Viscoelastic dynamics of a soft strip subject to a large deformation.

To produce sounds, we adjust the tension of our vocal folds to shape their properties and control the pitch. This efficient mechanism offers inspiration for designing reconfigurable materials and adaptable soft robots. However, understanding how flexible structures respond to a significant static strain is not straightforward. This complexity also limits the precision of medical imaging when applied to tensioned organs like muscles, tendons, ligaments and blood vessels among others. In this article, we experimentally and theoretically explore the dynamics of a soft strip subject to a substantial static extension, up to 180%. Our observations reveal a few intriguing effects, such as the resilience of certain vibrational modes to a static deformation. These observations are supported by a model based on the incremental displacement theory. This has promising practical implications for characterizing soft materials but also for scenarios where external actions can be used to tune properties.

Soft elastomers: A playground for guided waves.

Mechanical waves propagating in soft materials play an important role in physiology. They can be natural, such as the cochlear wave in the inner ear of mammalians, or controlled, such as in elastography in the context of medical imaging. In a recent study, Lanoy, Lemoult, Eddi, and Prada [Proc. Natl. Acad. Sci. U.S.A. 117(48), 30186-30190 (2020)] implemented an experimental tabletop platform that allows direct observation of in-plane guided waves in a soft strip. Here, a detailed description of the setup and signal processing steps is presented as well as the theoretical framework supporting them. One motivation is to propose a tutorial experiment for visualizing the propagation of guided elastic waves. Last, the versatility of the experimental platform is exploited to illustrate experimentally original features of wave physics, such as backward modes, stationary modes, and Dirac cones.

Experimental Implementation of Wave Propagation in Disordered Time-Varying Media.

Here, we study and implement the temporal analog in time disordered sytems. A spatially homogeneous medium is endowed with a time structure composed of randomly distributed temporal interfaces. This is achieved through electrostriction between water surface and an electrode. The wave field observed is the result of the interferences between reflected and refracted waves on the interfaces. Although no eigenmode can be associated with the wave field, several common features between space and time emerge. The waves grow exponentially depending on the disorder level in agreement with a 2D matrix evolution model such as in the spatial case. The relative position of the momentum gap appearing in the time modulated systems plays a central role in the wave field evolution. When tuning the excitation to compensate for the damping, transient waves, localized in time, appear on the liquid surface. They result from a particular history of the multiple interferences produced by a specific sequence of time boundaries.

Liquid walls and interfaces in arbitrary directions stabilized by vibrations.

Gravity shapes liquids and plays a crucial role in their internal balance. Creating new equilibrium configurations irrespective of the presence of a gravitational field is challenging with applications on Earth as well as in zero-gravity environments. Vibrations are known to alter the shape of liquid interfaces and also to change internal dynamics and stability in depth. Here, we show that vibrations can also create an "artificial gravity" in any direction. We demonstrate that a liquid can maintain an inclined interface when shaken in an arbitrary direction. A necessary condition for the equilibrium to occur is the existence of a velocity gradient determined by dynamical boundary conditions. However, the no-slip boundary condition and incompressibility can perturb the required velocity profile, leading to a destabilization of the equilibrium. We show that liquid layers provide a solution, and liquid walls of several centimeters in height can thus be stabilized. We show that the buoyancy equilibrium is not affected by the forcing.

Dirac cones and chiral selection of elastic waves in a soft strip.

We study the propagation of in-plane elastic waves in a soft thin strip, a specific geometrical and mechanical hybrid framework which we expect to exhibit a Dirac-like cone. We separate the low frequencies guided modes (typically 100 Hz for a 1-cm-wide strip) and obtain experimentally the full dispersion diagram. Dirac cones are evidenced together with other remarkable wave phenomena such as negative wave velocity or pseudo-zero group velocity (ZGV). Our measurements are convincingly supported by a model (and numerical simulation) for both Neumann and Dirichlet boundary conditions. Finally, we perform one-way chiral selection by carefully setting the source position and polarization. Therefore, we show that soft materials support atypical wave-based phenomena, which is all of the more interesting as they make most of the biological tissues.

Author Correction: Floating under a levitating liquid.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Floating under a levitating liquid.

