Mixing of Granular Materials in Pharmaceutical Applications: DEM Modeling and Experiments

1. Measurement of Mixing Quality In Multiphase Systems Mixing of Granular Materials in PharmaceuticalApplications: DEM Modeling and Experiments J. Doucet, F. Bonniol, F. Bertrand, J. Chaouki Departement of Chemical Engineering Ecole Polytechnique de Montréal AIChE Meeting – Minneapolis – October 17th 2011

2. Objective of this presentation • Focus on macroscopiccharacterization of mixing • Present the motivation to develop a simpler macro mixingmeasure • Idea of the proposedmeasure • Present the algorithm for implementation • Compare the performance againstotherconventional macro mixingmeasures (RSD, COV)

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

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

5. Questions asked 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?

6. The measure introduced • Measures the correlationbetweennormalized initial positions of tracers and theirnormalized positions atany time t by looking in the direction of maximal correlation. • System issaidweak-sense mixed if thereis no correlation (tends towards 0) • Wecanalsomeasure the correlationbetweentheir initial normalized positions and theirnormalized position/propertiesatany time t • System issaidstrongsense mixed if thereis no correlation (tends toward 0) • System issaidsegregative if the strongsensemeasureisdifferentfrom the weaksensemeasure. • Look at the system in the direction of maximum correlation

7. A definition The distribution of particles at time tis independent of the initial distribution with respect to space Segregation of two sets of particles with identical particle size distributions (PSD) but two different colors, which are mixed in a tumbling mixer • The distribution of particles at time tisnotindependent of the initial distribution with respect to size

8. The algorithm • Distribute tracers on the wholevelocityfield (or use all particlesfrom a lagrangian simulation) and store their initial normalized positions in • Record positions of the sameparticletracersatevery time t and store in • Calculate the correlation matrix C[dim(), dim()] between and • Calculate the matrix • Diagonalize, maximum eigenvalueis and associated eigenvector is • The mixing index isthen and direction of weak mixing is

9. Numerical case I Bidisperse spherical particles (119 696 particles, (1.3 mm; 3 mm, 50%-50% vol) r Radial component z Axial component t=5s t=0s t=1s t=2s t=3s t=4s t=10s t=20s

10. Numerical case I

11. Numerical case I • Decompositioninto axial and radial components

12. Numerical case I

13. Numerical case II Fluidization air Spheronizer with bidisperse spherical particles 88 360 particles, 1.0 mm; 2 mm, 50%-50% particlewise) Bouffard, J., Bertrand, F., Chaouki, J. (2011), Discreteelement investigation of flow patterns and segregation in a spheronizer. Subm. to Comp. Chem. Eng. FBRG

14. Numerical case II Radial component Axial component t=5s t=0s t=1s t=2s t=3s t=4s t=10s t=20s

15. Numerical case II Bouffard, J et al. 2011

16. Numerical case II 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 • 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)

18. 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

19. 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

20. Applications V-blender Cylindrical drum Remark. Number of tracers was observed to have little impact on the results Mixing is relatively poor, due to inefficient axial dispersion, as reported in the literature Radial component of the correlation decays to 0, contrary to the axial component

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 bws • Strong sense mixing measure bss • These definitions and measures provide a link between mixing time and flow dynamics • Comparison with other mixing criteria

22. Acknowledgments • NSERC • Ratiopharm • MerckFrosst • M. Heniche, J. Bouffard and P.A. Tanguy For more information • http://www.urpei.polymtl.ca/ Main reference Doucet, J., Bertrand, F., Chaouki, J. (2008) A measure of mixingfromLagrangiantracking and its application to granular and fluid flow systems. Chem. Eng. Res. Des. (86) 1313-1321.