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Long-range orientational order in two-dimensional microfluidic dipoles

Nature Physics volume 10, pages 140–144 (2014)Cite this article

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Abstract

Dynamic restructuring and ordering are prevalent in driven many-body systems with long-range interactions, such as sedimenting particles1,2,3, dusty plasmas4, flocking animals5,6,7 and microfluidic droplets8. Yet, understanding such collective dynamics from basic principles is challenging because these systems are not governed by global minimization principles, and because every constituent interacts with many others. Here, we report long-range orientational order of droplet velocities in disordered two-dimensional microfluidic droplet ensembles. Droplet velocities exhibit strong long-range correlation as 1/r2, with a four-fold angular symmetry. The two-droplet correlation can be explained by representing the entire ensemble as a third droplet. The correlation amplitude is non-monotonous with density owing to excluded-volume effects. Our study puts forth a many-body problem with long-range interactions that is solvable from first principles owing to the reduced dimensionality, and introduces new experimental tools to address open problems in many-body non-equilibrium systems9,10.

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Figure 1: The microfluidic 2D droplet ensemble and velocity fluctuations.
Figure 2: Velocity correlations.
Figure 3: Velocity variance determined by competition of single- and dual-droplet effects.

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Acknowledgements

This work was supported by a Yeda-Sela Grant (R.H.B-Z). T.B. was supported by the Cross Disciplinary Postdoctoral Fellowship of the Human Frontier Science Program. T.T. is the Helen and Martin Chooljian Founders Circle Member in the Simons Center for Systems Biology of the Institute for Advanced Study, Princeton.

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  1. Department of Physics, Cornell University, Ithaca, New York 14853, USA

Authors and Affiliations

  1. Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, Weizmann 76100, Israel

    Itamar Shani, Tsevi Beatus & Roy H. Bar-Ziv

  2. Simons Center for Systems Biology, Institute for Advanced Study, Princeton, New Jersey 08540, USA

    Tsvi Tlusty

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  1. Itamar Shani
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  2. Tsevi Beatus
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  3. Roy H. Bar-Ziv
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Correspondence to Tsevi Beatus, Roy H. Bar-Ziv or Tsvi Tlusty.

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Shani, I., Beatus, T., Bar-Ziv, R. et al. Long-range orientational order in two-dimensional microfluidic dipoles. Nature Phys 10, 140–144 (2014). https://doi.org/10.1038/nphys2843

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