Synchronous universal droplet logic and control

Abstract

Droplets are versatile digital materials; they can be produced at high throughput, perform chemical reactions as miniature beakers and carry biological entities. Droplets have been manipulated with electric, optical, acoustic and magnetic forces, but all these methods use serial controls to address individual droplets. An alternative is algorithmic manipulation based on logic operations that automatically compute where droplets are stored or directed, thereby enabling parallel control. However, logic previously implemented in low-Reynolds-number droplet hydrodynamics is asynchronous and thus prone to errors that prevent scaling up the complexity of logic operations. Here we present a platform for error-free physical computation via synchronous universal logic. Our platform uses a rotating magnetic field that enables parallel manipulation of arbitrary numbers of ferrofluid droplets on permalloy tracks. Through the coupling of magnetic and hydrodynamic interaction forces between droplets, we developed AND, OR, XOR, NOT and NAND logic gates, fanouts, a full adder, a flip-flop and a finite-state machine. Our platform enables large-scale integration of droplet logic, analogous to the scaling seen in digital electronics, and opens new avenues in mesoscale material processing.

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Figure 1: Principle of operation and experimental set-up.
Figure 2: Synchronous droplet propagation.
Figure 3: Characterization of synchronous limits of propagation and synchronous droplet generation.
Figure 4: Combinational droplet logic: basic gates.
Figure 5: Combinational droplet logic: composite gates.
Figure 6: Sequential droplet logic: set/reset flip-flop and fundamental finite-state machine.

References

  1. 1

    Zuse, K. Calculating Space MIT Technical Translation AZT-70-164-GEMIT (Massachusetts Institute of Technology, 1970).

    Google Scholar 

  2. 2

    Landauer, R. The physical nature of information. Phys. Lett. A 217, 188–193 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  3. 3

    Wheeler, J. A. Information, physics, quantum: The search for links. Proc. III International Symposium on Foundations of Quantum Mechanics 354–368 (1989).

  4. 4

    Floyd, T. Digital Fundamentals 10th edn (Prentice Hall, 2008).

    Google Scholar 

  5. 5

    Chee, M. et al. Accessing genetic information with high-density DNA arrays. Science 274, 610–614 (1996).

    ADS  Article  Google Scholar 

  6. 6

    Winfree, E., Liu, F., Wenzler, L. A. & Seeman, N. C. Design and self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998).

    ADS  Article  Google Scholar 

  7. 7

    Mao, C., LaBean, T. H., Reif, J. H. & Seeman, N. C. Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407, 493–496 (2000).

    ADS  Article  Google Scholar 

  8. 8

    Teh, S-Y., Lin, R., Hund, L-H. & Lee, A. P. Droplet microfluidics. Lab Chip 8, 198–220 (2008).

    Article  Google Scholar 

  9. 9

    Garstecki, P., Fuerstman, M. J., Stone, H. A. & Whitesides, G. M. Formation of droplet and bubbles in a microfluidic T-junction-scaling and mechanism of break-up. Lab Chip 6, 437–446 (2006).

    Article  Google Scholar 

  10. 10

    Schwarz, J. A., Vykoukal, J. V. & Gascoyne, P. R. Droplet-based chemistry on a programmable micro-chip. Lab Chip 4, 11–17 (2004).

    Article  Google Scholar 

  11. 11

    Song, H., Chen, D. L. & Ismagilov, R. F. Reactions in droplets in microfluidic channels. Angew. Chem. Int. Ed. 45, 7336–7356 (2006).

    Article  Google Scholar 

  12. 12

    Schneider, T., Kreutz, J. & Chiu, D. T. The potential impact of droplet microfluidics in biology. Anal. Chem. 85, 3476–3482 (2013).

    Article  Google Scholar 

  13. 13

    Gascoyne, P. R. et al. Dielectrophoresis-based programmable fluidic processors. Lab Chip 4, 299–309 (2004).

    Article  Google Scholar 

  14. 14

    Link, D. R. et al. Electric control of droplets in microfluidic devices. Angew. Chem. Int. Ed. 45, 2556–2560 (2006).

    Article  Google Scholar 

  15. 15

    Ahn, K. et al. Dielectrophoretic manipulation of drops for high-speed microfluidic sorting devices. Appl. Phys. Lett. 88, 024104 (2006).

    ADS  Article  Google Scholar 

  16. 16

    Brzobohaty, O., Siler, M., Jezek, J., Jakl, P. & Zemanek, P. Optical manipulation of aerosol droplet using a holographic dual and single beam trap. Opt. Lett. 38, 4601–4604 (2013).

    ADS  Article  Google Scholar 

  17. 17

    Wixforth, A. et al. Acoustic manipulation of small droplets. Anal. Bioanal. Chem. 379, 982–991 (2004).

    Article  Google Scholar 

  18. 18

    Pamme, N. Magnetism and microfluidics. Lab Chip 6, 24–38 (2006).

