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Synchronous universal droplet logic and control


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.


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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




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).

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