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Cluster formation by acoustic forces and active fluctuations in levitated granular matter

Abstract

Mechanically agitated granular matter often serves as a prototype for exploring the rich physics associated with hard-sphere systems, with an effective temperature introduced by vibrating or shaking1,2,3,4,5,6. While depletion interactions drive clustering and assembly in colloids7,8,9,10, no equivalent short-range attractions exist between macroscopic grains. Here we overcome this limitation and investigate granular cluster formation by using acoustic levitation and trapping11,12,13. Scattered sound establishes short-range attractions between small particles14, while detuning the acoustic trap generates active fluctuations15. To illuminate the interplay between attractions and fluctuations, we investigate transitions among ground states of two-dimensional clusters composed of a few particles. Our main results, obtained using experiments and modelling, reveal that, in contrast to thermal colloids, in non-equilibrium granular ensembles the magnitude of active fluctuations controls not only the assembly rates but also their assembly pathways and ground-state statistics. These results open up new possibilities for non-invasively manipulating macroscopic particles, tuning their interactions and directing their assembly.

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Fig. 1: Assembling and manipulating clusters composed of macroscopic particles using acoustic levitation.
Fig. 2: Tuning six-particle assembly between sticky and ergodic limits.
Fig. 3: Out-of-plane motion as a measure of active fluctuations.
Fig. 4: Seven-particle cluster assembly, ground-state statistics and transition states.

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References

  1. Olafsen, J. & Urbach, J. Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett. 81, 4369–4372 (1998).

    Article  ADS  Google Scholar 

  2. D’Anna, G., Mayor, P., Barrat, A., Loreto, V. & Nori, F. Observing Brownian motion in vibration-fluidized granular matter. Nature 424, 909–912 (2003).

    Article  ADS  Google Scholar 

  3. Feitosa, K. & Menon, N. Fluidized granular medium as an instance of the fluctuation theorem. Phys. Rev. Lett. 92, 164301 (2004).

    Article  ADS  Google Scholar 

  4. Keys, A. S., Abate, A. R., Glotzer, S. C. & Durian, D. J. Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material. Nat. Phys. 3, 260–264 (2007).

    Article  Google Scholar 

  5. Komatsu, Y. & Tanaka, H. Roles of energy dissipation in a liquid–solid transition of out-of-equilibrium systems. Phys. Rev. X 5, 031025 (2015).

    Google Scholar 

  6. Workamp, M., Ramirez, G., Daniels, K. E. & Dijksman, J. Symmetry-reversals in chiral active matter. Soft Matter 14, 5572–5580 (2018).

    Article  ADS  Google Scholar 

  7. Manoharan, V. N., Elsesser, M. T. & Pine, D. J. Dense packing and symmetry in small clusters of microspheres. Science 301, 483–487 (2003).

    Article  ADS  Google Scholar 

  8. Sacanna, S., Irvine, W. T. M., Chaikin, P. M. & Pine, D. J. Lock and key colloids. Nature 464, 575–578 (2010).

    Article  ADS  Google Scholar 

  9. Meng, G., Arkus, N., Brenner, M. P. & Manoharan, V. N. The free-energy landscape of clusters of attractive hard spheres. Science 327, 560–563 (2010).

    Article  ADS  Google Scholar 

  10. Kraft, D. J. et al. Surface roughness directed self-assembly of patchy particles into colloidal micelles. Proc. Natl Acad. Sci. USA 109, 10787–10792 (2012).

    Article  ADS  Google Scholar 

  11. Gorkov, L. P. Forces acting on a small particle in an acoustic field within an ideal fluid. Sov. Phys. Doklady 6, 773–775 (1962).

    ADS  Google Scholar 

  12. Wang, M. et al. Sound-mediated stable configurations for polystyrene particles. Phys. Rev. E 96, 052604 (2017).

    Article  ADS  Google Scholar 

  13. Lee, V., James, N. M., Waitukaitis, S. R. & Jaeger, H. M. Collisional charging of individual submillimeter particles: using ultrasonic levitation to initiate and track charge transfer. Phys. Rev. Mater. 2, 035602 (2018).

    Article  Google Scholar 

  14. Settnes, M. & Bruus, H. Forces acting on a small particle in an acoustical field in a viscous fluid. Phys. Rev. E 85, 016327 (2012).

