Particles must be well-dispersed in a fluid medium before particle size measurements can be done. Engineers at Malvern Instruments Ltd. used ANSYS Maxwell to take a new magnetic drive design, optimize it and produce a solution that comfortably drives any magnetic stirrer bead over the required range of stir speeds and dispersant viscosities to achieve sufficient particle dispersion.

1. Modelling a Magnetic Stirrer Coupling for
the Dispersion of Particulate Materials
1 © 2014 ANSYS, Inc. October 1, 2014 ANSYS Confidential
2014 Convergence Conference
David Maffioli
Senior Development Scientist
Malvern Instruments Ltd.

2. Modelling a Magnetic Stirrer Coupling for the
Dispersion of Particulate Materials
David Maffioli
Senior Development Scientist
Malvern Instruments Ltd.
Ansys Convergence Regional Conference 2014

3. Outline
› Particle Size
› Laser diffraction and particulate dispersion
› New dispersion system
› Modelling a magnetic stirrer coupling in Maxwell
› Model verification - using the Malvern Kinexus
› Optimisation - with Maxwell-Optimetrics
› Parametric study of design performance
› Prototype testing
› Conclusions and Questions

4. Particle Size
› The particle size has a direct influence on material properties
such as:
Reactivity or dissolution rate - e.g. catalysts, tablets.
Stability in suspension – e.g. sediments, paints.
Efficacy of delivery – e.g. asthma inhalers.
Texture and feel – e.g. food ingredients.
Appearance – e.g. powder coatings and inks.
Flowability and handling – e.g. granules.
Viscosity – e.g. nasal sprays.
Packing density and porosity
– e.g. ceramics.

5. Laser diffraction in 60 seconds
Mastersizer 3000
Particle size range: 10nm – 3.5mm
0 20 40 60 80 100 120 140 160 180
6
10
5
10
4
10
3
10
2
10
1
10
0
10
-1
10
-2
10
Intensity of Un, p and s polarised light, between [0, 180], scattered from 1.500um radius sphere
Unpolarised
P-polarisation
S-polarisation
Scattering by latex
spheres in water.
Size
%
Analysis approximates to:
Intensity (log scaled)
Angle
where: A = Model matrix (Mie Fraunhofer theory)
x = Particle Size Distribution
b = Data (flux pattern)

6. Dispersion of particulates
› The dispersion of the sample is critical when using light-scattering
techniques.
› Dry
› Wet
› For accurate measurement we require:
• Correct concentration
• Stable and bias free sampling
• Rapid agglomerate dispersion

7. New Dispersion System
Magnetic stirrer bead
Laser
Magnetic drive
Air Gap
Glass
Dispersant

8. Drive Coupling Anomalies
› Coverage of PTFE coating over the magnetic bead was variable.
› Large variation in bead-magnet strength.
› This variation was enough to cause the bead to
decouple - at half speed - with about 1 in every
5 beads.
1
0.5
0
-2 -1.5 -1 -0.5 0 0.5 1
-0.5
-1
-1.5
-2
-2.5
-3
Z offset from centre in mm
X offset from centre in mm

9. Initial modelling – Design A
N
28mm
diameter
flywheel.
5mm depth
Magnet cylinders
have a 7.5mm
diameter with a
3.2mm depth.
9mm offset from
centre
› Modelling with Maxwell modeller
› Automated using Python script.

10. Design B
› Experimental Results favoured design B.
› Modelling suggested an increase in the pull
force magnitude (nominal bead position).
› |Aforce| = 24mN.
› |Bforce| = 40mN.

11. Model Verification - using the Malvern Kinexus
› Torque measured with bead rotated between 0º and
180º.
› Gap between drive and bead varied between 2mm
and 8mm.
› Correlation factors of
2.3 and 1.3.
350
300
250
200
150
100
50
0
Correlation between Rheology results and Maxwell
0 20 40 60 80 100 120 140 160 180
Torque in μN
Angle of rotation (degrees)
2mm Maxwell
2mm Rh Good
2mm Rh Bad
4mm Maxwell
4mm Rh Good
4mm Rh Bad
6mm Maxwell
6mm Rh Good
6mm Rh Bad
8mm Maxwell
8mm Rh Good
8mm Rh Bad

12. B2 C D
E F
Design proliferation
› Experimentation run
concurrently with modelling.
› Buy and try approach.
Modelling Strategy:
› Parametrically
Model
› Optimise
› Compare

13. Design Optimisation
Displacement in x
› Simplest Hypothesis - maximise
restorative force in x and z:
Maximise

14. .

15. › Transform metric to allow us to use
minimisation:
Minimise

16. .

17. Displacement in z
› Optimisation – having applied a 2mm
offset in x and z.

18. Optimisation Results
*
* Force applied to bead displaced by 2mm in x and z.

19. H-Field Plots of Optimised Designs
A B C
D E F

20. Parametric study
› Parametric force study F(x, z, θ) in the
domain x ∈ [0, 6], z ∈ [0, 6] and bead
rotation θ ∈ [0°, 10°].
› Matlab used for averaging, interpolation
and plotting.
› Designs C and A gave the best
restorative force with A providing the
best force balance.
› Gain better understanding of design
performance over x, z plane with
different bead orientations.

21. Average X-Force Map (mN, θ ∈ [0°, 10°])
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
15
10
5
0
-5
-10
This design gives the best

22. Average Z-Force Map (mN, θ = [0°, 10°])
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
20
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
20
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
20
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
20
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
20
15
10
5
0
-5
-10
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
20
15
10
5
0
-5
-10

23. Average Forcexyz Magnitude (mN, θ = [0°, 10°])
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6
6
5
4
3
2
1
0
X offset (mm)
Z offset (mm)
35
30
25
20
15
10
5
0

24. Torque Applied To Bead At Different Angles
210
160
110
60
10
› Experiments found typical bead lag angles of between 15º and 25º.
› Maxwell shows very little difference between the torque in the
interval [0º, 30º] - design F being the exception.
-40
0 20 40 60 80 100 120 140 160 180
Torque in ?N
Lag angle in degrees
A
B
B2
C
D2
E
F
Poly. (A)
Poly. (B)
Poly. (B2)
Poly. (C)
Poly. (D2)
Poly. (E)
Poly. (F)

25. Empirical Testing
› Analysis inferred that an optimised Design A
would provide the best performance.
› Tested using a rapidly prototyped design with:
Mixture of good and bad beads.
Range of drive speeds.
Range of dispersant viscosities.
› All tests passed.
Design A: lag ~ 17º at
1800rpm

26. Production Ready Design
› A parametric analysis was performed to check optimality.
1
0.99
0.98
0.97
0.96
0.95
0.94
Normalised Scalar Projections
5 5.5 6 6.5 7 7.5 8 8.5 9
Magnet offset (mm)
Scalar projection
in x and z
Full scalar
projection
Poly. (Scalar
projection in x and
z)
Poly. (Full scalar
projection)

27. Conclusions
› Maxwell allowed us to:
Accurately model an existing set of designs.
Produce simulation results which correlated well with
experimental data.
Parametrically model further design ideas.
Optimise each design - allowing us to make a fair comparison.
Compare the performance of each optimised design using a
parametric study.
Draw the correct inference from the simulation results.
› Ultimately, we were able to take a deprecated design, optimise it,
and produce a solution which could comfortably drive any bead,
over the required range of stir speeds and dispersant viscosities.

28. Questions?

29. Acknowledgements
› Ansys - David Twyman
› Malvern Instruments – Dr Jon Powell and David Stringfellow