1. Chaos in droplet based microfluidics Patrick TABELING, Herve WILLAIME, Valessa BARBIER, Laure MENETRIER, Alice Mc DONALD ESPCI, MMN, 75231 Paris 0140795153

2. Complex dynamical behavior is not unfrequent in droplet based microfluidics

3. From a dynamical point of view, a droplet emitter is a a non linear oscillator Droplets are emitted periodically H. Willaime, V. Barbier, P. Tabeling, Phys. Rev. Lett., 96, 054501 (2006) Local intensity measurement

4. Perturbing the emitter with a mechanical actuator gives rise to complex dynamics PDMS Working channel Actuation channel Local intensity measurement H. Willaime, V. Barbier, P. Tabeling, Phys. Rev. Lett., 96, 054501 (2006) GLASS

5. Water + Fluorescein Oil + Span 80 actuator Movie slowed down three times Natural emission frequency = 5 Hz There exists frequency locking states

6. Periodic state f f = 1.5 Hz Quasi-periodic state f f =0.7 Hz There also exists quasi periodic states

7. Different regimes obtained at different forcing amplitudes and frequencies Quasi periodic Periodic 1/3 Periodic 1/1 Periodic 2/3

8. 0.2 0.30.40.50.71 (a) (b) W Arnold tongues and devil staircases in microdroplet flows H. Willaime, V. Barbier, P. Tabeling, Phys. Rev. Lett., 96, 054501 (2006)

9. Why is it so ? The parametric excitation Oscillating plate

10. The mechanism leading to complex behavior is parametric excitation Step 1 : The emission frequency of an individual emitter depends of the water flow-rate QwQw QwQw QOQO Step 2 : The actuator modulates Q w and therefore modulates the frequency

11. Devil staircases also exist with electric fields

12. Tongues staircases…

13. water oil Feeding the droplet computer requires droplet emittors connected to each other through the device oil water Droplet-based microfluidic computer Output

14. The behaviour of an elementary parallel system - Section of the channels : 250 x 40 µm 2 water oil sensors 10 mm V. Barbier, H. Willaime, F. Jousse, P. Tabeling, Phys Rev E (2006)

15. SYNCHRONIZED REGIMES

16. Synchronized regimes are favorable for the production of monodisperse emulsions

17. Surprisingly, chaos frequently appears in this system V. Barbier, H. Willaime, F. Jousse, P. Tabeling, Phys Rev E (2006)

18.  P/(P w -P 0) ≈ 1% Synchronized regimes may be sensitive to small imperfections

19. RORO RORO R’ S RSRS QWQW QWQW QOQO qoqo q’ o q’ s qsqs P P’ PSPS P0P0 The mechanism is also parametric excitation Model g = coupling parameter

20. The main regimes (locked, QP, chaos) are qualitatively reproduced by the dynamical system we used Modelling an elementary parallel system g=0.7 g=0.35 g=0.05

21. Dynamical phenomena must be taken seriously in droplet-based microfluidic systems

22. water oil An ubiquitous presence of chaos may jeopardize the possibility of devising droplet based computers oil water Droplet-based microfluidic computer Output R R R R

23. Microfluidic computer M does not include just resistance-type terms, but something generally more complicated InputOutput May microfluidic computers have a rich dynamics ?

24. Microfluidic computer InputOutput Should we decouple each element from each other to avoid complex behavior ? X + R?

25. Complex dynamical phenomena must be taken seriously in droplet-based microfluidic systems Conclusion

26. MMN 2004-2007