2. Linear stability theories

2.1 Instability of an isolated perfect liquid cylinder (Rayleigh)

This first approach to atomization, although not very applicable to ordinary atomizers (except for vibration atomization), represents the basis of all atomization models based on stability studies. We will therefore detail its development here, so as to make other, more complex models understandable, using the same steps and presenting only the results.

Consider an axisymmetric cylinder of incompressible perfect (non-viscous) liquid, whose surface deforms when a disturbance passes over it. The initial radius R of the cylinder then changes to R + η.

The aim of this approach is to determine which type of disturbance will be amplified during liquid flow. It is assumed that...