Resonance penetration of gas bubbles through a thin liquid layer: a capillary resonator and its use for the generation of droplets

As it is well known, a bounded layer of liquid forms an oscillatory system (resonator) for surface waves. We consider a capillary wave resonator that is composed by a thin liquid layer placed on a substrate and surrounded by a solid ring. The dimensions of the system are chosen so that gravity forces are small compared with forces from surface tension. Standing capillary waves are excited by a gas flow supplied through a small orifice in the substrate. Stable oscillations in various resonator modes are described which are accompanied by ordered formation and destruction of gas bubbles producing the regular streams of identical droplets. The mechanism of self-oscillatory behaviour based on the correspondence between bubble growth time and oscillation period is proposed and analysed. Possible applications of the phenomenon, in particular, for the generation of monodisperse droplets without special periodic stimulation, are discussed.