    Article  ADS  Google Scholar 

  15. Rudnick, J. & Barmatz, M. Oscillational instabilities in single-mode acoustic levitators. J. Acoust. Soc. Am. 87, 81–92 (1990).

    Article  ADS  Google Scholar 

  16. Perry, R. W., Holmes-Cerfon, M. C., Brenner, M. P. & Manoharan, V. N. Two-dimensional clusters of colloidal spheres: ground states, excited states, and structural rearrangements. Phys. Rev. Lett. 114, 228301 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  17. Asakura, S. & Oosawa, F. On interaction between two bodies immersed in a solution of macromolecules. J. Chem. Phys. 22, 1255–1256 (1954).

    Article  ADS  Google Scholar 

  18. Kudrolli, A., Wolpert, M. & Gollub, J. P. Cluster formation due to collisions in granular material. Phys. Rev. Lett. 78, 1383–1386 (1997).

    Article  ADS  Google Scholar 

  19. Goldhirsch, I. & Zanetti, G. Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619–1622 (1993).

    Article  ADS  Google Scholar 

  20. Brilliantov, N., Saluena, C., Schwager, T. & Pöschel, T. Transient structures in a granular gas. Phys. Rev. Lett. 93, 134301 (2004).

    Article  ADS  Google Scholar 

  21. Royer, J. R. et al. High-speed tracking of rupture and clustering in freely falling granular streams. Nature 459, 1110–1113 (2009).

    Article  ADS  Google Scholar 

  22. Lee, V., Waitukaitis, S. R., Miskin, M. Z. & Jaeger, H. M. Direct observation of particle interactions and clustering in charged granular streams. Nat. Phys. 11, 733–737 (2015).

    Article  Google Scholar 

  23. Lumay, G. & Vandewalle, N. Controlled flow of smart powders. Phys. Rev. E 78, 061302 (2008).

    Article  ADS  Google Scholar 

  24. Fushimi, T., Hill, T. L., Marzo, A. & Drinkwater, B. W. Nonlinear trapping stiffness of mid-air single-axis acoustic levitators. Appl. Phys. Lett. 113, 034102 (2018).

    Article  ADS  Google Scholar 

  25. Zhang, S. et al. Acoustically mediated long-range interaction among multiple spherical particles exposed to a plane standing wave. New J. Phys. 18, 113034 (2016).

    Article  ADS  Google Scholar 

  26. Silva, G. T. & Bruus, H. Acoustic interaction forces between small particles in an ideal fluid. Phys. Rev. E 90, 063007 (2014).

    Article  ADS  Google Scholar 

  27. Glynne-Jones, P., Mishra, P. P., Boltryk, R. J. & Hill, M. Efficient finite element modeling of radiation forces on elastic particles of arbitrary size and geometry. J. Acoust. Soc. Am. 133, 1885–1893 (2013).

    Article  ADS  Google Scholar 

  28. Jambon-Puillet, E., Josserand, C. & Protière, S. Wrinkles, folds, and plasticity in granular rafts. Phys. Rev. Mater. 1, 042601 (2017).

    Article  Google Scholar 

  29. Owens, C. E., Shields, C. W., Cruz, D. F., Charbonneau, P. & López, G. P. Highly parallel acoustic assembly of microparticles into well-ordered colloidal crystallites. Soft Matter 12, 717–728 (2016).

    Article  ADS  Google Scholar 

  30. Chen, Q., Bae, S. C. & Granick, S. Directed self-assembly of a colloidal kagome lattice. Nature 469, 381–384 (2011).

    Article  ADS  Google Scholar 

  31. van Anders, G., Ahmed, N. K., Smith, R., Engel, M. & Glotzer, S. C. Entropically patchy particles: engineering valence through shape entropy. ACS Nano 8, 931–940 (2013).

    Article  Google Scholar 

  32. Cavallaro, M., Botto, L., Lewandowski, E. P., Wang, M. & Stebe, K. J. Curvature-driven capillary migration and assembly of rod-like particles. Proc. Natl Acad. Sci. USA 108, 20923–20928 (2011).

    Article  ADS  Google Scholar 

  33. Andrade, M. A. B., Buiochi, F. & Adamowski, J. C. Finite element analysis and optimization of a single axis acoustic levitator. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 469–479 (2010).

