculated from the total granule volume based on the measured granule diameter dgran;M1 and the total porosity of sample G1 using image analysis. Based on the measured real primary particle size distribution and the determined porosity and therewith solid fraction within the granule structure the amount of primary particles is calculated. A total number of 12,497 primary particles, distributed within 25 particle size classes representing the real primary particle size distribution, is generated (Fig. 5). According to DEM model specifications and calculation time optimization, all primary particles are modeled as spheres, even if the determined average sphericity of the primary particles is 0.75. The influence of this simplification on simulation results will be investigated in future works. Following Eq. (9) the critical time step depends directly on the mass of the object and indirectly on the stiffness. To increase the critical time step and therewith reduce the calculation time for the simulation, the mass of single objects (particles) is increased by scaling the particle size by factor 1000. At a constant density of 3.94 g/cm3 [43] this results in an

383 384 385 386 387 388 389 390

3

G1 M1

[MPa]

391

30 single granules within the size range of 45–63 lm equally to the size fraction for structure quantification were tested per sample. For a summarizing characterization of the mechanical properties of the investigated samples G1–G3 average values concerning fracture strength and fracture strain were calculated and presented in Table 3. The fracture stiffness characterizes the slope of the stress-strain diagram until the fracture point is achieved and gives information regarding the deformation behavior and therewith the ductility of the samples. All mechanical properties are discussed in in detail compared to the simulation results in Section 5.

382

Compression Stress

6

Fracture point M1

1

0

396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433

0

10

20

30 40 Strain [%]

50

60

70

Fig. 4. Average stress-strain diagram of the sample G1 in comparison to the stressstrain diagram of the selected measurement M1.

Table 4 Mechanical granule properties of selected measurement M1 in comparison to the average results of sample G1. Granule sample Mechanical granule properties Average test granule size Fracture force Fracture strain Fracture strength Fracture stiffness

lm mN % MPa MPa/%

G1

M1

51.2 ± 3.2 3.5 ± 0.7 15.8 ± 3.9 1.7 ± 0.4 0.12 ± 0.04

52.1 3.0 17.3 1.4 0.08

100 Sum Distribution Q0(x) [%]

395

Fracture point G1

2

80 60

40

Real Particle Size Distribution

20

Calculated Particle Size Distribution for Simulation

0 0,1

1 10 Primary Particle Size x [µm]

100

Fig. 5. Calculated sum distribution function of the simulated primary particles in comparison to experimentally determined.

increased particle volume, particle mass and therewith calculation time step. Parallel all other objects within the simulation (boundary and compression walls) are also scaled by factor 1000. As the calculated time step also depends indirectly on particle stiffness, this implemented parameter needs to be as low as possible. With

Table 3 Mechanical granule properties of samples G1–G3. Granule sample Mechanical granule properties Average test granule size Fracture force Fracture strain Fracture strength Fracture stiffness

lm mN % MPa MPa/%

G1

G2

G3

51.2 ± 3.2 3.5 ± 0.7 15.8 ± 3.9 1.7 ± 0.4 0.12 ± 0.04

49.5 ± 3.8 7.3 ± 1.2 13.7 ± 2.1 3.9 ± 0.7 0.29 ± 0.06

54.6 ± 5.3 2.0 ± 0.8 7.1 ± 2.8 0.9 ± 0.3 0.14 ± 0.08

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all these simplifications a time step of 1.460e7 s could be realized for the simulations within this study. For the generation of the granule structures, the following procedure was applied: All particles representing the primary particle size distribution were generated randomly distributed within a spherical volume space. To ensure no overlap, all particles were generated in a reduced size. The spherical space representing the granule volume is limited by temporary walls during the structure generation process. The primary particle size is increased stepwise until the final desired particle size distribution is achieved. Between each expansion step, several simulation cycles were performed to compensate eventually generated overlaps. As the final primary particle size distribution is achieved the real internal integral granule structure with a central macro pore and a dense packed shell is simulated by assigning a velocity to every particle within the granule volume. All particles move in the direction of the position vector of each individual primary particle. To achieve an outward movement of the particles in the direction of the temporary wall, the origin of the coordinate system was set to the center of the granule model. During the structure generation process the particles move radially from the center of the granule forming a packed structure granule shell as can be seen in Fig. 6 in comparison to the real granule cross section. During this structure formation process information regarding actual particle velocity, total contact number and radius of the internal macro pore are updated continuously. The migration process is stopped as no further changes of total contact number and radius of internal void is detected. The structure generation process is visualized in Fig. 7. The grids around the simulated structures of image 7 visualize the outer granule border. In Table 5 the parameters of the final simulated structure S1 are compared to the real granule structure G1. The structure differences between the simulation S1 and the experimental batch G1 are an effect of the particle shape and the adjustment of the real primary particle size distribution with 25 size classes: At a constant total porosity of simulation and experiment of 50.1% the application of spherical particles results in thinner shells and increased macro porosity for the simulation S1. If all experimental structure properties were adapted with the given simulated primary particles this would result in a reduced contact number of the primary particles and therewith in an instable system not suitable for the simulation of a compression test [13].

