Effect of a deep corrugated wall on the natural frequencies and the Faraday instability of a fluid interface

Abstract

The natural frequency of an interface between a bilayer of immiscible fluids is shown to depend on the morphology of the bottom wall in addition to the density difference of the fluids, the interfacial tension, the fluid depths, and the disturbance wave number. To take into account deep wall-wave amplitudes and the viscosities of the fluids, a reduced-order method is employed that assumes the thickness of the bilayer to be small in comparison to the container width. A key result is that the wavy wall is shown to lower the natural frequencies unless the number of waves of the wall pattern is twice that of the number of waves at the interface. In addition, there are no restrictions on the types of interfacial modes that can be obtained. These theoretical findings carry over to the resonant frequency determined by parametric excitation, i.e., Faraday excitation. The theoretical results are qualitatively validated by physical experiments that use Faraday excitation over frequency ranges to obtain different interfacial modes under conditions that approximate slippery sidewalls. As a result of the shift in the resonant frequency there is a shift in the instability regions when fluid layers are subject to Faraday excitation. © 2024 American Physical Society.