Powder Flow Issues in ADDoPT - Formulation · 2018-04-23 · ADVANCED DIGITAL DESIGN OF PHARMACEUTICAL THERAPEUTICS Alejandro López 1, Vincenzino Vivacqua, Mojtaba Ghadiri, Chunlei

ADVANCED DIGITAL DESIGN OF PHARMACEUTICAL THERAPEUTICS

A l e jandro Ló pez 1, V i n cenz ino V i vacqua 1, Mo jtab a G h ad ir i 1, Ch u nle i Pe i 2, J am e s E l l i ott 2, Ro b e rt H am m o nd 1 an d Kev i n J Ro b e rts 1

1U n i v e rs i t y o f L e e d s a n d 2U n i v e rs i t y o f C a m b r i d g e

Powder Flow Issues in ADDoPT

POWDER FLOW 2018: COHESIVE POWDER FLOW, 12 APRIL 2018, ROYAL SOCIETY OF CHEMISTRY, LONDON, UK

ADDoPT: A UK Government-Industry-Academia collaboration

2

Part-funded under the Advanced

Manufacturing Supply Chain Initiative (AMSCI*)

*A BIS initiative delivered by Finance Birmingham and Birmingham City Council

Instigated by the Medicines Manufacturing Industry Partnership (MMIP)

Digital Design – An Integrated Pathway from Molecules to Crystals to Medicines

3

Quality systems

Release profiles Materials properties

Particle attributes

Surface chemistry

Formulation Processing rules

Manufacturing classification Downstream Upstream

Product and Process Design

Product Performance

Crystallisation Filtration Washing Drying

Active Ingredient

(API)

Milling Blending

Compaction Coating

Primary Manufacturing - Secondary Manufacturing

15/04/2018

Define a system for top-down, knowledge-driven Digital Design and Control for drug products and their manufacturing processes

Bring together the range of predictive models

Design and control of optimised development & manufacturing processes through data analysis and first principle models

Processes Products Performance

Two-Pronged Approach in Cohesive Powder Flow Analysis

4

q Cambridge: Quasi-static characterisation and role of material properties by DEM Modelling of Ring Shear Test for powder flowability (Chunlei Pei and James Elliott)

q Leeds: Powder characterisation under dynamic conditions

Schulze Ring Shear Test RST-XS (standard)

Volume: ~ 30 ml

Cross-sectional (annular) area: 24.23 cm2

Outer radius: 32 mm; inner radius: 16 mm

16 bars (3 mm in height) at top and bottom*

Rotational speed • 7.5 mm/min; 0.05 rpm ( half of the max.) • 0.5 rpm (modelling)

8

DEM model for ring shear test ß Linear cohesion vs JKR ß Flow function (ffc) ß Particle shape ß Rescaling

Cohesion Model in DEM 6

ÿ Linear cohesion (LC) model ÿ Cohesive energy density (J/m3) ÿ Proportional to the contact area ÿ Without the work of adhesion

ÿ JKR model ÿ Surface energy (J/m2) ÿ Work of adhesion

Flow Function from DEM 7

Normal stress at pre-shear: 2081 Pa

Particle Shape 8

ω

Fconst ÿ Spherical vs Elongated ß Equivalent volume diameter ß JKR cohesion ongoing

Aspect ratio = 2

Aspect ratio = 4

Sphere N

omin

al sh

ear s

tress

(Pa)

Breakage Models The Influence of Particle Shape and Adhesion 9

The particle shape plays a role in the angle of friction of failure which also varies the intercept on the axis of shear stress.

