DRAFTINFLUENCE OF PHYSICS OF

TABLET COMPRESSION

Small-Scale Presenter: Alberto Cuitino

November 3rd, 2010

DRAFTDesign Pharmaceutical Solids

-12-10 -8 -6 -4 -2 0 2 4

-1000-800-600-400-200

0200

Die Filling Compression Breakup DissolutionMixing

EXPERIMENTS

MODELING & SIMULATIONS

Integrated

Integrated

DRAFT

Die Filling – Feed frame EXPERIMENTS

initial

exit 1 exit 2

exit 3

152.3mmA

B

DRAFT

Die Filling – Feed frame

Void/porous MicrostructureIMPACTS

STRENGTH and DISSOLUTION

MODELING & SIMULATIONS Smaller ParticlesMore Surface Area

Larger ParticlesLess Surface Area

DRAFT

Pressure (MPa)

Den

sity

(g/m

l)

0 5 10 15 20 250

0.5

1

1.5

Sample Info

Mass = 0.4 g

Size = 996.1 mm3

Composition = 55% (D),

15%(S2), 15%(S3)

15%(S4)

Expected solid density =

1.68 g/ml

Long-range prediction

Pressure (MPa)

Den

sity

(g/m

l)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

predictexpt1expt2

0

2

4

6

8

10

0

2

4

6

8

Z

0

2

4

6

X Y

Z

dens

1.251.21.151.11.0510.950.90.85

Density distribution

0

2

4

6

8

10

0

2

4

6

8

Z

0

2

4

6

X Y

Z

Szz

-0.53-0.55-0.57-0.59-0.61-0.63-0.65-0.67

Pressure distribution

0

2

4

6

8

10

0

2

4

6

8

Z

0

2

4

6

X Y

Z

dens

1.251.21.151.11.0510.950.90.85

Density distribution

0

2

4

6

8

10

0

2

4

6

8

Z

0

2

4

6

X Y

Z

Szz

-0.53-0.55-0.57-0.59-0.61-0.63-0.65-0.67

Pressure distribution

Micro-structure from X-ray CT

ConsolidationMODELING & SIMULATIONS

EXPERIMENTSMultiscale Modeling – Concurrent particle-continuum description

Tablet Compaction Model:

– Multiscale– Preserves local heterogeneous

structure of the powder bed– Predicts macroscopic trends

DRAFT

Displacement fields in a uniaxially loaded tablet during the formation of a crack.

Bonding-DebondingEXPERIMENTS

Crack

Non-uniform fields

Fracture dominated by weakest regions

DRAFT-12 -10 -8 -6 -4 -2 0 2 4

-1000

-800

-600

-400

-200

0

200

Bonding-DebondingMODELING & SIMULATIONS

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

Time

Bo

nd

ing

Str

eng

th

σ A – contact area

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 20

Separation

Fo

rce

an

d P

ote

nti

al

Inter-particle Kernel

development ofhistory dependent inter-particle bonding

Microscopic

Compact StrengthEvolving Force Field

force

TABLET

Macroscopic

Displacement

COMPRESSION

TENSION

Non-uniform fields

DRAFTStructure “carried” downstream

DissolutionMODELING & SIMULATIONS

EXPERIMENTS

VALIDATION

0

20

40

60

80

100

0 20 40 60 80Time (min)

%

Dru

g R

ele

as

e

Blend 6 640rpmBlend 3 160rpmModel Tablet Blend 6 640rpmModel Tablet Blend 3 640rpm

DRAFT• A ballistic deposition technique is used to simulate die-filling.

• Powder composition• Particle size distribution• Powder cohesion

Die Filling

DRAFT• Individual particles are

dropped from the top of the container, falling until they reach a stable position.

• Multiple powders can be considered with different size distributions and physical properties.

Multicomponents

DRAFT• Particle cohesivity determines the stability of structures in the powder bed.• Cohesion is considered through the critical angle, at which a particle will start

rolling.

