Parametric instability of a single drop and an ensemble of drops under circular vibrations

Abstract

This article discusses forced oscillations and parametric instability of a cylindrical drop and an ensemble of drops under circular vibrations. The drop is surrounded by an incompressible liquid of a different density and is sandwiched between two parallel plates. In equilibrium, the drop has the shape of a circular cylinder bounded in the axial direction by these plates. The dynamic and average shape of the drop is constructed. A system of amplitude equations for small perturbations of the forced oscillations is obtained and the parametric instability of the single drop is studied. By analogy, a system of equations was written to study the parametric instability for an arbitrary drop in an ensemble of interacting drops. The regions of instability are constructed both for interacting modes and for modes of a higher order. It is shown that in the case of nonzero interaction, the lower modes are more dangerous in the presence of frequency detuning.