Mod

ellin

g

Expe

rimen

tal

Work Outline: Dynamic Regime

15/04/2018

Account for environmental effects (Manipulation of surface energy) -Silanisation of glass beads and/or paracetamol

CFD-DEM Rocky DEM + Ansys Fluent

EDEM + Ansys Fluent

Effect of cohesion

Effect of shape

Effect of strain rate

Effect of air drag

DEM Rocky DEM

EDEM (Clumped spheres)

Calibration ÿ Coefficient of Restitution ÿ Friction (static, dynamic) ÿ Surface Energy – Drop test

Rheological Model

10

Validation FT4

FT4 Screw Feeder

Rocky DEM (ESSS) 11

ÿDeltahedron (faces=16, corners=10): ÿFaceted cylinder (faces=12, corners=20): ÿActual paracetamol shape (faces=25, corners=44):

ÿDodecahedron (faces=12, corners=20):

ÿTruncated polyhedron (faces=14, corners=16):

Rocky DEM (ESSS) Contact model 12

ÿContact deformation: Linear spring hysteresis model ÿ 𝑘𝑘𝑛𝑛𝑛𝑛 ÿ 𝑘𝑘𝑛𝑛𝑛𝑛 ÿ µ

ÿ Adhesion model ÿ Luding’s model1 ÿ 𝑘𝑘𝑎𝑎𝑎𝑎𝑎

1Luding, S. (2008), Granular matter, 10, 235-246.

Surface Energy vs Adhesive Stiffness 13

Comparison in terms of work of adhesion based on parameters by Thornton & Ning2

2Ning, Z. (1995). Elasto-Plastic Impact of Fine Particles and Fragmentation of Small Agglomerates. PhD Thesis. Aston University

3Pasha, M. et al. (2014), Granular matter, 16, 151-162

Luding1 Pasha et al.3

Faceted vs Rounded Particles 14

Material Property Particles Geometry

Density (kg/m3) 2450 7800

Young’s Modulus (GPa) 0.1 100

Interaction Property Particles-particles Particle-geometry

Restitution coefficient (no cohesion) 0.8 0.8

Restitution coefficient (with cohesion) 0.4 0.4

Sliding friction coefficient 0.3 0.1

Rolling friction coefficient 0.01 0.01

Parameters used in the simulations

Faceted vs Rounded Particles 14

2 mm mean volume diameter

Faceted

0

1000

2000

3000

4000

5000

0 5 10 15 20 25 30 35 40

Cum

ulat

ive

Ener

gy m

J

Penetration Depth mm

spheres

rounded cylindersL/D=3

faceted

Aspect Ratio L/D:3 # of faces:16 # of corners:10

L/D=3

Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle

15


0

500

1000

1500

2000

2500

0 5 10 15 20 25 30 35 40

Cum

ulat

ive

Ener

gy m

J


spheresdeltahedron L/D=1faceted cylinder L/D=1Actual shapeDodecahedronTruncated Polyhedron

No Cohesion

Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle

15


16

Energy Comparison at 100 mm s-1 and 5° Helix Angle

0

1000

2000

3000

4000

0 5 10 15 20 25 30 35 40

Cum

ulat

ive

Ener

gy m

J


Paracetamol Kadh=0

Truncated Poly Kadh=0

Paracetamol Kadh=0.1

Truncated Poly Kadh=0.1

Paracetamol Kadh=0.15

Truncated Poly Kadh=0.15

100

1000

10000

100000

0.01 0.1 1 10

Aver

age

Dev

iato

ric S

tres

s Pa

Tip Speed m/s

Spheres

Faceted

Regime Transition: Effect of Shape 17

2 mm mean volume diameter, no cohesion

Regime Transition: Effect of Cohesion 18

Spheres, 2 mm diameter

100

1000

10000

0.01 0.1 1 10

Aver

age

Devi

ator

ic S

tres

s Pa

Tip Speed m/s

No cohesion Kadh=0.1 Kadh=0.2

Regime Transition: Effect of Cohesion 18

Spheres, 2 mm diameter

Inertial Number 19

Inertial number, I= 𝑑𝑑𝑝𝑝𝛾𝛾𝜌𝜌𝑝𝑝𝑃𝑃

Local Rheology The process is described by a single dimensionless number

q special case: γ(dp/g)0.5, assuming that P equals to ρpdpg

q ratio between the inertial timescale dp/(P/ρp)0.5

and macroscopic deformation timescale (1/γ). 𝛾𝛾 = 𝑉𝑉𝑤𝑤 𝐿𝐿⁄

Inertial Number 19



𝜏𝜏 = 𝜇𝜇 𝐼𝐼 𝑃𝑃 𝜇𝜇 𝐼𝐼 is the bulk friction coefficient




Constitutive law:

