Instability of an ensemble of drops and dynamic regimes in a vibrational field

Abstract

The parametric instability of an ensemble of interacting droplets of liquid in a vibration field is studied. In the equilibrium position, the drops have the form of cylinders of rotation limited in the axial direction by two parallel solid surfaces and surrounded by an immiscible liquid. Both linear and nonlinear stability of forced oscillations of droplets of such an ensemble are considered. Regions of parametric instability are obtained, nonlinear subcritical and supercritical regimes are studied. In the case of non-zero interaction, the main modes are more dangerous in the presence of frequency disorder. The existence of three different dynamic regimes is demonstrated.