Faraday waves in soft elastic solids

Abstract

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.

Faraday Instability in Viscous Fluids Covered with Elastic Polymer Films

“…This influence trend is different from that of soft elastomers. In the case of soft elastomer layers, the larger the driving frequency, the smaller the critical amplitude [43]. This result shows that people can increase the driving frequency to prevent Faraday instability of viscous fluid from causing safety hazards.…”

“…Giulia et al conducted an experimental analysis of soft elastic bodies and used Floquet theory to describe the Faraday wave in soft elastic bodies. It was found that the Faraday wave in soft elastic bodies was dominated by harmonic resonance modes, which provided a method for distinguishing fluids from soft elastic bodies [43]. Maksymov and Pototsky excited Faraday wave in living earthworms, which can be used to detect and possibly control important physiological processes of organisms, providing a method for solving fundamental biological problems, and developing new technology for detecting and controlling biological and physiological processes in vivo [15].…”

Dynamic self-organisation and pattern formation by magnon-polarons

“…2 therefore raise an intriguing question of how an excitation that is reasonably homogeneous (across >200 µm) results in such a heterogeneous ripple pattern with periodicity on the order of 10-20 µm. One possible explanation could be provided by the Faraday waves that appear predominantly in fluids subject to a periodic vertical oscillation [23], but which are also possible in solids [24]. However, taking into account the elastic parameters of YIG crystals together with the excitation frequency, we are able to rule out this possibility.…”

Elasto-capillary necking, bulging and Maxwell states in soft compressible cylinders

“…The observations of Fu et al (2021) for a solid cylinder have also been fully extended to the case of an incompressible hollow tube by Emery and Fu (2021b,c). Circumferential buckling instabilities in cylinders and tubes under surface tension and axial loading (Emery and Fu, 2021a), growth (Bevilacqua et al, 2020), and uniform pressure and geometric everting (Wang et al, 2021) have also been extensively studied in recent years.…”