Inertial Number 19



𝜏𝜏 = 𝜇𝜇 𝐼𝐼 𝑃𝑃 𝜇𝜇 𝐼𝐼 is the bulk friction coefficient




Constitutive law:

𝜎𝜎𝑖𝑖𝑖𝑖 = −𝑃𝑃𝛿𝛿𝑖𝑖𝑖𝑖 + 𝜏𝜏𝑖𝑖𝑖𝑖 𝜏𝜏𝑖𝑖𝑖𝑖 = 𝜂𝜂𝑒𝑒𝑒𝑒𝑒𝑒 𝐼𝐼𝜕𝜕𝑢𝑢𝑖𝑖𝜕𝜕𝑥𝑥𝑖𝑖

𝜂𝜂𝑒𝑒𝑒𝑒𝑒𝑒 =𝜇𝜇 𝐼𝐼 𝑃𝑃

𝛾𝛾

3D Generalisation1

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑇𝑇𝑆𝑆𝑇𝑇𝑆𝑆𝑇𝑇𝑆𝑆 𝐸𝐸𝐸𝐸𝐸𝐸𝑆𝑆𝐸𝐸𝑆𝑆𝐸𝐸𝐸𝐸𝑆𝑆 𝐸𝐸𝐸𝐸𝑆𝑆𝐸𝐸𝑇𝑇𝑆𝑆𝐸𝐸𝑆𝑆𝑣𝑣

1P. Jop, Y. Forterre, O. Pouliquen, A constitutive law for dense granular flows, Nature 441 (2006), 727-30.

Bulk Friction Coefficient 20

non-cohesive deltahedra

non-cohesive spheres

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.005 0.05 0.5

Bul

k fr

ictio

n co

effic

ient

m

Inertial number I

0.01 m/s

0.025 m/s

0.05 m/s

0.1 m/s

0.25 m/s

0.5 m/s

1 m/s

1.5 m/s

0

0.1

0.2

0.3

0.4

0.5

0.6

0.005 0.05 0.5

Bul

k fr

ictio

n co

effiv

ient

m

Inertial number I

0.01 m/s

0.05 m/s

0.1 m/s

0.25 m/s

0.5 m/s

1 m/s

1.5 m/s

Eq 𝜇𝜇 =𝜏𝜏𝑝𝑝

= 𝜇𝜇1 +𝜇𝜇2 − 𝜇𝜇1𝐼𝐼0 𝐼𝐼 + 1⁄

Apparent Viscosity for Non-Cohesive Deltahedra 21

0

1

2

3

4

5

6

-5.5 -4.5 -3.5 -2.5 -1.5 -0.5

ln (t

/g) P

a¥s

ln(I)

1 m/s 0.5 m/s 0.2 m/s 0.1 m/s 0.05 m/s 0.01 m/s

Faceted Particles 22

0

1

2

3

4

5

6

7

8

9

10

-5.5 -4.5 -3.5 -2.5 -1.5 -0.5

ln (t

/rpd

p2g2

)

ln(I)

spheres 2 mm

Deltahedra 2 mm

Dodecahedra 2 mm

Faceted cylinder 2 mm

Paracetamol 2 mm

Truncated Polyhedra 2 mm

Truncated cube 2 mm

no cohesion

𝜏𝜏𝜌𝜌𝑝𝑝𝑑𝑑𝑝𝑝2𝛾𝛾2

= 𝐸𝐸 𝐼𝐼

Different Cohesion Levels 23

0

2

4

6

8

10

12

-5.5 -4.5 -3.5 -2.5 -1.5 -0.5

ln (t

/rpd

p2g2

)

ln(I)

