The role of a soft-gel on the natural frequencies and in the evolution of Faraday waves at the free surface of a fluid layer

The natural frequency of a fluid layer overlying on a rigid wall depends on the density of the fluid, surface tension at the free surface and the waveform that evolves at the free surface. However, the presence of a soft-gel layer underneath the fluid layer is expected to alter the natural frequency of the fluid layer. In this work, a linear stability analysis is carried out to show that the natural frequency of the fluid layer is altered by the elasticity of the compliant soft-gel layer. As a consequence of a shift in the natural frequency, linear stability calculations shown that there is also a shift in the instability regions when the fluid layer lying on the soft-gel is subjected to Faraday forcing. This indicates that the soft-gel layer either has a stabilizing effect or a destabilizing effect because the presence of a deformable soft-gel layer either raises or lowers the Faraday threshold to induce an instability.