Cohesion

DRAFTNo cohesion Cohesion

Cohesion

DRAFTParticle Rearrangement

DRAFT• Once the particles are closely packed, further increases in pressure lead to

particle deformation as the only mechanism available for volume reduction.• The compaction stage is modeled using a mixed discrete-continuum

approach.• The particle motion is constrained by a grid with dimensions of the same

order as the size of the system.• Standard Finite Element techniques are utilized to generate a grid, with the

motion of each simulated particle described in terms of the behavior of the vertexes of the grid’s nodes. Inter-particle interactions are modeled using local constitutive relations.

Compaction

DRAFT2

3

2 3

4

R

E

R

F

• The particle interactions during the compaction process have a strong influence on the mechanical properties of solid product. The types of interactions include contact forces (elastic, elastic-plastic, fully plastic) as well as tensile forces. •In the current implementation of the numerical method, the elastic contact is modeled using a Hertzian law.

2

22

1

21

21

111,

111

EEERRR

where

Ei and νi are the Young’s moduli and Poisson ratios of the particles in contact and R i are their radii. The plastic regime following the elastic response is modeled using a power law, characterized by a hardening exponent.

Compaction Forces

DRAFTparticle-particle distance

inte

rac

tio

n p

ote

nti

al

R

α

θ

Hd

Where γ is the liquid surface tension

• Caused by the formation of liquid bridges – as liquid vapors from the ambient gas phase condensate on the particle surfaces, a liquid meniscus forms, bonding particles to each other.

dH

RF

/1

cos2

Compaction Forces

DRAFT 2

212

221

2

221

221

221

221 ln

22

6 rrR

rrR

rrR

rr

rrR

rrA

21 rrR

• Van der Waals forces – short range forces, usually dominant for either small particles or during the particle fragmentation stages of compaction.

particle-particle distance

inte

rac

tio

n p

ote

nti

al

Δ – the distance between the particles.

Compaction Forces

DRAFTTertiary MixtureD and S2, S3, S4

0

2

4

6

8

10

0

2

4

6

8

Z

0

2

4

6

X Y

Z

dens

1.251.21.151.11.0510.950.90.85

Density distribution

0

2

4

6

8

10

0

2

4

6

8

Z

0

2

4

6

X Y

Z

Szz

-0.53-0.55-0.57-0.59-0.61-0.63-0.65-0.67

Pressure distribution

Initial configuration

Configuration after rearrangement

Pressure (MPa)

De

nsi

ty(g

/ml)

0 5 10 15 20 250

0.5

1

1.5

Sample Info

Mass = 0.4 g

Size = 996.1 mm3

Composition = 55% (D),

15%(S2), 15%(S3)

15%(S4)

Expected solid density =

1.68 g/ml

Long-range prediction

Pressure (MPa)

De

nsi

ty(g

/ml)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

predictexpt1expt2

Mass (g)Dimensions

(mm)Number ofParticles

ExpectedSolid Density

(g/ml)0.4 9×9×6.1 33,764 1.68 0.75

V

Filling/Rearrangement/Compaction

DRAFT• PressterTM tablet press simulator

• Set to mimic Stokes B2 press• Tooling

• Oval, deep cut• i.e., tablets are oval with domelike top and

bottom surfaces• Presster data:

• Upper compression force• Tablet x-section area • Tablet thickness • Tablet weight • radial die wall force, ejection forces, stage speed …

Presster™ Studies

DRAFTPresster data collected at different compaction forces (10kN, 15kN, and 20kN )

Presster™ Studies

DRAFT• The model can be used to simulate the evolution of the configuration of the powder bed with time as well as monitor the values of various quantities indicative of its mechanical properties. • Several different powders have been considered, both individually and in a blend to demonstrate the versatility of the method.

• Each blend can be mapped to granulation parameters by:

• Simulations vs. PressterTM Data• Error minimization

Identification of critical blend properties from 500 simulations

DRAFTSmall-Scale Study

• Provides mechanistic parameters for granulations

• The parameters can be used for generating SIMULATED surface response models for conditions other than tested using models