Spheres

Kadh=0 Kadh=0.1

Kadh=0.2

Screw Feeder vs FT4 24

Regions where properties are evaluated

Rotational velocity: 2, 5, 10 and 20 rad/s

0

5

10

15

20

25

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

ln (t

/rpd

p2g2

)

ln (I)

Truncated cubes -> 20 rad/s

Kadh 0.1 -> 10 rad/s

Kadh=0.2 -> 10 rad/s

Kadh=0.2 -> 10 rad/s Spheres




Kadh 0.15 -> 10 rad/s



The powder rheology in screw

feeders and FT4 are similar

Both systems – dimensionless

shear stress = f(I)




0

2

4

6

8

10

12

-5.5 -4.5 -3.5 -2.5 -1.5 -0.5ln

(t/r

pdp2

g2)

ln(I)

Screw Feeder

spheres Kadh=0

spheres Kadh=0.2

Truncated Cube Kadh=0.1, 20 rad/s




shear stress = f(I)




0

2

4

6

8

10

12

-5.5 -4.5 -3.5 -2.5 -1.5 -0.5

ln (t

/rpd

p2g2

)

ln(I)

FT4

Kadh=0 Kadh=0.1 Kadh=0.2

0

2

4

6

8

10

12

-5.5 -4.5 -3.5 -2.5 -1.5 -0.5ln

(t/r

pdp2

g2)

ln(I)

Screw Feeder

spheres Kadh=0

spheres Kadh=0.2

Truncated Cube Kadh=0.1, 20 rad/s




shear stress = f(I)



Rheological models 26

Conclusions 27

ÿ Quasi-static and dynamic shear deformation of cohesive large particles have been simulated and the incipient yield and dynamic bulk friction and ‘effective’ shear viscosity are predicted.

ÿ Particle shape influences the angle of friction in bulk failure of particles

ÿ The presence of vertices in faceted shapes strongly influences the resistance to shear deformation

ÿ Approximating real crystal shapes by truncated polyhedron shapes provides a close match in flow energy and shear deformation behaviour between the two shapes

ÿ Shear stress normalised by the inertial stress is unified for faceted shapes with and without cohesion when expressed in terms of the inertial number

ÿ The same pattern of unification prevails for the conditions in screw feeders

ÿ Experimental validation is ongoing

28

Thank you for your attention

Slide Number 1ADDoPT: A UK Government-Industry-Academia collaboration Digital Design – An Integrated Pathway from Molecules to Crystals to MedicinesTwo-Pronged Approach in Cohesive Powder Flow AnalysisSchulze Ring Shear TestCohesion Model in DEMFlow Function from DEMParticle ShapeSlide Number 9Work Outline: Dynamic RegimeRocky DEM (ESSS)Rocky DEM (ESSS) Contact modelSurface Energy vs Adhesive StiffnessFaceted vs Rounded ParticlesFaceted vs Rounded ParticlesShape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Shape Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Combined Shape and Cohesion Effect: Flow Energy Comparison at 100 mm s-1 and 5° Helix Angle Regime Transition: Effect of ShapeRegime Transition: Effect of CohesionRegime Transition: Effect of CohesionRegime Transition: Effect of CohesionRegime Transition: Effect of CohesionRegime Transition: Effect of CohesionInertial NumberInertial NumberInertial NumberBulk Friction Coefficient Apparent Viscosity for Non-Cohesive DeltahedraFaceted ParticlesDifferent Cohesion LevelsScrew Feeder vs FT4Screw Feeder vs FT4Screw Feeder vs FT4Screw Feeder vs FT4Rheological modelsConclusionsSlide Number 43

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Powder Flow Issues in ADDoPT - Formulation · 2018-04-23 · ADVANCED DIGITAL DESIGN OF PHARMACEUTICAL THERAPEUTICS Alejandro López 1, Vincenzino Vivacqua, Mojtaba Ghadiri, Chunlei