Influence of a soft-gel substrate on the evolution of Faraday waves at a fluid free surface

This study examines Faraday waves on the surface of a fluid layer resting on a soft-gel substrate. The fluid is modeled as Newtonian, while the soft-gel is treated as a linear viscoelastic material. First, a heuristic model is used to analyze the natural frequency of the soft-gel layer alone, showing that its elastic properties have either a stabilizing or a destabilizing effect on the free surface frequency. In the long-wave limit, a simple expression for the square of the natural frequency is obtained. This expression shows that as the elasticity of the gel increases, the natural frequency reduces, indicating the stabilizing effect of the soft-gel layer. Next, numerical calculations are performed for the natural frequencies of a fluid layer over the soft-gel. These calculations reveal that the gel can either increase or decrease the fluid's natural frequency. The increase results from stabilizing elastic stresses, while the decrease is due to destabilizing stresses at the gel fluid interface. These changes in natural frequency modify the threshold for Faraday instability at the fluid's surface, either raising or lowering it depending on the stabilizing or destabilizing effect of the soft-gel layer. The physics behind the dynamics of the soft-gel layer is explained using the elastocapillary number. A higher elastocapillary number indicates the dominance of elastic waves, and, on the contrary, a lower elastocapillary number indicates the dominance of surface tension.