Ultrasonic atomization of liquids: Stability analysis of the viscous liquid film free surface

One of the fundamental steps in the process of liquid fan ultrasonic atomization is the hydrodynamic instability. The resulting surface,waves become unstable and tear. This causes a mist of uniform droplets to be formed and ejected. The study of ideal liquid film free surface behavior in the steps prior to droplet formation leads to a stability analysis based on the Mathieu-Hill equation. Unfortunately, a similar analysis cannot realistically be developed for a viscous liquid. The present work performs a linear analysis derived from the hydrodynamics, which allows a stability analysis of viscous bounded liquid film free surface. Actual results are compared to those obtained in the case of an inviscid fluid.