481

4.2. Model calibration

482

After the generation of the internal structure the coordination number of primary particles was determined and bonds were simulated at every contact point. The existence of material bonds within experimental structures is proven by SEM images of granule fracture surfaces visualizing polymeric bonds (Fig. 8).

483 484 485 486

Z

For the experimental granule sample G1 PVA was used as binder additive. From the applied amount of 3 wt% binder within experimental granulation process, the total number of contact points within the simulated structure S1 and the average primary particle size, the radius multiplier kPB of the cylindrical bonds within the DEM model were calculated. The radius multiplier kPB relates the bond bridge diameter to the diameter of the smaller particle of the two contacting entities. Within PFC3D the solid bridge bonds are implemented at point contacts. Options with sustained solid bridge bonds between particles that are not in direct contact or only close to each other are not considered and implemented, even if this is obviously a possible scenario (Fig. 8). Studies considering these bond types can be found in literature [44–46] e.g. Spettl et al. [45] investigated the compression behavior of granules using a specially developed bonded particle model. For the simulation of the compression test, the DEM granule structure was positioned between two simulated flat walls, representing the steel walls of the experimental setup. Wall stiffness n s values in normal and shear direction (kW and kW ) were defined, the implemented stiffness values were lower than real stiffness values for steel to minimize the calculation time step. To keep realistic relations, higher stiffness values than for the particles and binder material were chosen. During the simulated compression test, a stress-strain diagram was obtained until the fracture point and compared to the experimentally determined graph of measurement M1. Within the calibration process the solid bridge binder n s properties normal and shear area related stiffness (kPB and kPB ) n s and normal and shear strength (rPB and rPB ) of the PVA bonds were modified to achieve a strength deformation graph of the modeled structure that meets as closest as possible the real curve of the selected measurement M1. n For the parallel bond parameters kPB ¼ 0:733, kPB ¼ 2:45e11 Pa , m kPB ¼ 9:87e10 Pa , rnPB ¼ 4e8 Pa and rsPB ¼ 4e7 Pa the following m strength deformation graph was simulated (Simulation Sim0 in Fig. 9). For the adaption of the simulated stress-strain diagram to the experimental target diagram, a reduction of the fracture strain ebreak and therewith increase of the fracture stiffness in combination with a slight reduction of strength rbreak was necessary. The modeled stress-strain diagram was fitted to the experimentally measured one only by the modification of the PVA solid bridge bond parameters. Stiffness and strength values are flexible, whereas the bond radius multiplier kPB is fixed because of the defined applied polymer amount. A reduction of fracture strength can be achieved by a decrease of normal and shear strength rnPB , rsPB of the bonds. The desired reduction of fracture strain is an n s effect of increased normal or shear stiffness kPB , kPB or decreased n normal strength rPB . The granule fracture stiffness can be increased n s by larger normal or shear area related stiffness kPB or kPB as well as shear strength rsPB of bonds. The calibrated stress-strain diagram is s

Z Y

Y X

X

Fig. 6. Cross sections of real (left) and simulated (middle and right) granule structures.

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Fig. 7. Schematic diagram of DEM structure formation process.

Shell thickness (with regard to granule radius) Macro porosity Micro porosity Total porosity

% % % %

G1

S1

81.9 ± 2.6 2.8 ± 0.9 48.7 ± 1.7 50.1

66.0 4.0 48.0 50.1

[MPa]

Granule sample

2,5

Compression Stress

Table 5 Simulated structure S1 properties compared to reference experimental structure G1.

Fracture Point Experiment

Fracture Point Simulation

2 1,5

1 0,5

Experiment M1 Simulation Sim1

0 0

5

10 Strain [%]

15

20

Fig. 10. Calibrated stress-strain diagram of simulation Sim1.

