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Faraday waves in soft elastic solids.
Giulia Bevilacqua1, Xingchen Shao2, John R Saylor2
1MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, Italy.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 19, 2020
Summary
Faraday instability in soft solids exhibits harmonic resonance, unlike the subharmonic resonance in fluids. This finding offers a new method to distinguish solid-like from fluid-like soft matter responses.
Area of Science:
- Soft matter physics
- Continuum mechanics
- Nonlinear dynamics
Background:
- Faraday waves are well-understood in viscous fluids but lack theoretical explanation in soft solids.
- Previous studies focused on fluid dynamics, leaving the solid-state phenomenon unexplained.
Purpose of the Study:
- To theoretically characterize Faraday waves in soft incompressible slabs.
- To investigate the onset of harmonic and subharmonic resonance eigenmodes in elastic solids.
Main Methods:
- Utilized Floquet theory to analyze the incremental boundary value problem.
- Transformed the problem into an algebraic eigenvalue problem.
- Identified three dimensionless parameters governing gravity, capillary, and elastic waves.
Main Results:
- Discovered that Faraday instability in soft solids is characterized by harmonic resonance.
- This contrasts with the subharmonic resonance typically observed in viscous fluids.
- The findings are valid within the physical range of material parameters.
Conclusions:
- The study provides the first theoretical explanation for Faraday waves in soft solids.
- Harmonic resonance in solids offers a distinct signature compared to fluid systems.
- This opens avenues for using Faraday waves as a precise method to differentiate solid-like and fluid-like behaviors in soft matter.
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