Finite-wavelength instability of acoustically forced thin liquid films

We develop a mechanistic thin-film theory for the instability and rupture of micrometer-scale liquid films subjected to high-frequency acoustic forcing. Starting from the compressible Navier–Stokes equations, a controlled multiscale expansion yields an averaged momentum balance in which acoustic radiation pressure and steady streaming stresses arise from a unified quadratic momentum flux. A lubrication reduction produces a closed evolution equation for the film thickness. Linear stability analysis identifies a finite-wavelength instability governed by an effective acoustic forcing that competes with capillarity and gravity, and a weakly nonlinear reduction distinguishes regimes of saturation and rupture within the thin-film limit. The framework yields scaling relations connecting viscous penetration, forcing amplitude, and a pre-rupture correlation length, clarifying that excitation frequency enters indirectly through penetration and acoustic efficiency rather than acting as a universal droplet-size selector.