On droplet formation from capillary waves on a vibrating surface

The formation of sprays from a liquid film on a vibrating surface is used by ultrasonic atomizers for applications ranging from humidification to metal–powder manufacturing. The received opinion in the literature is that droplets are formed periodically from the apexes of an orderly pattern of standing capillary waves, with a wavelength that can be related to vibration frequency by stability analysis. It is described how this assumption may be incorrect in that, after droplet formation commences, the orderliness of the standing–wave pattern is lost due to one or more secondary instability phenomena. These phenomena, which lead to disorderliness, are investigated by using high–speed imaging techniques and a low–frequency vibrating film to model the high–frequency case, because of the difficulty of penetrating clouds of small droplets in the latter case. Different modes of droplet formation are identified and the flow patterns responsible for these modes are discussed. Physical mechanisms are proposed from which it is deduced that only a proportion of standing–wave crests can eject droplets, for a given wall–vibration period, and the identity of these ejecting waves should vary from period to period. The model thus developed demonstrates an apparently random ejection of droplets from one wave cell, even though the model itself is deterministic. The disorder of the capillary waves and the occurrence of several droplet–formation routes are sufficient to explain the range of droplet sizes that is produced by ultrasonic atomization.