When placed over a less dense medium, a liquid layer will typically collapse downwards if it exceeds a certain size, as gravity acting on the lower liquid interface triggers a destabilizing effect called a Rayleigh-Taylor instability1,2. Of the many methods that have been developed to prevent the liquid from falling3-6, vertical shaking has proved to be efficient and has therefore been studied in detail7-13. Stabilization is the result of the dynamical averaging effect of the oscillating effective gravity. Vibrations of liquids also induce other paradoxical phenomena such as the sinking of air bubbles14-19 or the stabilization of heavy objects in columns of fluid at unexpected heights20. Here we take advantage of the excitation resonance of the supporting air layer to perform experiments with large levitating liquid layers of up to half a litre in volume and up to 20 centimetres in width. Moreover, we predict theoretically and show experimentally that vertical shaking also creates stable buoyancy positions on the lower interface of the liquid, which behave as though the gravitational force were inverted. Bodies can thus float upside down on the lower interface of levitating liquid layers. We use our model to predict the minimum excitation needed to withstand falling of such an inverted floater, which depends on its mass. Experimental observations confirm the possibility of selective falling of heavy bodies. Our findings invite us to rethink all interfacial phenomena in this exotic and counter-intuitive stable configuration.

Space-Time Folding of the Wake Produced by a Supervelocity Rotating Point Source.

Wave sources moving faster than the waves they emit create a wake whose topological features are directly related to the geometry of the source trajectory. These features can be understood by considering space-time surfaces representing past emitted wave fronts. Specifically, for a supervelocity source moving along a circular path the space-time envelope folds and a cusp appears on the inner part of the wake. As a result, the wake is ultimately contained within two parallel corotating spiraling branches. In this Letter we take advantage of the low phase speed of water waves to study experimentally supervelocity sources moving at velocities up to several time the wave speed. We image in real time their emission patterns and characterize the topological features of their wakes.

Phase-conjugate mirror for water waves driven by the Faraday instability.

The Faraday instability appears on liquid baths submitted to vertical oscillations above a critical value. The pattern of standing ripples at half the vibrating frequency that results from this parametric forcing is usually shaped by the boundary conditions imposed by the enclosing receptacle. Here, we show that the time modulation of the medium involved in the Faraday instability can act as a phase-conjugate mirror--a fact which is hidden in the extensively studied case of the boundary-driven regime. We first demonstrate the complete analogy with the equations governing its optical counterpart. We then use water baths combining shallow and deep areas of arbitrary shapes to spatially localize the Faraday instability. We give experimental evidence of the ability of the Faraday instability to generate counterpropagating phase-conjugated waves for any propagating signal wave. The canonical geometries of a point and plane source are implemented. We also verify that Faraday-based phase-conjugate mirrors hold the genuine property of being shape independent. These results show that a periodic modulation of the effective gravity can perform time-reversal operations on monochromatic propagating water waves, with a remarkable efficiency compared with wave manipulation in other fields of physics.

Peeling an elastic film from a soft viscoelastic adhesive: experiments and scaling laws.

The functionality of adhesives relies on their response under the application of a load. Yet, it has remained a challenge to quantitatively relate the macroscopic dynamics of peeling to the dissipative processes inside the adhesive layer. Here we investigate the peeling of a reversible adhesive made of a polymer gel, measuring the relationship between the peeling force, the peeling velocity, and the geometry of the interface at small-scale. Experiments are compared to a theory based on the linear viscoelastic response of the adhesive, augmented with an elastocapillary regularization approach. This theory, fully quantitative in the limit of small surface deformations, demonstrates the emergence of a "wetting" angle at the contact line and exhibits scaling laws for peeling which are in good agreement with the experimental results. Our findings provide a new strategy for design of reversible adhesives, by quantitatively combining wetting, geometry and dissipation.

Interaction of two walkers: wave-mediated energy and force.

A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global surface wave field that retains information on its past trajectory. Here we investigate the energy stored in this wave field for two coupled walkers and how it conveys an interaction between them. For this purpose, we characterize experimentally the "promenade modes" where two walkers are bound and propagate together. Their possible binding distances take discrete values, and the velocity of the pair depends on their mutual binding. The mean parallel motion can be either rectilinear or oscillating. The experimental results are recovered analytically with a simple theoretical framework. A relation between the kinetic energy of the droplets and the total energy of the standing waves is established.

Initial spreading of low-viscosity drops on partially wetting surfaces.

Liquid drops start spreading directly after coming into contact with a partially wetting substrate. Although this phenomenon involves a three-phase contact line, the spreading motion is very fast. We study the initial spreading dynamics of low-viscosity drops using two complementary methods: molecular dynamics simulations and high-speed imaging. We access previously unexplored length and time scales and provide a detailed picture on how the initial contact between the liquid drop and the solid is established. Both methods unambiguously point toward a spreading regime that is independent of wettability, with the contact radius growing as the square root of time.