Faraday wave lattice as an elastic metamaterial

Abstract

Metamaterials enable the emergence of novel physical properties due to the existence of an underlying sub-wavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern undergoes an oscillating secondary instability and exhibits spontaneous vibrations that are analogous to transverse elastic waves. By locally forcing these waves, we fully characterize their dispersion relation and show that a Faraday pattern presents an effective shear elasticity. We propose a physical mechanism combining surface tension with the Faraday structured interface that quantitatively predicts the elastic wave phase speed, revealing that the liquid interface behaves as an elastic metamaterial.PACS numbers: 47.35.Pq, 62.30.+d, 81.05.Xj An artificial material made of organized subwavelength functional building blocks is called a metamaterial [1,2] when it exhibits properties that differ greatly from that of the unit cell. These new physical properties are intrinsic of the presence of an underlying structure. Although metamaterials are still strongly associated with negative index materials in optics [3], they also refer to structures with mechanical [4], acoustic [5] or even thermodynamic properties [6]. By engineering building blocks from micro to metric scale, several new mechanical properties emerge in metamaterials, such as cloaking in elastic plates [7], auxetic behavior [8,9], ultralight materials [10] or seismic wave control [11]. So far the main challenge has been to design appropriate unit cells to obtain efficient metamaterial constructions. Here, we propose a novel approach that uses stationary waves to produce the underlying structure of a macroscopic metamaterial.Spatial patterns arising in systems driven away from equilibrium have been extensively studied over the last decades [12]. The Faraday instability is often used as a model system in non-linear physics and the patterns emerging from a vertically vibrated fluid layer are well documented [13][14][15][16][17]. This hydrodynamic instability appears at the interface between two fluids subjected to a vertical oscillation. Above a certain threshold of acceleration a c , the surface shows a stationary deformation that oscillates at half the excitation frequency. This pattern is both stable in time and regular in space, with a Faraday wavelength λ F defined by the inviscid gravity-capillary wave dispersion relationwhere k F = 2π/λ F is the Faraday wavenumber, g = 9.81 m.s −2 is the acceleration of gravity, σ is the surface tension of the fluid, h the fluid depth and ρ its density. For specific experimental conditions, one can achieve the formation of well structured and stable patterns (squares, hexagons, triangles... [15]). Although the pattern selection of this instability is quite complex, for a square vessel it is most often a square pattern that is obtained, with its two main directions aligned with the sides of the container. The pattern becomes unstable upon increasing the driving amplitude, and lead...

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Wave-based liquid-interface metamaterials

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“…Similar relations have recently been studied in the Faraday wave system (Welch, Liebman-Pelaez & Corwin 2016). It would be interesting to see how they can be connected to other properties of the liquid-gas interface perturbed by waves (Domino et al 2016). The behaviour of the small discs r p < L f does not allow for such a simple relation to be written but instead reflects the memory of this strongly out-of-equilibrium flow via diffusion coefficients that are proportional the flow r.m.s.…”