    Article  Google Scholar 

  19. 19

    Prakash, M. & Gershenfeld, N. Microfluidic bubble logic. Science 315, 832–835 (2007).

    ADS  Article  Google Scholar 

  20. 20

    Cheow, L. F., Yobas, L. & Kwong, D-L. Digital microfluidics: Droplet based logic gates. Appl. Phys. Lett. 90, 054107 (2007).

    ADS  Article  Google Scholar 

  21. 21

    Cybulski, O. & Garstecki, P. Dynamic memory in a microfluidic system of droplets travelling through a simple network of microchannel. Lab Chip 10, 484–493 (2010).

    Article  Google Scholar 

  22. 22

    Fuertman, M. J., Gartecki, P. & Whitesides, G. M. Coding/decoding and reversibility of droplet trains in microfluidic networks. Science 315, 828–832 (2007).

    ADS  Article  Google Scholar 

  23. 23

    Chang, H. Magnetic Bubble Technology: Integrated-Circuit Magnetics for Digital Storage and Processing (IEEE Press and Wiley, 1975).

    Google Scholar 

  24. 24

    Romankiw, L., Slusarczuk, M. M. G. & Thompson, D. A. Liquid magnetic bubbles. IEEE Trans. Magn. 11, 25–28 (1975).

    ADS  Article  Google Scholar 

  25. 25

    Donolato, M. et al. Magnetic domain wall conduits for single cell applications. Lab Chip 11, 2976–2983 (2011).

    Article  Google Scholar 

  26. 26

    Lim, B. et al. Magnetophoretic circuits for digital control of single particles and cells. Nature Commun. 5, 3846 (2014).

    ADS  Article  Google Scholar 

  27. 27

    White, R. Viscous Fluid Flow 3rd edn (McGraw-Hill, 2006).

    Google Scholar 

  28. 28

    Rabaud, D. et al. Manipulation of confined bubbles in a thin microchannel: Drag and acoustic Bjerknes forces. Phys. Fluids 23, 042003 (2011).

    ADS  Article  Google Scholar 

  29. 29

    McCaig, M. & Clegg, A. G. Permanent Magnets in Theory and Practice 2nd edn (Pentech Press, 1985).

    Google Scholar 

  30. 30

    Jiles, D. Introduction to Magnetism and Magnetic Materials 2nd edn (CRC Press, 1998).

    Google Scholar 

  31. 31

    Dangla, R. 2D Droplet Microfluidics Driven by Confinement Gradients Thesis, Ch. 3 (École Polytechnique 2012).

  32. 32

    Nguyen, N-T., Ng, K. M. & Huang, X. Maninulation of ferrofluid droplet using planar coils. Appl. Phys. Lett. 89, 052509 (2006).

    ADS  Article  Google Scholar 

  33. 33

    Toussaint, R., Akselvoll, J., Helgesen, G., Skjeltorp, A. T. & Flekkoy, E. G. Interaction model for magnetic holes in a ferrofluid layer. Phys. Rev. E 69, 011407 (2004).

    ADS  Article  Google Scholar 

  34. 34

    Gans, B. J., Blom, C., Philipse, A. P. & Mellema, J. Linear viscoelasticity of an inverse ferrofluid. Phys. Rev. E 60, 4518–4527 (1999).

    ADS  Article  Google Scholar 

  35. 35

    Gans, B. J., Duin, N. J., van den Ende, D. & Mellema, J. The influence of particle size on the magnetorheological properties of an inverse ferrofluid. J. Chem. Phys. 113, 2032–2042 (2000).

    ADS  Article  Google Scholar 

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Acknowledgements

We acknowledge all members of the Prakash Lab for useful discussions. G.K. is supported by the Onassis Foundation and the A.G. Leventis Foundation. J.S.C. is supported by a grant from the Gordon and Betty Moore Foundation. M.P. is supported by the Pew Foundation, the Moore Foundation, the Keck Foundation, a Terman Fellowship and a NSF Career Award. We acknowledge S. X. Wang and A. El-Ghazaly for providing an alternating gradient magnetometer and helping with measurements of the Permalloy material. We also acknowledge Z. Hossain with regards to the C and Python codes written to obtain and read the data from the embedded microcontrollers.

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Contributions

G.K. and M.P. designed the research and planned the experiments. G.K. performed the micro-fabrication, conducted the experiments and developed image processing tools. G.K. and J.S.C. developed the reduced-order models. G.K. derived the scaling laws and developed the logic gates. All authors analysed the data, interpreted the results and wrote the manuscript.

Corresponding author

Correspondence to Manu Prakash.

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Competing interests

A patent has been filed by Stanford University based on ideas presented here (PCT/US2013/056821).

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Katsikis, G., Cybulski, J. & Prakash, M. Synchronous universal droplet logic and control. Nature Phys 11, 588–596 (2015). https://doi.org/10.1038/nphys3341

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