Dispersion relations, capillary waves, and the Rayleigh-Plateau instability

Abstract

The paper shows the importance of the dispersion relation in characterizing the capillary waves seen on liquid jets. Several theoretical models are given to better understand the stability of cylindrical interfaces when various parameters are considered, such as confinement, bulk elasticity, or the viscosity ratio between the two liquid phases. Theoretical predictions are compared with experimental data in terms of the fastest-growing mode for several liquid-in-air systems. Capillary-wave decay factors are also investigated, for stationary wave trains created at the impact of a liquid jet on a horizontal liquid bath, via the dispersion relation.