(116i) Effect of a Deep Corrugated Wall on the Natural Frequencies and the Faraday Instability of a Fluid Interface

The natural frequency is the frequency that a system oscillates at when disturbed with the absence of external forcing. For an immiscible bilayer of fluid, the natural frequency of the interface is dependent on several factors such as the shape of the bottom wall, density differences across the interface, the height of the fluid layers, as well as the interfacial tension and interfacial wavenumber. In this study, we investigate the impact of a deep periodic wavy wall on the natural frequency by employing the thin film approximation to develop a reduced order model. The approximation assumes that the fluid layer height is small in comparison to the container width. When the interface is subjected to a wavy bottom wall, the natural frequency decreases, except when twice the number of waves at the interface is equal to the number of waves of the wall's pattern. The results of this study extend to the resonant frequency determined by Faraday excitation under parametric vertical forcing. The theoretical model was confirmed by physical experiments that tested different wall shapes, frequency ranges, and many interfacial patterns. Important results from this study show the change in natural frequency causes a shift in the instability regions. This shift in the instability region can decrease or increase the critical point of instability compared to a flat wall depending on the operation frequency. Furthermore, the results of this study have implications for understanding the behavior of multiphase flows in microfluidic devices, where the confinement and geometry can strongly influence the fluid dynamics. The findings also suggest potential applications in areas such as microscale heat exchangers and microfluidic mixers.

Acknowledgements

The authors acknowledge funding from NSF via grant number CBET-2025117