Fig. 8. Visualization of polymer bonds between primary alumina particles on fracture surfaces of a spray dried granule.

Compression Stress

[MPa]

2,5

Fracture Fracture Point Point Experiment Simulation

2 1,5 1 0,5

Experiment M1 Simulation Sim0

0 0

10

20 Strain [%]

30

parameters (particle and bond properties) is summarized in Table 7.

540

5. Model verification – effect of changed internal structure on mechanical properties

542

5.1. Increase of particle number – increase of solid volume fraction

544

For the numerical investigation of the experimental effect of increased solid content, a DEM structure based on the structure quantification results of sample G2 was simulated. Compared to granule sample G1 sample G2 was spray dried from a suspension with increased solid content and therewith increased particle number (Table 1). An increased average shell thickness Sgran of 91.1% as well as a reduced micro porosity emicro of 46.5% were determined experimentally. The increased solid content within the suspension and therewith higher number of primary particles result at constant granule volume and primary particle size distribution in a reduced total porosity etotal of 46.9% for sample G2. Based on the experimentally determined total porosity of sample G2, the comparable granule diameter dgran;M1 and the similar primary particle sizes, an

545

40

Fig. 9. Starting point for the calibration of the simulated strength deformation graph.

Table 6 Mechanical properties of simulation Sim1 compared to the reference properties of sample M1. Granule sample

537 538 539

shown in Fig. 10. The mechanical properties of the calibrated simulation Sim1 in comparison to the experimental reference structure M1 are compared in Table 6. The set of finally implemented

Fracture strain Fracture strength Fracture stiffness

% MPa MPa/%

M1 (G1)

Sim1

17.3 1.43 0.083

16.1 1.43 0.089

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5 October 2016 S. Eckhard et al. / Advanced Powder Technology xxx (2016) xxx–xxx Table 7 Input parameters for the simulation of structure S1. Granule sample

S1

Granule properties Granule diameter Total porosity

dgran;DEM

etotal

Particle properties Primary particle number Primary particle size (dPP,10,1/dPP,50,1/dPP,90,1) Particle shape Particle normal stiffness Particle shear stiffness

560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584

n kPP s kPP

52.1 50.1

– mm – N/m

12,497 0.7/1.1/2.1 Sphere 6e5

N/m

6e5

Particle friction coefficient

lPP

–

0.5

Parallel bond properties Number Radius multiplier Bond normal stiffness

nPB kPP n kPB

– – Pa/m

40,832 0.733 1.7e12

Bond shear stiffness

kPB

s

Pa/m

6.86e11

Pa Pa

9e8 5e7

rnPB rsPB

Bond normal strength Bond shear strength 559

nPP

mm %

increased particle number of 13,474 was calculated for the simulated structure S2 compared to the simulation S1. The simulated structure formation process was comparable to structure S1. In Fig. 11 cross sections of the compared internal structures after structure generation are visualized. For simulated structure S2 an increased shell thickness and reduced macro porosity are visible. The contact number for the simulated structure S2 was increased to 44,296. As solid bridge bonds are implemented at every contact point within the structures, the solid bond bridge number was increased to 44,296 for simulated structure S2 compared to structure S1 were a lower number of 40,832 solid bridge bonds were generated. The structure properties of both simulated structures are compared in Table 8. The lower micro porosity and shell thickness values in both simulated cases compared to the experimental tests are an effect of the ideal spherical shape of the implemented DEM particles. Real primary particles show an angular shape – during the droplet drying the structure formation process will result in loose packed structures with higher porosity because of the particle shape. For ideal spherical particles an optimized packing during the structure formation process can be achieved: The missing edges of the simulated primary particles affect the increased packing densities of the micro structures compared to the experimentally determined micro porosity. The radius multiplier for the implemented bonds representing the 3 wt% PVA binder was adapted to kPB ¼ 0:730 because of the increased contact number. All other binder param-

