The effect of parametric forcing on the supercritical Marangoni instability

This study investigates the behavior of a liquid-passive fluid bilayer heated from the liquid side, in the absence of gravity, and subject to parametric forcing. In large confinements without parametric forcing, a long-wave Marangoni instability and subsequent dry-out occur when the temperature difference exceeds a specific threshold. The primary objective is to explore mechanisms to prevent dry-out through mechanical parametric forcing. The results obtained using linear stability analysis and computations with a WRIBL-based nonlinear reduced-order model show that the liquid film can be rendered stable with a flat free surface within a specific range of forcing amplitudes. Beyond this range, the flow becomes unstable, leading to either Marangoni instability with dry spot formation at lower amplitudes or Faraday instability with large free surface oscillations at higher amplitudes. Beyond a critical value of the parametric frequency, stabilization to quiescent conditions cannot be achieved. Instead, we proceed directly from a Marangoni-dominated flow characterized by long-wavelengths to a short-wavelength resonance-dominated flow, again avoiding dry-out. The study identifies two critical factors for the occurrence of a critical parametric frequency: the finiteness of the container width and the presence of "resonant tongues," characterizing the threshold amplitude for Faraday instability.