Thwarting Marangoni instability in a viscoelastic liquid film via parametric forcing

Abstract

We explore how fluid elasticity affects the stabilization of an inherently unstable Marangoni-driven thin-film system through the application of parametric forcing. In the absence of elasticity, parametric forcing increases the threshold for the long-wave Marangoni instability mode in a thin liquid film, thereby stabilizing the system. A quiescent stable state is achievable within a finite forcing amplitude range, provided the forcing frequency is below a critical value. Outside this parameter range, the system is unstable on account of either Marangoni or Faraday instability. We find that the behavior for a film of viscoelastic liquid is different in two significant ways, as a result of fluid elasticity. Firstly, the neutral stability diagram in the amplitude versus frequency plane displays an island of stability, bounded by an upper and a lower frequency, as opposed to the Newtonian case, which displays only an upper frequency bound. Below the lower frequency bound and above the upper frequency bound, the film can be simultaneously subject to both Maranogni and Faraday instability. Secondly, fluid elasticity lowers the forcing amplitude at the neutral stability bound for both the Marangoni and Faraday instabilities, with a more significant reduction in the latter. As a result, both the threshold amplitude and the amplitude range for full stabilization of the thin-film system are reduced, which is attributed to the memory effect imparted by fluid elasticity. © 2025 American Physical Society.