Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Synchronous universal droplet logic and control

Nature Physics volume 11, pages 588–596 (2015)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

References

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

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Stanford University, 450 Serra Mall, California 94305, USA

    Georgios Katsikis & James S. Cybulski

  2. Department of Bioengineering, Stanford University, 450 Serra Mall, California 94305, USA

    Manu Prakash

Authors
  1. Georgios Katsikis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James S. Cybulski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manu Prakash
    View author publications

    You can also search for this author in PubMed Google Scholar

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.

Ethics declarations

Competing interests

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

Supplementary information

Supplementary Information

Supplementary Information (PDF 3748 kb)

Supplementary Movie

Supplementary Movie 1 (MOV 13828 kb)

Supplementary Movie

Supplementary Movie 2 (MOV 2041 kb)

Supplementary Movie

Supplementary Movie 3 (MOV 2444 kb)

Supplementary Movie

Supplementary Movie 4 (MOV 2305 kb)

Supplementary Movie

Supplementary Movie 5 (MOV 5713 kb)

Supplementary Movie

Supplementary Movie 6 (MOV 8722 kb)

Supplementary Movie

Supplementary Movie 7 (MOV 8382 kb)

Supplementary Movie

Supplementary Movie 8 (MOV 2015 kb)

Supplementary Movie

Supplementary Movie 9 (MOV 807 kb)

Supplementary Movie

Supplementary Movie 10 (MOV 1030 kb)

Supplementary Movie

Supplementary Movie 11 (MOV 1686 kb)

Supplementary Movie

Supplementary Movie 12 (MOV 5682 kb)

Supplementary Movie

Supplementary Movie 13 (MOV 4280 kb)

Supplementary Movie

Supplementary Movie 14 (MOV 809 kb)

Supplementary Movie

Supplementary Movie 15 (MOV 5711 kb)

Supplementary Movie

Supplementary Movie 16 (MOV 12134 kb)

Supplementary Movie

Supplementary Movie 17 (MOV 17339 kb)

Supplementary Movie

Supplementary Movie 18 (MOV 3571 kb)

Supplementary Movie

Supplementary Movie 19 (MOV 4167 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3341

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing