Faraday wave lattice as an elastic metamaterial

TL;DR

This paper demonstrates that a fluid-air interface patterned by Faraday instability acts as an elastic metamaterial, exhibiting shear elasticity and supporting elastic-like waves, thus enabling new ways to engineer wave propagation in fluids.

Contribution

It introduces a novel approach to creating elastic metamaterials using Faraday patterns on fluid interfaces, linking surface tension and pattern structure to effective elasticity.

Findings

Faraday patterns support elastic transverse waves.

The phase speed of waves matches predictions from the elastic model.

The interface behaves as an elastic metamaterial with tunable properties.

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.