Resonant and antiresonant bouncing droplets

Droplet superpropulsion in an energetically constrained insect

Food consumption and waste elimination are vital functions for living systems. Although how feeding impacts animal form and function has been studied for more than a century since Darwin, how its obligate partner, excretion, controls and constrains animal behavior, size, and energetics remains largely unexplored. Here we study millimeter-scale sharpshooter insects (Cicadellidae) that feed exclusively on a plant's xylem sap, a nutrient-deficit source (95% water). To eliminate their high-volume excreta, these insects exploit droplet superpropulsion, a phenomenon in which an elastic projectile can achieve higher velocity than the underlying actuator through temporal tuning. We combine coupled-oscillator models, computational fluid dynamics, and biophysical experiments to show that these insects temporally tune the frequency of their anal stylus to the Rayleigh frequency of their surface tension-dominated elastic drops as a single-shot resonance mechanism. Our model predicts that for these tiny insects, the superpropulsion of droplets is energetically cheaper than forming jets, enabling them to survive on an extreme energy-constrained xylem-sap diet. The principles and limits of superpropulsion outlined here can inform designs of energy-efficient self-cleaning structures and soft engines to generate ballistic motions.

Facile fabrication of hierarchical textures for substrate-independent and durable superhydrophobic surfaces

On account of their wide range of applications in self-cleaning, anti-icing, frost suppression, etc., superhydrophobic surfaces have attracted considerate attention. However, most of the superhydrophobic surfaces can only be prepared on the surfaces of specific materials and are easily damaged in the case of friction. In this work, we propose a facile method to achieve superhydrophobicity on various substrate surfaces. By femtosecond laser direct processing, micron-level grooves and protrusions are constructed on substrates to form a protective layer. Then, the substrates covered by polytetrafluoroethylene (PTFE) were scanned to make the surfaces of the substrates superhydrophobic. Since the PTFE micro-nano-particles are evenly distributed on the grooves and protrusions, the surfaces exhibit robust superhydrophobicity with excellent anti-friction performance that is independent of the substrate properties. This work provides an efficient and environmentally friendly path for achieving robust superhydrophobic surfaces on various substrates.

Droplet motion on sonically excited hydrophobic meshes

The sonic excitation of the liquid droplet on a hydrophobic mesh surface gives rise to a different oscillation behavior than that of the flat hydrophobic surface having the same contact angle. To assess the droplet oscillatory behavior over the hydrophobic mesh, the droplet motion is examined under the external sonic excitations for various mesh screen aperture ratios. An experiment is carried out and the droplet motion is recorded by a high-speed facility. The findings revealed that increasing sonic excitation frequencies enhance the droplet maximum displacement in vertical and horizontal planes; however, the vertical displacements remain larger than those of the horizontal displacements. The resonance frequency measured agrees well with the predictions and the excitation frequency at 105 Hz results in a droplet oscillation mode (n) of 4. The maximum displacement of the droplet surface remains larger for the flat hydrophobic surface than that of the mesh surface with the same contact angle. In addition, the damping factor is considerably influenced by the sonic excitation frequencies; hence, increasing sonic frequency enhances the damping factor, which becomes more apparent for the large mesh screen aperture ratios. The small-amplitude surface tension waves create ripples on the droplet surface.

Hydrodynamic quantum analogs

The walking droplet system discovered by Yves Couder and Emmanuel Fort presents an example of a vibrating particle self-propelling through a resonant interaction with its own wave field. It provides a means of visualizing a particle as an excitation of a field, a common notion in quantum field theory. Moreover, it represents the first macroscopic realization of a form of dynamics proposed for quantum particles by Louis de Broglie in the 1920s. The fact that this hydrodynamic pilot-wave system exhibits many features typically associated with the microscopic, quantum realm raises a number of intriguing questions. At a minimum, it extends the range of classical systems to include quantum-like statistics in a number of settings. A more optimistic stance is that it suggests the manner in which quantum mechanics might be completed through a theoretical description of particle trajectories. We here review the experimental studies of the walker system, and the hierarchy of theoretical models developed to rationalize its behavior. Particular attention is given to enumerating the dynamical mechanisms responsible for the emergence of robust, structured statistical behavior. Another focus is demonstrating how the temporal nonlocality of the droplet dynamics, as results from the persistence of its pilot wave field, may give rise to behavior that appears to be spatially nonlocal. Finally, we describe recent explorations of a generalized theoretical framework that provides a mathematical bridge between the hydrodynamic pilot-wave system and various realist models of quantum dynamics.

Two-frequency forcing of droplet rebounds on a liquid bath

Droplets can bounce indefinitely on a liquid bath vertically vibrated in a sinusoidal fashion. We here present experimental results that extend this observation to forcing signals composed of a combination of two commensurable frequencies. The Faraday and Goodridge thresholds are characterized. Then a number of vertical bouncing modes are reported, including walkers. The vertical motion can become chaotic, in which case the horizontal motion is an alternation of walk and stop.

Quantumlike statistics of deterministic wave-particle interactions in a circular cavity

A deterministic low-dimensional iterated map is proposed here to describe the interaction between a bouncing droplet and Faraday waves confined to a circular cavity. Its solutions are investigated theoretically and numerically. The horizontal trajectory of the droplet can be chaotic: it then corresponds to a random walk of average step size equal to half the Faraday wavelength. An analogy is made between the diffusion coefficient of this random walk and the action per unit mass ℏ/m of a quantum particle. The statistics of droplet position and speed are shaped by the cavity eigenmodes, in remarkable agreement with the solution of Schrödinger equation for a quantum particle in a similar potential well.

Strings of droplets propelled by coherent waves

Bouncing walking droplets possess fascinating properties due to their peculiar wave-particle interaction leading to unexpected quantumlike behaviors. We propose a study consisting in droplets walking along annular cavities. We show that, in this geometry, they spontaneously form a string of synchronized bouncing droplets that share a common coherent wave propelling the group at a speed faster than single walkers. The formation of this coherent wave and the collective droplet behaviors are captured by a model. Those are at the opposite of the ones found in two-dimensional geometries. Our results shed light on walking dynamics.