Mixing of Granular Materials in PharmaceuticalApplications: DEM Modeling and Experiments

J. Doucet, F. Bonniol, F. Bertrand, J. ChaoukiDepartement of Chemical Engineering

Ecole Polytechnique de Montréal

Measurement of Mixing Quality In Multiphase Systems

AIChE Meeting – Minneapolis – October 17th 2011

Objective of this presentation

• Focus on macroscopic characterization of mixing

• Present the motivation to develop a simpler macro mixing measure

• Idea of the proposed measure• Present the algorithm for implementation• Compare the performance against other

conventional macro mixing measures (RSD, COV)

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Motivation and background

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(Doucet et al., 2008)

(Farhat et al., 2007)

Experimental work

 

 

 

 

Sampling

Population

Motivation and background

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(URPEI)

Numerical work

 

 

Virtual sampling

(URPEI)

Advection

Questions asked

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Single phase mixingHow can we use all the trajectories instead of “many” single samples?How can we identify the principal directions of mixing?

Special topic in multiphase systemsHow can we determine the presence of phase segregation and in what direction it occurs?

Applications to non-intrusive Lagrangian trackingHow can we use particle tracking data to quantify macroscopic mixing?

The measure introduced

• Measures the correlation between normalized initial positions of tracers and their normalized positions at any time t by looking in the direction of maximal correlation.– System is said weak-sense mixed if there is no correlation

(tends towards 0)• We can also measure the correlation between their initial

normalized positions and their normalized position/properties at any time t– System is said strong sense mixed if there is no correlation

(tends toward 0)– System is said segregative if the strong sense measure is

different from the weak sense measure.• Look at the system in the direction of maximum

correlation6

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A definition

The distribution of particles at time t is independent of the initial distribution with respect to space

The distribution of particles at time t is not independent of the initial distribution with respect to size

Segregation of two sets of particles with identical particle size distributions (PSD) but two different colors,

which are mixed in a tumbling mixer

The algorithm

• Distribute tracers on the whole velocity field (or use all particles from a lagrangian simulation) and store their initial normalized positions in

• Record positions of the same particle tracers at every time t and store in

• Calculate the correlation matrix C[dim(), dim()] between and

• Calculate the matrix • Diagonalize , maximum eigenvalue is and associated

eigenvector is • The mixing index is then and direction of weak mixing is

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Numerical case I

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Bidisperse spherical particles (119 696 particles, (1.3 mm; 3 mm, 50%-50% vol)

t=0s t=1s t=2s t=3s t=4s t=5s t=10s t=20s

Radial component

Axial component z

r

Numerical case I

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𝑤1=(0,1)

Numerical case I

• Decomposition into axial and radial components

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Numerical case I

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Numerical case II

13Fluidization airFBRG

Spheronizer with bidisperse spherical particles 88 360 particles, 1.0 mm; 2 mm, 50%-50% particlewise)

Bouffard, J., Bertrand, F., Chaouki, J. (2011), Discrete element investigation of flow patterns and segregation in a spheronizer. Subm. to Comp. Chem. Eng.

Numerical case II

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t=0s t=1s t=2s t=3s t=4s t=5s t=10s t=20s

Radial component

Axial component

Numerical case II

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Bouffard, J et al. 2011

Numerical case II

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0s

1s

2s

3s

4s

5s

10s

20sBouffard, J et al. 2011

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Numerical case III

Mixing of a viscous Newtonian fluid in a Kenics static mixer

• m = 78 Pa s• Re = 0.01• 6 mixing elements• Simulation with POLY3DTM • Trajectories of 105 massless buoyant particles computed

using an element-by-element procedure• More details in Heniche and Tanguy (2005)

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Numerical case III

Poincaré sections after 0, 2, 4 and 6 mixing elements

•Values of bws were computed for the 6 749 particles crossing the 6 mixing elements•Decay of bws can be observed, which is due to the shuffling of the tracers•Direction of a alternates between the x and y axes, due to the orientation of the mixing elements

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Application with Lagrangian tracking

Radioactive Particle Tracking• Sc46 /Na24 used as isotope• Single radioactive tracer• 10 NaI detectors

Assuming that ergodicity holds, which means that the time average of one particle is equal to the population average of many particles, many particle trajectories can be built

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Applications

Mixing is relatively poor, due to inefficient axial dispersion, as reported in the literature

V-blender Cylindrical drum

Radial component of the correlation decays to 0, contrary to the axial component

Remark. Number of tracers was observed to have little impact on the results

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Concluding remarks

• Two definitions of mixing have been introduced, both of which are applicable to dry granular and fluid flow systems– Mixing in the weak sense is concerned with the correlation

between the initial position of particles and their later position, irrespective of their properties (e.g. size, density, color)

– Mixing in the strong sense which, in addition to the position of the particles, is concerned by their properties

• These two definitions have led to two mixing measures– Weak sense mixing measure bws

– Strong sense mixing measure bss

• These definitions and measures provide a link between mixing time and flow dynamics

• Comparison with other mixing criteria

Acknowledgments

• NSERC• Ratiopharm• Merck Frosst• M. Heniche, J. Bouffard and P.A. TanguyFor more information• http://www.urpei.polymtl.ca/

Main referenceDoucet, J., Bertrand, F., Chaouki, J. (2008) A measure of mixing from Lagrangian tracking and its application to granular and fluid flow systems. Chem. Eng. Res. Des. (86) 1313-1321.

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