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Experimental characterization of the chaotic dynamics of cohesionless particles: application to a V-blender

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Abstract

So far, most of the investigations of the dynamics of granular material in blenders have been done in 2D tumblers due to the current lack of accurate measurement methods for the investigation of complex 3D flows. However, recent advances in the field of non-intrusive methods have paved the way to the characterization of the chaotic dynamics in 3D blenders. This work aims to present such an analysis in the case of a V-blender using radioactive particle tracking (RPT). Special attention is given to the chaotic properties of mixing by performing a time-series analysis of the position of a single tracer in motion in this blender. An original investigation of the mixing properties is also presented. More generally, this work shows that the mixing properties of a blender can be characterized by using tools of dynamical systems theory through a time-series analysis of data obtained from non-intrusive measurements.

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References

  1. Alexander A., Muzzio F.J. and Shinbrot T. (2003). Segregation patterns in V-blenders. Chem. Eng. Sci. 58: 487–496

    Article  Google Scholar 

  2. Alexander A., Shinbrot T., Johnson B. and Muzzio F.J. (2005). V-blender segregation patterns for free-flowing materials: effects of blender capacity and fill level. Int. J. Pharm. 269: 19–28

    Article  Google Scholar 

  3. Brone D., Alexander A. and Muzzio F.J. (1998). Quantitative characterization of mixing of dry powders in V-blenders. AIChE J. 44: 271–278

    Article  Google Scholar 

  4. Cassanello M., Larachi F., Marie M.N., Guy C. and Chaouki J. (1995). Experimental characterization of the solid phase chaotic dynamics in three-phase fluidization. Ind. Eng. Chem. Res. 34(9): 2971–2980

    Article  Google Scholar 

  5. Cassanello M., Larachi F., Legros R. and Chaouki J. (1999). Solids dynamics from experimental trajectory time-series of a single particle motion in gas-spouted beds. Chem. Eng. Sci. 54(13-14): 2545–2554

    Article  Google Scholar 

  6. Devaney R.L. (1988). An Introduction to Chaotic Dynamical Systems. Addison-Wesley, Reading

    Google Scholar 

  7. Doucet, J., Chaouki, J., Bertrand, F.: An extended radioactive particle tracking method for systems with irregular moving boundaries. Powder Technol. (2007). doi:10.1016/j.powtec.2006.12.019

  8. Eckmann J.P. and Ruelle D. (1985). Ergodic theory of chaos and strange attractors. Rev. Modern Phys. 57: 617–656

    Article  ADS  MathSciNet  Google Scholar 

  9. Farmer J.D., Ott E. and Yorke J.A. (1983). The dimension of chaotic attractors. Phys. D 7: 153–180

    Article  MathSciNet  Google Scholar 

  10. Grassberger P. and Procaccia I. (1983). Characterization of strange attractors. Phys. Rev. Lett. 50: 346–349

    Article  ADS  MathSciNet  Google Scholar 

  11. Grassberger P. and Procaccia I. (1983). Estimation of the Kolmogorov entropy from chaotic signal. Phys. Rev. A 28: 2591–2593

    Article  ADS  Google Scholar 

  12. Khakhar D.V., McCarthy J.J., Gilchrist J.F. and Ottino J.M. (1999). Chaotic mixing of granular materials in 2D tumbling mixers. Chaos 9: 193–205

    ADS  Google Scholar 

  13. Kuo H.P., Knight P.C., Parker D.J. and Seville J.P.K. (2005). Solids circulation and axial dispersion of cohesionless particles in a v-mixer. Powder Technol. 152: 133–140

    Article  Google Scholar 

  14. Larachi, F., Kennedy, G., Chaouki, J.: Gamma-ray detection system for 3-d particle tracking in multiphase reactors. Nucl. Instrum. Methods Phys. Res. A A338(2-3), 568–576 (1994). http://dx.doi.org/10.1016/0168-9002(94)91343-9

  15. Lemieux, M., Leonard, G., Doucet, J., Leclaire, L.A., Bertrand, F., Chaouki, J.: Large scale numerical investigation of granular mixing in a V-blender using a discrete element method. Powder Technol. (2007). doi:10.1016/j.powtec.2006.12.007

  16. Moakher M., Shinbrot T. and Muzzio F.J. (2000). Experimentally validated computations of flow, mixing and segregation of non cohesive grains in 3D tumbling blenders. Powder Technol. 109: 58–71

    Article  Google Scholar 

  17. Muzzio F.J., Goodridge C.L., Alexander A., Arratia P., Yang H., Sudah O. and Mergen G. (2003). Sampling and characterization of pharmaceutical powders and granular blends. Int. J. Pharm. 250: 51–64

    Article  Google Scholar 

  18. Ottino J.M. (1989). The kinematics of mixing: stretching, chaos and transport. Cambridge University Press, New York

    MATH  Google Scholar 

  19. Ottino J.M. and Khakhar D.V. (2001). Fundamental research in heaping, mixing and segregation of granular materials: challenges and perspectives. Powder Technol. 121: 117–122

    Article  Google Scholar 

  20. Rosenstein M.T., Collins J.J. and De~Luca C. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D 65: 117–134

    Article  MATH  MathSciNet  Google Scholar 

  21. Sherritt R.G., Chaouki J., Mehrotra A.K. and Behie L.A. (2003). Axial dispersion in the three-dimensional mixing of particles in a rotating drum reactor. Chem. Eng. Sci. 58(2): 401–415

    Article  Google Scholar 

  22. Sprott J.C. (2003). Chaos and Time-Series Analysis. Oxford University Press, New York

    MATH  Google Scholar 

  23. Sundaresan S., Eaton J., Koch D.L. and Ottinio J.M. (2003). Appendix 2: report of study group on disperse flow. Int. J. Multiph. Flow 29: 1069–1087

    Article  Google Scholar 

  24. Takens F. (1981). Lecture Notes in Mathematics, vol. 898. Springer, Heidelberg

    Google Scholar 

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Authors and Affiliations

  1. Department of Chemical Engineering, École Polytechnique de Montreal, P.O. Box 6079, Station Centre-Ville, Montreal, QC, Canada, H3C 3A7

    J. Doucet, F. Bertrand & J. Chaouki

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  1. J. Doucet
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  2. F. Bertrand
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  3. J. Chaouki
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Correspondence to J. Doucet.

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Doucet, J., Bertrand, F. & Chaouki, J. Experimental characterization of the chaotic dynamics of cohesionless particles: application to a V-blender. Granular Matter 10, 133–138 (2008). https://doi.org/10.1007/s10035-007-0075-x

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