# The Development and Analysis of a Multistage Spraying Method for Liquids in an Ultrasonic Field
## 2 The Method of Multistage Ultrasonic Spraying  
Ultrasonic spraying's productivity in the generation of highly dispersed aerosols is limited, primarily by the fact that the formation of droplets occurs in a single stage, consisting of the detachment of a droplet from the surface of the liquid layer. Vibration frequencies of up to 200 kHz are used in the application of known implementations of ultrasonic spraying techniques of a liquid in a layer for the generation of highly dispersed liquid droplets [14; 22; 23; 24]. However, the generation of high-frequency vibrations with the amplitude required for spraying limits the emitting surface area. Such vibrations are rapidly attenuated in the sprayed liquid and intensely absorbed in the ultrasonic emitter material. For these reasons, it is fundamentally impossible to achieve high dispersing performance at high dispersities by means of ultrasonic exposure in a single stage. Therefore, in order to ensure the high-performance generation of highly dispersed aerosols under the impact of ultrasonic vibrations, a method of multistage ultrasonic spraying with the introduction of acoustic energy to the liquid through gas was proposed. The concept of implementation of the proposed technique of ultrasonic spraying is explained by the diagram provided in Figure 1.  
The proposed method involves the sprayed liquid being subjected to dispersion into large droplets by any known method of spraying, ensuring sufficient productivity with large droplet diameters, up to several millimeters (e.g., by hydraulic and ultrasonic  
Figure 1: Multistage ultrasonic spraying. spraying at a low frequency of exposure, etc.) at the first stage. The productivity of initial large droplet formation will determine that of the overall multistage process. The initial droplets generated with high productivity, which are in the air and moving in the direction of gravity (or the gas flow transporting the droplets), are exposed to ultrasonic vibrations (standing ultrasonic wave) on the gas side. Due to this, the droplets are deformed and destroyed, and the disperse composition of the droplets undergoes further evolution. The described process is repeated for each of the newly formed droplets many times, as many times as the droplets interact with the velocity anti-node in the standing ultrasonic wave. The process of droplet deformation and destruction while the droplet is in ultrasonic field continues until the surface tension forces do not equal the effect of the acoustic field forces. Thus, the sound pressure level is the main quantity that determines the minimum size to which a droplet can collapse. Analyzing the forces effecting the particle, the value of the threshold intensity of particle destruction can be determined [18]:  
\[I_{t}=2W_{l}\left(\frac{\sigma_{stp}}{D\omega p_{l}}\right)^{2} \tag{3}\]  
where \(\sigma_{stp}\) is the strength of the particle, \(\omega\) is the frequency of emission, \(\rho_{l}\) is the density of the fluid, \(W_{l}=\rho_{l}\)\(c\) is the wave resistance, and \(c\) is the speed of sound. It should be borne in mind that the strength of water \(\sigma_{stp}\) under pulse impact is several orders of magnitude less than the reference (theoretical) value [25]. An equation for the minimum droplet diameter at which the droplet can break down at a given level of exposure intensity \(I\) is obtained from Equation (3):  
\[D_{\min}=\frac{\sigma_{stp}}{\omega\rho_{l}}\sqrt{\frac{2W_{l}}{I}} \tag{4}\]  
The intensity of exposure is related to the sound pressure level \(p\) by a known relationship:  
\[I=\frac{p^{2}}{2W_{l}} \tag{5}\]  
Thus, there is a limiting size up to which a droplet can be destroyed, depending on the intensity of ultrasonic vibrations. At low intensities of ultrasonic vibrations, this size will be larger than the initial size of the droplets, which means they will not be destroyed.