9

eters were kept constant because of the used identical binder system. Simulating the deformation process of the generated structure S2 between two plates at a comparable scaled stressing velocity n s n of 100 mm/s and calibrated bond parameters kPB , kPB , rnPB , sigmaPB a modified stress-strain diagram was measured (Sim2 within Fig. 12). In previous tests the insensitivity of the simulation results from the applied stressing velocity was investigated. The granule fracture strength is slightly increased, whereas the fracture strain is decreased – fracture stiffness increases. This structure effect on the mechanical properties reproduces the experimentally derived effect comparing the average stress-strain diagrams of batches G1 and G2 in Fig. 13. The changes of mechanical granule properties obtained by simulation can be explained by the changed internal granule structure properties: As already published in [1] for the experimental structure variation, an increased shell thickness as well as an increased packing density of the primary particles (reduced micro porosity) lead to an increase of the granule strength. The simulated reduced fracture strain and therewith increased fracture stiffness can be explained with the increased packing density of primary particles. Due to the decreasing porosity the dislocation of the primary particles into hollow spaces during stressing is limited. The changes of the mechanical granule properties obtained by simulation and experiment are concluded in Table 9. Comparable trends regarding the changes of fracture deformation, strength and stiffness can be seen, although the absolute changes are different. A reason can be found in the already described adapted spherical particle shape: real irregular particles can interlock and therewith result in increased fracture strengths. Furthermore, simplifications like the homogeneous distribution of bonds at all contact points, the limitations regarding bond shape or the simplification of the bond breaking event have to be considered. Within this simulation the solid bridge bond is permanently linked to the particle. Real varying fracture events (break in the bridge, break at contact zone between particle and bond) cannot be considered.

585

5.2. Decrease of parallel bond size – binder amount reduction

622

If the binder amount is reduced the granule fracture strength and strain decrease, as it was measured experimentally comparing granule samples G1 and G3 (Fig. 14). To simulate the experimental reduction of the binder content from 3 wt% to 1 wt% two different methods are possible: The first

623

Z

Z

Y

Y X

X Fig. 11. Cross sections of simulated structures S1 (left) and S2 (right).

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Table 8 Internal structure properties for S1 and S2 after DEM structure generation process. Granule sample Structure properties Particle number Solid bridge bond number Micro porosity Macro porosity Total porosity Shell thickness

nPP nPB

emicro emicro etotal Sgran

2

Fracture Point Sim1

1,5

1,0

0,5

Simulation Sim1 0,0

Simulation Sim2 0

5

10 Strain [%]

15

[MPa] Compression Stress

[MPa] Compression Stress

1 G1, 40 wt% solid content G2, 68 wt% solid content 0 20

30 Strain [%]

40

50

629 630 631 632

20

30 40 Strain [%]

way is the reduction of the bond number within the simulated structure. The second way is the reduction of the bond size at constant solid bridge bond number. For this actual study the second possibility is chosen: The reduction of the solid bridge bond size can be realized decreasing the implemented solid bridge bond

50

60

Fracture Point Sim1

Simulation Sim1 Simulation Sim3

1,5

1,0 Fracture Point Sim3

0,5

0,0

60

Fig. 13. Average experimental stress-strain diagram of samples G1 and G2 in comparison.

628

10

2,0

Fracture Point G1

10

Fracture Point G3

Fig. 14. Average stress-strain diagram of samples G1 and G3 in comparison.

3

0

13,474 44,296 45.8 2.0 46.9 72.9

Fracture Point G1

1

0

Fracture Point G2

2

12,497 40,832 48.1 3.9 50.1 66.0

0

20

Fig. 12. Simulated stress-strain diagrams of structures S1 (Sim1) and S2 (Sim2).

4

S2

G1, 3 wt% binder G3, 1 wt% binder

[MPa]

Fracture Point Sim2

Compression stress

[MPa]

2,0

Compression Stress

– – % % % %

S1

0

5

10 Strain [%]

15

20

Fig. 15. Simulated stress-strain diagram of structures S1 (Sim1, 3 wt% PVA) and S3 (Sim3, 1 wt% PVA).

multiplier. For the simulation S1 of granule sample G1 with 3 wt % binder additive a solid bridge bond multiplier of kPB ¼ 0:733 was calculated. If the binder amount is reduced to 1 wt% a kPB of 0.564 was calculated for the simulated structure S3. All other structure parameters of S3 were kept constant compared to S1:

Table 9 Mechanical properties of reference simulation Sim1 and simulation Sim2 with increased particle number compared to experimental results. S1 Sim1