    Article  Google Scholar 

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Acknowledgements

We thank E. Klein and the Manoharan group for naming the seven-particle cluster configurations. We thank S. Waitukaitis, N. Schade, T. Witten, S. Nagel and R. Behringer for insightful discussions, and J. Z. Kim for a critical reading of the manuscript. This work is dedicated to the memory of R. Behringer. The research was supported by the National Science Foundation through grants DMR-1309611 and DMR-1810390. A.S. and V.V. acknowledge primary support through the Chicago MRSEC, funded by the NSF through grant DMR-1420709.

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Authors and Affiliations

Authors

Contributions

M.X.L. and H.M.J. conceived of the project and designed the experiments. M.X.L. performed the experiments and analysed the data. M.X.L and A.S. calculated the acoustic forces. M.X.L., A.S. and V.V. developed the model and performed the theoretical analysis. All authors contributed to writing the manuscript.

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Correspondence to Melody X. Lim.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Figures 1–4, Supplementary Tables 1 and 2, and Supplementary References 1 and 2.

Supplementary Video 1

Topological reconfigurations of six-particle clusters. Part 1: bottom view of a six-particle cluster levitated in an acoustic field, which is close to its resonant frequency (∆f/f0 = 0.25 × 10−3). The cluster rearranges between its three distinct ground states. Playback is slowed down by a factor of 10. The real-time duration of the movie is 3.5 seconds. Part 2: bottom view of a six-particle cluster levitated in an acoustic field, which is driven far from its resonant frequency (∆f/f0 = 2.5 × 10−3). The cluster rearranges between its three distinct ground states. Playback is slowed down by a factor of 10. The real-time duration of the movie is 1.8 seconds.

Supplementary Video 2

Out-of-plane cluster fluctuations. Part 1: side view of a six-particle cluster levitated in an acoustic field, which is close to its resonant frequency (∆f/f0 = 0.25 × 10−3). The cluster oscillates vertically in the trap, until it strikes the acrylic reflector, breaking the cluster. The cluster remains in a planar configuration before and after the collision. Playback is slowed down by a factor of 10. The real-time duration of the movie is 2 seconds. Part 2: bottom view of a six-particle cluster levitated in an acoustic field, which is driven far from its resonant frequency (∆f/f0 = 2.5 × 10−3). The cluster oscillates vertically in the trap, exciting out-of-plane bending modes. Playback is slowed down by a factor of 10. The real-time duration of the movie is 0.7 seconds.

Supplementary Video 3

Cluster rearrangement via particle ejection. Part 1: bottom view of a six-particle cluster levitated in an acoustic field, which is close to its resonant frequency (∆f/f0 = 0.25 × 10−3). The cluster (initially Parallelogram) rearranges by breaking into a five-particle cluster and a single particle, which then recombine to a different six-particle configuration (Chevron). Playback is slowed down by a factor of 100. The real-time duration of the movie is 1.7 seconds. Part 2: bottom view of a seven-particle cluster levitated in an acoustic field, which is detuned from its resonant frequency (∆f/f0 = 1.3 × 10−3). The cluster (initially Flower) rearranges by breaking into a five-particle cluster and two single particles, which then recombine to a different seven-particle configuration (Turtle). Playback is slowed down by a factor of 33. The real-time duration of the movie is 0.6 seconds.

Supplementary Video 4

Cluster rearrangement via hinge motion. Part 1: bottom view of a six-particle cluster levitated in an acoustic field, which is driven far from its resonant frequency (∆f/f0 = 2.5 × 10−3). The cluster (initially Parallelogram) rearranges via a hinge motion to a different six-particle configuration (Triangle). Playback is slowed down by a factor of 100. The real-time duration of the movie is 9 milliseconds. Part 2: bottom view of a seven-particle cluster levitated in an acoustic field, which is driven far from its resonant frequency (∆f/f0 = 2.2 × 10−3). The cluster (initially Boat) rearranges via a hinge motion to a different seven-particle configuration (Turtle). Playback is slowed down by a factor of 100. The real-time duration of the movie is 20 milliseconds.

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Lim, M.X., Souslov, A., Vitelli, V. et al. Cluster formation by acoustic forces and active fluctuations in levitated granular matter. Nat. Phys. 15, 460–464 (2019). https://doi.org/10.1038/s41567-019-0440-9

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