Stability of an air-assisted viscous liquid sheet in the presence of acoustic oscillations

The linear temporal stability of a viscous liquid sheet is studied in the presence of acoustic oscillations. The viscous potential flow theory is applied to account for liquid viscosity. Acoustic oscillations are provided by imposing a sinusoidal oscillation of the gas velocity or density. Results suggest that the viscosity has a stabilizing effect with a zero mean velocity, and dual effects with a non-zero mean velocity. The effect of oscillations at low velocity is more significant than effects realized at high velocity. Oscillations are a destabilizing factor, although they have a weaker effect at a larger frequency than that at a lower frequency due to the liquid viscosity. Acoustic oscillations promote the instability of the liquid sheet; however, the effects of mean velocity, the gas-to-liquid density ratio, liquid sheet thickness and surface tension are analogous, whether acoustic oscillations exist or not.