Mixing of Granular Materials in Pharmaceutical Applications: DEM Modeling and Experiments J. Doucet, F. Bonniol, F. Bertrand, J. Chaouki Departement of Chemical Engineering Ecole Polytechnique de Montréal Measurement of Mixing Quality In Multiphase Systems AIChE Meeting – Minneapolis – October 17 th 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) 2

Motivation and background 3 (Doucet et al., 2008) (Farhat et al., 2007) Experimental work Sampling Population

Motivation and background 4 (URPEI) Numerical work Virtual sampling (URPEI) Advection

Questions asked 5 Single phase mixing How can we use all the trajectories instead of “many” single samples? How can we identify the principal directions of mixing? Special topic in multiphase systems How can we determine the presence of phase segregation and in what direction it occurs? Applications to non-intrusive Lagrangian tracking How 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 correlation 6

7 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 8

Numerical case I 9 Bidisperse spherical particles ( particles, (1.3 mm; 3 mm, 50%-50% vol) t=0s t=1st=2s t=3st=4s t=5s t=10s t=20s Radial component Axial component z r

Numerical case I 10

Numerical case I Decomposition into axial and radial components 11

Numerical case I 12

Numerical case II 13 Fluidization air FBRG Spheronizer with bidisperse spherical particles 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 14 t=0s t=1st=2s t=3st=4s t=5s t=10s t=20s Radial component Axial component

Numerical case II 15 Bouffard, J et al. 2011

Numerical case II 16 0s 1s 2s 3s 4s 5s 10s 20s Bouffard, J et al. 2011

17 Numerical case III Mixing of a viscous Newtonian fluid in a Kenics static mixer  = 78 Pa s Re = mixing elements Simulation with POLY3D TM Trajectories of 10 5 massless buoyant particles computed using an element-by-element procedure More details in Heniche and Tanguy (2005)

18 Numerical case III Poincaré sections after 0, 2, 4 and 6 mixing elements Values of  ws were computed for the particles crossing the 6 mixing elements Decay of  ws can be observed, which is due to the shuffling of the tracers Direction of  alternates between the x and y axes, due to the orientation of the mixing elements

19 Application with Lagrangian tracking Radioactive Particle Tracking Sc 46 /Na 24 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

20 Applications Mixing is relatively poor, due to inefficient axial dispersion, as reported in the literature V-blenderCylindrical 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

21 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  ws –Strong sense mixing measure  ss 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. Tanguy For more information Main reference Doucet, 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)

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