Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter

TL;DR

The study tackles acoustic collapse in levitated particle systems caused by interparticle scattering by introducing controlled electrostatic repulsion to create a mermaid potential, enabling stable expanded, collapsed, and hybrid configurations. The approach is implemented by charging particles on a biased plate, allowing dynamic reconfiguration via quasistatic discharge or bounce-charging, and demonstrated across small clusters (n=2–5) with both experiments and MD simulations that incorporate Rayleigh-limit acoustic forces, soft-sphere repulsion, and drag. For larger assemblies, the work reveals energy transfer from the acoustic field that drives complex rotational and oscillatory dynamics, including the formation of an acoustic clock motif. Overall, the method provides a simple, accessible means to study non-equilibrium assembly and many-body acoustics in gravity- and container-free conditions, with potential to extend to larger or aspherical particles and richer dynamical phenomena.

Abstract

Acoustic levitation provides a unique method for manipulating small particles as it completely evades effects from gravity, container walls, or physical handling. These advantages make it a tantalizing platform for studying complex phenomena in many-particle systems, save for one severe limitation -- particles suspended by sound interact via acoustic scattering forces, which cause them to merge into a single dense object. To overcome this "acoustic collapse", we have developed a strategy that combines acoustic levitation with controlled electrostatic charging to assemble, adapt, and activate complex, many-particle systems. The key idea is to introduce electrostatic repulsion, which renders a so-called "mermaid" potential where interactions are attractive at short range and repulsive at long range. By controlling the balance between attraction/repulsion, we are able to levitate fully expanded structures where all particles are separated, fully collapsed structures where they are all in contact, and hybrid ones consisting of both expanded and collapsed components. We find that fully collapsed and expanded structures are inherently stable, whereas hybrid ones exhibit transient stability governed by acoustically unstable dimers. Furthermore, we show how electrostatics allow us to adapt between configurations on the fly, either by quasistatic discharge or discrete up/down charge steps. Finally, we demonstrate how large structures experience selective energy pumping from the acoustic field -- thrusting some particles into motion while others remain stationary -- leading to complex dynamics including coupled rotations and oscillations. Our approach provides an easy-to-implement and easy-to-understand solution to the pervasive problem of acoustic collapse, while simultaneously providing new insights into the assembly and activation of many-particle systems with complex interactions.

Figures (4)

• Figure 1: Acoustic levitation of like-charged particles. (A) Schematic of the experimental setup. A transducer generates a standing wave between its horn and a reflecting plate. The plate is composed of ITO-coated glass layered with PTFE for electrical insulation and mounted on a motorized vertical translation stage for precise alignment of the acoustic cavity. Conductive particles placed on the plate acquire charge when the ITO surface is connected to a high-voltage source. Charged particles levitate in the acoustic cavity and can be imaged from both the side and bottom via a mirror. A soft X-ray source enables controlled discharge. (B) Bottom-view images of compact rafts consisting of 2, 10, and 35 particles. (C) Schematics of experimental procedures: initially, particles acquire charge via contact with the biased ITO plate; next, we switch on the acoustic field to levitate charged particles; finally, the ITO plate is no longer voltage biased and charged particles levitate only in the acoustic field. (D) Measured charge $Q$ on a silver-coated PMMA particle (diameter $\mathrm{d \simeq 288~\mu m}$) as a function of the applied electric field $\mathrm{E}$. Purple circles represent the mean charge measured among (at most) 60 trials per data point. The dashed blue line is a linear fit to the data points, with a slope of $\sim$4.3. The black line shows the theoretical prediction based on Maxwell's approximation for a conducting sphere on a conducting plane. Error bars represent the standard deviation. (E) Interparticle forces as a function of center-to-center separation $r$. The repulsive Coulomb force (red) and attractive acoustic scattering force (blue) are shown along with their sum (black), representing the total interaction force. The total force crosses zero at $r = r_*$ and $r = r_s$, corresponding to an unstable and a stable equilibrium point, respectively. (F) Bottom-view images of two levitated particles: (i) in contact when acoustic scattering forces dominate, and (ii) separated when Coulomb repulsion dominates.
• Figure 2: Structure formation and statistics for $\mathrm{n = 2-5}$ particles. (A) Panel (i) shows bottom-view images of self-assembled clusters of $\mathrm{n =3}$, 4, and 5 levitated charged particles (diameter $=250-300~\mathrm{\mu m}$). Beside fully collapsed configurations where no particle is separated and fully expanded ones where all particles are separated, we observe a variety of hybrid configurations, which consist of mixed arrangements between collapsed and expanded clusters. The corresponding simulated structures shown in panel (ii) are obtained via Molecular Dynamics and fully reproduce the experimental results. (B) Bottom-view image sequence showing the transient formation and rearrangement of a hybrid structure with an unstable dimer. Colored circles identify the same particle through all four panels. Scales bars are 1 mm. (C) Experimental bar plots showing the occurrence frequency and stability of each configuration, obtained by 400 V ITO bias. Stable occurrences (teal) persist for more than 15 seconds, while transient occurrences (yellow) rearrange or disintegrate within 15 seconds.
• Figure 3: Manipulating assembled configurations via controlled discharges and bounce-charging. (A) Bottom-view images showing structural evolution under two discharge protocols. Panels (i–iv) show a single, terminated discharge event. Panels (v–viii) illustrate a two-step discharge sequence using timed X-ray exposure.. Solid circles indicate current particle positions; dashed circles indicate positions from the previous frame. (B) Bottom-view sequence showing configuration shuffling with the bounce-charging method. Each panel corresponds to a successive bounce on the ITO plate biased at $\mathrm{500~V}$, leading to structural rearrangements.
• Figure 4: Assembly and dynamics of large hybrid configurations. (A) Bottom-view time-lapse of the "acoustic clock", assembled from smaller particles with diameters in the range of $180-212~\mathrm{\mu m}$. Colored circles trace the trajectories of individual particles from their initial positions in (i) to the formation of the collapsed central cluster in (iv). The red arrow in (iv) indicates the direction of cluster rotation. Panels ii-iv are $2\times$ zoom views of the area within the dashed square in panel i. All scale bars are 1 mm. (B) Purple curve shows the normalized displacement of a satellite particle (indicated by dashed purple circle in panel iv); blue curve plots the core’s rotation angle versus time, showing periodic coupling between core rotation and satellite particle motion.