Droplet Bouncing: Fundamentals, Regulations, and Applications

Droplet impact is a ubiquitous phenomenon in nature, daily life, and industrial processes. It is thus crucial to tune the impact outcomes for various applications. As a special outcome of droplet impact, the bouncing of droplets keeps the form of the droplets after the impact and minimizes the energy loss during the impact, being beneficial in many applications. A unified understanding of droplet bouncing is in high demand for effective development of new techniques to serve applications. This review shows the fundamentals, regulations, and applications of millimeter-sized droplet bouncing on solid surfaces and same/miscible liquids (liquid pool and another droplet). Regulation methods and current applications are summarized, and potential directions are proposed.

Conceiving Particles as Undulating Granular Systems Allows Fundamentally Realist Interpretation of Quantum Mechanics

The strange behavior of subatomic particles is described by quantum theory, whose standard interpretation rejected some fundamental principles of classical physics such as causality, objectivity, locality, realism and determinism. Recently, a granular relativistic electrodynamical model of the electron could capture the measured values of its observables and predict its mass from the stability of its substructure. The model involves numerous subparticles that constitute some tight nucleus and loosely bound envelope allegedly forming real waves. The present study examines whether such a substructure and associated dynamics allow fundamentally realist interpretations of emblematic quantum phenomena, properties and principles, such as wave-particle duality, loss of objectivity, quantization, simultaneous multipath exploration, collapse of wavepacket, measurement problem, and entanglement. Drawing inspiration from non-linear dynamical systems, subparticles would involve realist hidden variables while high-level observables would not generally be determined, as particles would generally be in unstable states before measurements. Quantum mechanics would constitute a high-level probabilistic description emerging from an underlying causal, objective, local, albeit contextual and unpredictable reality. Altogether, by conceiving particles as granular systems composed of numerous extremely sensitive fluctuating subcorpuscles, this study proposes the possible existence of a local fundamentally realist interpretation of quantum mechanics.

Moulding hydrodynamic 2D-crystals upon parametric Faraday waves in shear-functionalized water surfaces

Faraday waves, or surface waves oscillating at half of the natural frequency when a liquid is vertically vibrated, are archetypes of ordering transitions on liquid surfaces. Although unbounded Faraday waves patterns sustained upon bulk frictional stresses have been reported in highly viscous fluids, the role of surface rigidity has not been investigated so far. Here, we demonstrate that dynamically frozen Faraday waves-that we call 2D-hydrodynamic crystals-do appear as ordered patterns of nonlinear gravity-capillary modes in water surfaces functionalized with soluble (bio)surfactants endowing in-plane shear stiffness. The phase coherence in conjunction with the increased surface rigidity bears the Faraday waves ordering transition, upon which the hydrodynamic crystals were reversibly molded under parametric control of their degree of order, unit cell size and symmetry. The hydrodynamic crystals here discovered could be exploited in touchless strategies of soft matter and biological scaffolding ameliorated under external control of Faraday waves coherence.

The vortex-driven dynamics of droplets within droplets

Understanding the fluid-structure interaction is crucial for an optimal design and manufacturing of soft mesoscale materials. Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realisation of devices of interest in bio-technology, such as drug-delivery, tissue engineering and regenerative medicine. Here, we study the physics of multi-core emulsions flowing in microfluidic channels and report numerical evidence of a surprisingly rich variety of driven non-equilibrium states (NES), whose formation is caused by a dipolar fluid vortex triggered by the sheared structure of the flow carrier within the microchannel. The observed dynamic regimes range from long-lived NES at low core-area fraction, characterised by a planetary-like motion of the internal drops, to short-lived ones at high core-area fraction, in which a pre-chaotic motion results from multi-body collisions of inner drops, as combined with self-consistent hydrodynamic interactions. The onset of pre-chaotic behavior is marked by transitions of the cores from one vortex to another, a process that we interpret as manifestations of the system to maximize its entropy by filling voids, as they arise dynamically within the capsule.

Vacuum Landscaping: Cause of Nonlocal Influences without Signaling

In the quest for an understanding of nonlocality with respect to an appropriate ontology, we propose a “cosmological solution”. We assume that from the beginning of the universe each point in space has been the location of a scalar field representing a zero-point vacuum energy that nonlocally vibrates at a vast range of different frequencies across the whole universe. A quantum, then, is a nonequilibrium steady state in the form of a “bouncer” coupled resonantly to one of those (particle type dependent) frequencies, in remote analogy to the bouncing oil drops on an oscillating oil bath as in Couder’s experiments. A major difference to the latter analogy is given by the nonlocal nature of the vacuum oscillations. We show with the examples of double- and n-slit interference that the assumed nonlocality of the distribution functions alone suffices to derive the de Broglie–Bohm guiding equation for N particles with otherwise purely classical means. In our model, no influences from configuration space are required, as everything can be described in 3-space. Importantly, the setting up of an experimental arrangement limits and shapes the forward and osmotic contributions and is described as vacuum landscaping.

