Mutual adaptation of a Faraday instability pattern with its flexible boundaries in floating fluid drops

Acoustic, Phononic, Brillouin Light Scattering and Faraday Wave-Based Frequency Combs: Physical Foundations and Applications

Frequency combs (FCs)-spectra containing equidistant coherent peaks-have enabled researchers and engineers to measure the frequencies of complex signals with high precision, thereby revolutionising the areas of sensing, metrology and communications and also benefiting the fundamental science. Although mostly optical FCs have found widespread applications thus far, in general FCs can be generated using waves other than light. Here, we review and summarise recent achievements in the emergent field of acoustic frequency combs (AFCs), including phononic FCs and relevant acousto-optical, Brillouin light scattering and Faraday wave-based techniques that have enabled the development of phonon lasers, quantum computers and advanced vibration sensors. In particular, our discussion is centred around potential applications of AFCs in precision measurements in various physical, chemical and biological systems in conditions where using light, and hence optical FCs, faces technical and fundamental limitations, which is, for example, the case in underwater distance measurements and biomedical imaging applications. This review article will also be of interest to readers seeking a discussion of specific theoretical aspects of different classes of AFCs. To that end, we support the mainstream discussion by the results of our original analysis and numerical simulations that can be used to design the spectra of AFCs generated using oscillations of gas bubbles in liquids, vibrations of liquid drops and plasmonic enhancement of Brillouin light scattering in metal nanostructures. We also discuss the application of non-toxic room-temperature liquid-metal alloys in the field of AFC generation.

Self-excitation of Leidenfrost drops and consequences on their stability

Volatile liquids (water, alcohol, etc.) poured on hot solids levitate above a layer of vapor. Unexpectedly, these so-called Leidenfrost drops often suddenly start to oscillate with star shapes, a phenomenon first reported about 140 y ago. Similar shapes are known to be triggered when a liquid is subjected to an external periodic forcing, but the unforced Leidenfrost case remains unsolved. We show that the levitating drops are excited by an intrinsic periodic forcing arising from a vibration of the vapor cushion. We discuss the frequency of the vibrations and how they can excite surface standing waves possibly amplified under geometric conditions of resonance-an ensemble of observations that provide a plausible scenario for the origin, mode selection, and sporadic nature of the Leidenfrost stars.

Faraday waves in soft elastic solids

Recent experiments have observed the emergence of standing waves at the free surface of elastic bodies attached to a rigid oscillating substrate and subjected to critical values of forcing frequency and amplitude. This phenomenon, known as Faraday instability, is now well understood for viscous fluids but surprisingly eluded any theoretical explanation for soft solids. Here, we characterize Faraday waves in soft incompressible slabs using the Floquet theory to study the onset of harmonic and subharmonic resonance eigenmodes. We consider a ground state corresponding to a finite homogeneous deformation of the elastic slab. We transform the incremental boundary value problem into an algebraic eigenvalue problem characterized by the three dimensionless parameters, that characterize the interplay of gravity, capillary and elastic waves. Remarkably, we found that Faraday instability in soft solids is characterized by a harmonic resonance in the physical range of the material parameters. This seminal result is in contrast to the subharmonic resonance that is known to characterize viscous fluids, and opens the path for using Faraday waves for a precise and robust experimental method that is able to distinguish solid-like from fluid-like responses of soft matter at different scales.

Excitation of Faraday-like body waves in vibrated living earthworms

Biological cells and many living organisms are mostly made of liquids and therefore, by analogy with liquid drops, they should exhibit a range of fundamental nonlinear phenomena such as the onset of standing surface waves. Here, we test four common species of earthworm to demonstrate that vertical vibration of living worms lying horizontally on a flat solid surface results in the onset of subharmonic Faraday-like body waves, which is possible because earthworms have a hydrostatic skeleton with a flexible skin and a liquid-filled body cavity. Our findings are supported by theoretical analysis based on a model of parametrically excited vibrations in liquid-filled elastic cylinders using material parameters of the worm's body reported in the literature. The ability to excite nonlinear subharmonic body waves in a living organism could be used to probe, and potentially to control, important biophysical processes such as the propagation of nerve impulses, thereby opening up avenues for addressing biological questions of fundamental impact.

Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry, and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability, and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at 70Hz are in qualitative agreement with the predictions of our modeling.

Friction on water sliders

A body in motion tends to stay in motion but is often slowed by friction. Here we investigate the friction experienced by centimeter-sized bodies sliding on water. We show that their motion is dominated by skin friction due to the boundary layer that forms in the fluid beneath the body. We develop a simple model that considers the boundary layer as quasi-steady, and is able to capture the experimental behaviour for a range of body sizes, masses, shapes and fluid viscosities. Furthermore, we demonstrate that friction can be reduced by modification of the body's shape or bottom topography. Our results are significant for understanding natural and artificial bodies moving at the air-water interface, and can inform the design of aerial-aquatic microrobots for environmental exploration and monitoring.

Hysteretic Faraday waves

We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate subcritically toward highly nonlinear ones with twice their amplitude. We relate this hysteresis with the change of shear stress using a simple stress balance, in agreement with numerical results.

Swimming droplets driven by a surface wave

Self-propelling motion is ubiquitous for soft active objects such as crawling cells, active filaments, and liquid droplets moving on surfaces. Deformation and energy dissipation are required for self-propulsion of both living and non-living matter. From the perspective of physics, searching for universal laws of self-propelled motions in a dissipative environment is worthwhile, regardless of the objects' details. In this article, we propose a simple experimental system that demonstrates spontaneous migration of a droplet under uniform mechanical agitation. As we vary control parameters, spontaneous symmetry breaking occurs sequentially, and cascades of bifurcations of the motion arise. Equations describing deformable particles and hydrodynamic simulations successfully describe all of the observed motions. This system should enable us to improve our understanding of spontaneous motions of self-propelled objects.