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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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

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.

Corresponding author

Correspondence to Melody X. Lim.

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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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