Nonlinear Dynamics

, Volume 92, Issue 1, pp 75–84 | Cite as

Nonlinear systems synchronization for modeling two-phase microfluidics flows

Original Paper
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Abstract

The aim of this work is to identify a class of models that can represent the two-phase microfluidic flow in different experimental conditions. The identification procedure adopted is based on the nonlinear systems synchronization theory. The experimental time series were assumed as the asymptotic behavior of a generic state variable of an unknown Master system, and this information was used to drive a second Slave system, with a known model and undefined parameters. To reach the convergence between the time evolutions of the two systems, so the flow identification, an error was evaluated and optimized by tuning the parameters of the Slave system, through genetic algorithm. The Chua’s oscillator has been chosen as a Slave model, and an optimal parameters set of Chua’s system was identified for each of the 18 experiments. As proof of concept on approach validity, the changes in the parameters set in the different experimental conditions were discussed taking into account the results of the nonlinear time series analysis. The results confirm the possibility with a single model to identify a variety of flow regimes generated in two-phase microfluidic processes, independently of how the processes have been generated, no directed relations with the input flow rate used are in the model.

Keywords

Master–Slave coupling Chua’s model Genetic algorithm 
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References

  1. 1.
    Janasek, D., Franzke, J., Manz, A.: Scaling the design of miniaturized chemical-analysis system. Nature 42, 374–380 (2006)CrossRefGoogle Scholar
  2. 2.
    Whitesides, G.M.: The origin and the future of microfluidics. Nature 42, 368–373 (2006)CrossRefGoogle Scholar
  3. 3.
    Tabeling, P.: Introduction to Microfluidics. Oxford University Press, New York (2005)Google Scholar
  4. 4.
    Serizawa, A., Feng, Z., Kawara, K.: Two-phase flows in microchannels. Exp. Therm. Fluid Sci. 26, 703–714 (2002)CrossRefGoogle Scholar
  5. 5.
    Worner, M.: Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications. Microfluid. Nanofluidics 12, 841–886 (2012)CrossRefGoogle Scholar
  6. 6.
    Bruus, H.: Theoretical Microfluidics, Oxford Master Seies in Condensed Matter Physics. Oxford University Press, Oxford (2008)Google Scholar
  7. 7.
    Cairone, F., Gagliano, S., Bucolo, M.: Experimental study on the slug flow in a serpentine microchannel. Int. J. Exp. Therm. Fluid Sci. 76, 34–44 (2016)CrossRefGoogle Scholar
  8. 8.
    Schembri, F., Sapuppo, F., Bucolo, M.: Experimental identification of nonlinear dynamics in microfluidic bubbles’ flow. Nonlinear Dyn. 67, 2807–2819 (2012)Google Scholar
  9. 9.
    Schembri, F., Bucolo, M.: Periodic input flows tuning nonlinear two-phase dynamics in a snake microchannel. Microfluid. Nanofluidics 11, 189–197 (2011)CrossRefGoogle Scholar
  10. 10.
    Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)CrossRefMATHGoogle Scholar
  11. 11.
    Caponetto, R., Fortuna, L., Manganaro, G., Xibilia, M.: Chaotic system identification via genetic algorithm. Genet. Algorithms Eng. Syst. 414, 170–174 (1995)Google Scholar
  12. 12.
    Madan, R.N.: Chua’s Citcuit: A Paradigm for Chaos. Vol. 1. Series B. World Scientific Publishing, Singapore (1993)CrossRefGoogle Scholar
  13. 13.
    Madan, R.N.: Chua’s Circuit: A Paradigm for Chaos. In: World Scientific Series on Nonlinear Science, SERIE B vol. 1 (1993)Google Scholar
  14. 14.
    Golbert, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, Boston (1989)Google Scholar
  15. 15.
    Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (2004)MATHGoogle Scholar
  16. 16.
    Boccaletti, S., Kurths, J., Osipov, G., Vallardes, D., Zhou, C.: The synchronization of chaotic systems. Phys. Rep. 366, 1–101 (2002)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Boccara, N.: Modeling Complex Systems. Springer, New York (2004)MATHGoogle Scholar
  18. 18.
    Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78, 4193–4196 (1997)CrossRefMATHGoogle Scholar
  19. 19.
    Dormand, J.R., Prince, P.J.: A family of embedded Runge–Kutta formulae. J. Comput. Appl. Math. 6, 19–26 (1980)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Fabiana Cairone
    • 1
  • Princia Anandan
    • 1
  • Maide Bucolo
    • 1
  1. 1.Dipartimento di Ingegneria Elettrica Elettronica e Informatica DIEEIUniversità degli studi di CataniaCataniaItaly

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