S2 Sim2

DEM simulation Mechanical properties Fracture strength Fracture strain Fracture stiffness

rbreak ebreak

G1

G2

Experiment

MPa %

1.4 16.1

1.6 11.2

1.7 ± 0.4 15.8 ± 3.9

3.9 ± 0.7 13.7 ± 2.1

MPa/%

0.09

0.14

0.12 ± 0.04

0.29 ± 0.06

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S. Eckhard et al. / Advanced Powder Technology xxx (2016) xxx–xxx Table 10 Mechanical properties of reference simulation Sim1 compared to simulation Sim3 with reduced solid bridge bond size. S1 Sim1

S3 Sim3

DEM simulation Mechanical properties Fracture strength Fracture strain Fracture stiffness

rbreak ebreak

0.8 12.2

1.7 ± 0.4 15.8 ± 3.9

0.9 ± 0.3 7.1 ± 2.8

MPa/%

0.09

0.07

0.12 ± 0.04

0.14 ± 0.08

673

6. Conclusions

674

Within this study a DEM model of the internal structure of a real porous spray dried granule was generated. Internal structure parameters micro porosity, shell thickness, total porosity and primary particle size were used to generate a realistic DEM structure model. The generated model structure with real radial varying internal structure properties (macro pore and shell) consists of spherical particles bonded together with solid bridge bonds. The simulated primary particles represent the real primary particle size distribution as this showed a significant influence in previous experimental studies [1,19]. Compared to common DEM models of porous granule systems the actual structure simulation applies radial structure differences and the real primary particle size distribution, what is a significant improvement. The DEM model developed in this study is able to predict qualitatively the experimental obtained effects of changed internal structure parameters on the resulting mechanical properties.

640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671

675 676 677 678 679 680 681 682 683 684 685 686 687 688 689

Experiment

1.4 16.1

672

639

G3

MPa %

nPP = 12,497, nPB = 40,832, emicro = 48.1%, emacro = 3.9%, etotal = 50.1% and Sgran = 66%. Stressing the two compared simulated structures between two plates at identical particle, structure and solid bridge bond stiffness and strength properties shows a significant effect on the resulting stress-strain diagram. As can be seen in Fig. 15 and Table 10 the simulated fracture strength rDEM;B as well as fracture deformation values ebreak decrease if the binder amount and therewith the solid bridge bond size is reduced. Qualitatively this effect is comparable to the determined experimental effect on the mechanical granule properties: During the experimental compression test the binder amount reduction leads to a decrease of the determined average fracture strength from 1.7 MPa (G1) to 0.9 MPa (G3). Parallel the average fracture strain is reduced from 15.8% (G1) to 7.1% (G3). The experimentally studied influence of the binder amount on the mechanical granule properties is qualitatively in good accordance to the simulation results of this study. A contradiction was found regarding the calculated fracture stiffness values: Experimentally a slight increase of average fracture stiffness from 0.12 MPa/% (G1) to 0.14 MPa/% (G3) was measured if the binder amount was reduced. The thereby measured high standard deviation indicates a wide spread of determined fracture stiffness values. For the simulation only one example structure per sample was calculated. So the resulting slightly reduced fracture stiffness (0.09 MPa/% for S1 compared to 0.07 MPa/% for S3) and therewith increased ductility of the granule sample is not significant. Besides this, simplifications within the simulation compared to the experiment (particle shape, distribution and size of solid bridge bonds) might be reasons of these deviations. Independent of this described discrepancy of the calculated fracture stiffness, this simulation example shows once more the applicability of the DEM simulation to study the effect of varied internal granule structure on mechanical properties in principle.

638

G1

Increased shell thickness and reduced micro porosity lead to increased fracture strength and stiffness at parallel reduced fracture strain. Reduced solid bridge bond sizes result in decreased fracture strength and strain in experiment as well as in simulation. However, the simulations did not predicted the measured values exactly what can be explained with necessary simplifications made: The implementation of spherical particles instead of irregular shaped, the uniform distribution of binder bridge bonds at all contact points, the lack of solid bridge bonds between separated neighbor particles or the size scaling are simplifications affecting the resulting mechanical granule properties. A more realistic reproduction of internal granule structures will improve the quality of the simulation results and will be investigated in further studies.

690

Acknowledgements

704

The authors would like to thank the German Research Foundation DFG for the financial support of parts of this work within SPP 1423 ‘Prozess-Spray’.

705

References

708

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Please cite this article in press as: S. Eckhard et al., Dependencies between internal structure and mechanical properties of spray dried granules – Experimental study and DEM simulation, Advanced Powder Technology (2016), http://dx.doi.org/10.1016/j.apt.2016.09.008