# The Development and Analysis of a Multistage Spraying Method for Liquids in an Ultrasonic Field
## 4 Results and discussion
### The Dependence of Droplet Diameter on the Spraying Rate  
Figure 8, shows the histograms of droplet diameter distribution for an increased liquid supply rate of 10 mL/s.  
Figure 7: Distribution of formed droplets: (**a**) after the first breakdown stage; (**b**) at the tubular emitter outlet.  
It follows from the presented histograms (Figure 8a) that at the increased liquid supply rate, the proportion of coarse droplets increased in the first stage of spraying. Analysis of the recorded images of droplet breakdown for the increased liquid supply rate showed that due to the increase in the rate of emission of primary droplets from the nozzle, the supply rate was increased by increasing the pressure of the liquid in the nozzle. Since the droplet traveled into the anti-node region at a higher velocity, the time of their structural instability development was reduced. And, on the contrary, the time of formation of small droplets due to capillary Faraday waves was reduced. In addition, an increased concentration of secondary droplets flying apart following the breakdown of the primary droplet, resulting in their increased coagulation probability, can result in the generation of a higher number of large droplets.  
In turn, the disperse composition of the aerosol after passing all stages of spraying slightly shifted to the region of larger particles (Sauter's diameter is 38 \(\upmu\)m). The increase in the median diameter was not more than 5 \(\upmu\)m. The fact that the droplets successively decelerated as they traveled through the anti-nodes of ultrasonic vibration velocity correlates with no significant increase in particle size with increasing spraying productivity. As a result, the time of droplet exposure to the anti-nodes of ultrasonic vibration velocity was sufficient to generate Faraday capillary waves over the entire surface of the droplet (flattened into a disk). As a result, small droplets proportional to the length of excited capillary waves were formed.  
The dependence of the median diameter of the formed droplets on the sprayed liquid supply rate is shown in Figure 9a. Each experimental point in Figure 9a was obtained by averaging 10 Sauter diameter measurements (determined using Malvern SprayTech (Malvern Panalytical, Malvern, United Kingdom). Figure 9b shows a histogram of the droplet diameter distribution for the maximum output.  
Figure 8: Histograms of droplet diameter distribution at increased rate of 10 mL/s: (**a**) after the first breakdown stage; (**b**) at the tubular emitter outlet.  
Figure 9: Dispersion characteristics of droplets at different rates: (**a**) dependence of median diameter on supply rate; (**b**) histogram of droplet diameter distribution at maximum rate (15 mL/s).  
Thus, it was established that the characteristics of the droplets remained almost constant within a wide range of variations in the aerosol generation productivity. A slight increase in the median diameter of the formed droplets was associated with an increase in the probability of coagulation of droplets with an increase in their concentration. However, when the productivity exceeded a certain limit value (depending on the emitter sizes; for the studied design--10 mL/s), the median droplet diameter began to increase significantly (Figure 9a). It continued increasing up to the values corresponding to the median diameter of large droplets obtained in the first stage of droplet breakdown. In this case, the histogram of droplet diameter distribution takes the shape shown in Figure 9b.