Atom-Diffraction from Surfaces with Defects: A Fermatian, Newtonian and Bohmian Joint View

Bohmian mechanics, widely known within the field of the quantum foundations, has been a quite useful resource for computational and interpretive purposes in a wide variety of practical problems. Here, it is used to establish a comparative analysis at different levels of approximation in the problem of the diffraction of helium atoms from a substrate consisting of a defect with axial symmetry on top of a flat surface. The motivation behind this work is to determine which aspects of one level survive in the next level of refinement and, therefore, to get a better idea of what we usually denote as quantum-classical correspondence. To this end, first a quantum treatment of the problem is performed with both an approximated hard-wall model and then with a realistic interaction potential model. The interpretation and explanation of the features displayed by the corresponding diffraction intensity patterns is then revisited with a series of trajectory-based approaches: Fermatian trajectories (optical rays), Newtonian trajectories and Bohmian trajectories. As it is seen, while Fermatian and Newtonian trajectories show some similarities, Bohmian trajectories behave quite differently due to their implicit non-classicality.

Hydrodynamic schooling of flapping swimmers

Fish schools and bird flocks are fascinating examples of collective behaviours in which many individuals generate and interact with complex flows. Motivated by animal groups on the move, here we explore how the locomotion of many bodies emerges from their flow-mediated interactions. Through experiments and simulations of arrays of flapping wings that propel within a collective wake, we discover distinct modes characterized by the group swimming speed and the spatial phase shift between trajectories of neighbouring wings. For identical flapping motions, slow and fast modes coexist and correspond to constructive and destructive wing–wake interactions. Simulations show that swimming in a group can enhance speed and save power, and we capture the key phenomena in a mathematical model based on memory or the storage and recollection of information in the flow field. These results also show that fluid dynamic interactions alone are sufficient to generate coherent collective locomotion, and thus might suggest new ways to characterize the role of flows in animal groups.

Schooling or flocking of animals in nature is generally explained via an energy optimization approach. Here, Becker et al. mimic the conditions for an infinite array of swimmers in a water tank and show that fluid dynamic interactions alone are sufficient to lead to coherent and collective locomotion.

Double-slit experiment with single wave-driven particles and its relation to quantum mechanics

In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

Chaos driven by interfering memory

The transmission of information can couple two entities of very different nature, one of them serving as a memory for the other. Here we study the situation in which information is stored in a wave field and serves as a memory that pilots the dynamics of a particle. Such a system can be implemented by a bouncing drop generating surface waves sustained by a parametric forcing. The motion of the resulting "walker" when confined in a harmonic potential well is generally disordered. Here we show that these trajectories correspond to chaotic regimes characterized by intermittent transitions between a discrete set of states. At any given time, the system is in one of these states characterized by a double quantization of size and angular momentum. A low dimensional intermittency determines their respective probabilities. They thus form an eigenstate basis of decomposition for what would be observed as a superposition of states if all measurements were intrusive.

Non-Hamiltonian features of a classical pilot-wave dynamics

A bouncing droplet on a vibrated bath can couple to the waves it generates, so that it becomes a propagative walker. Its propulsion at constant velocity means that a balance exists between the permanent input of energy provided by the vibration and the dissipation. Here we seek a simple theoretical description of the resulting non-Hamiltonian dynamics with a walker immersed in a harmonic potential well. We demonstrate that the interaction with the recently emitted waves can be modeled by a Rayleigh-type friction. The Rayleigh oscillator has well defined attractors. The convergence toward them and their stability is investigated through an energetic approach and a linear stability analysis. These theoretical results provide a description of the dynamics in excellent agreement with the experimental data. It is thus a basic framework for further investigations of wave-particle interactions when memory effects are included.

Wavelike statistics from pilot-wave dynamics in a circular corral

Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.

Bouncing droplets on a billiard table

In a set of experiments, Couder et al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. I present a dynamical systems model, in the form of an iterative map, for a droplet on an oscillating bath. I examine the droplet bifurcation from bouncing to walking, and prescribe general requirements for the surface wave to support stable walking states. I show that in addition to walking, there is a region of large forcing that may support the chaotic motion of the droplet. Using the map, I then investigate the droplet trajectories in a square (billiard ball) domain. I show that in large domains, the long time trajectories are either non-periodic dense curves or approach a quasiperiodic orbit. In contrast, in small domains, at low forcing, trajectories tend to approach an array of circular attracting sets. As the forcing increases, the attracting sets break down and the droplet travels throughout space.