Competing Mechanisms at Vibrated Interfaces of Density-Contrast Fluids

TL;DR

This study uncovers a new multi-modal instability at fluid interfaces with high density contrast, where competing Rayleigh--Taylor and Faraday instabilities influence each other, with implications for understanding complex fluid mixing phenomena.

Contribution

It reveals the coexistence and competition of RT and Faraday instabilities at vibrated density-contrast fluid interfaces, supported by Floquet analysis and numerical simulations.

Findings

Identified a multi-modal instability from RT and Faraday mechanisms coexistence.

Vibrations control transitions between RT and Faraday instabilities.

RT modes suppress Faraday responses in nonlinear regimes.

Abstract

Fluid--fluid interfacial instability and subsequent fluid mixing are ubiquitous in nature and engineering. The hydrodynamic instability of fluid interfaces has long centered on the pressure gradient-driven long-wavelength Rayleigh--Taylor instability and the resonance-induced short-wavelength Faraday instability. However, neither instability alone can explain the dynamics when both mechanisms are present. We identify a previously unseen multi-modal instability emerging from their coexistence. When the denser fluid is polydimethylsiloxane, the mixed region at a high density contrast (Atwood number=0.9) spans a vibration amplitude range approximately twice the gravitational acceleration. Using Floquet stability analysis, we show how vibrations govern transitions between the RT and Faraday instabilities, leading to contention between these instabilities rather than resonant enhancement. The initial transient growth is represented by the exponential modal growth of the most unstable Floquet exponent, along with its accompanying periodic behavior. Direct numerical simulations validate these findings and track interface breakup into the multiscale and nonlinear regimes. Specifically, we show that growing RT modes nonlinearly suppress Faraday responses even when the initial growth rate of the Faraday instability is 3.63 times that of RT, so a bidirectional competition hinders their sustained coexistence.