LINEAR INSTABILITY OF A POWER-LAW PLANAR LIQUID FILM IN A NORMAL ACOUSTIC FIELD

The breakup behavior of gel propellants under oscillatory operating conditions inside rocket engines is investigated through a linear instability analysis of a planar liquid film subjected to an acoustic field. Understanding the mechanisms that govern film destabilization is important, as rupture and atomization directly affect combustion efficiency and stability in propulsion systems. Most studies on liquid-film stability have not taken into account the velocity asymmetry of the gas streams on both sides of the film. The problem is usually simplified to symmetric gas streams with either pure sinuous or pure varicose modes, and investigations involving power-law fluids remain relatively limited. In this work, the instability of a power-law liquid film sheared by gas streams of different velocities under acoustic oscillations is analyzed using Floquet theory for temporal instability. The governing dispersion relation is derived, and dispersion curves are examined to clarify the influence of gas velocity, density contrast, and fluid rheology. Two distinct instability modes are identified: A varicose-like mode governed by the weaker aerodynamic stream and a sinuous-like mode governed by the stronger stream. At low wavenumbers, these modes deviate significantly from classical pure modes, while at high wavenumbers the differences diminish. Acoustic oscillations are shown to induce parametric instability regions. The varicose-like mode is more prone to parametric resonance, whereas the sinuous-like mode is more sensitive to oscillation amplitude. Increasing the Bond number suppresses Kelvin-Helmholtz (K-H) instability but enhances parametric instability, while oscillation frequency plays a decisive role in determining the location of parametric regions: Higher frequencies suppress parametric instability yet strengthen K-H instability. Larger apparent Reynolds numbers and velocity factors accelerate destabilization, promoting earlier rupture of the film. These results provide insight into the interplay between acoustic forcing, fluid rheology, and aerodynamic effects, offering useful guidance for the stability assessment of gel propellant systems in rocket engines.