# The Development and Analysis of a Multistage Spraying Method for Liquids in an Ultrasonic Field
## 1 Introduction  
In practice, the most common method of spraying liquids is hydraulic spraying, pneumatic spraying, dual-liquid spraying [1], electrostatic spraying [2], pressurized spraying [3], and ultrasonic spraying [4; 5; 6]. This variety of spraying methods is caused by the requirements of specific technological applications: in some cases, high dispersion and a narrow droplet size distribution are required; in others, a certain spray geometry is required; and in others, a stable spray speed, etc., is required. There are a number of tasks that require both high droplet dispersion and high productivity in spray creation. The simultaneous fulfillment of such requirements is difficult to achieve. The novelty of this work lies in the development of a new method of liquid spraying, combining high dispersion and high productivity. Simultaneously high aerosol production and high droplet dispersion are required in technological processes such as spray drying, aerosol coating, aerosol surface treatment, and aerosol drug delivery [7; 8; 9]. In spray drying, for example, the material is subjected to spraying to create an aerosol, which then quickly dries, forming fine dispersed particles with high surface activity [10]. In aerosol coating, high droplet dispersion allows for uniform coating application on the surface, and high aerosol production ensures the efficient coverage of large areas [11]. In aerosol surface treatment, high droplet dispersion helps to evenly distribute the treating substance, and high aerosol production accelerates the treatment process [12]. In aerosol drug delivery, high droplet dispersion is necessary to ensure rapid and uniformpenetration of the drug into the body, and high aerosol production allows for the delivery of the required amount of medication in a short period of time [13]. Ultrasonic spraying can provide the fulfillment of the listed requirements of the technological process. The ultrasonic method is well known and offers numerous advantages over conventional hydraulic and pneumatic spray nozzles. The advantage of this method is the stable and predictable relationship between the operating parameters, spraying speed, and droplet diameter [6; 7]. Additionally, ultrasonic spraying results in the narrowest droplet size distribution compared to other spraying methods. In addition, the ultrasonic method provides reduced spray velocities, infinitely variable control of fluid spray rates, and significantly reduced operating power consumption. In contrast to conventional spraying mechanisms, which rely on relatively high hydraulic pressures or high-velocity gas streams for the atomization of sprayed liquid media, ultrasonic nozzles utilize the ultrasonic mechanical vibrations of a piezoelectric transducer to vibrate an atomizing surface and thereby atomize a fluid disposed thereon [14]. Two main techniques of ultrasonic spraying are used in contemporary practice: spraying in a fountain and spraying in a liquid layer. Spraying in a fountain enables the generation of aerosols with an average particle size of 2-5 \(\upmu\)m at a frequency of up to 5 MHz. Yet, the productivity of this spraying technique is less than 1 mL/min, which is insufficient for practical applications in industry (for example, for the application of coatings). Therefore, its most common application falls within inhalation therapy and humidifiers. In turn, the concept of ultrasonic spraying of a liquid in a layer is that the liquid in the form of a thin film disintegrates into small droplets when moving over a vibrating surface (frequency \(>\) 20 kHz). Two main hypotheses, namely the capillary wave hypothesis and cavitation hypothesis, have been proposed to explain the concept of liquid disintegration during ultrasonic spraying. The capillary wave hypothesis is based on [PERSON]'s instability criteria [15]. [PERSON] [16] measured surface disturbances by photographing capillary wave peaks on a vibrating surface.