# Development of High-Power Ultrasonic System Dedicated to Metal Powder Atomization
## 2 Ultrasonic Atomization Phenomena  
The physical mechanism of the phenomenon that causes the atomization effect is broadly studied by many scientific centers and described through various mathematical models [15]. According to one of the hypotheses presented by [PERSON] [16], the phenomenon of atomization of liquid metals occurs as a result of the formation of surface waves in the liquid metal layer. A large amplitude of vibration overcomes the surface tension forces and detaches the droplets (Figure 1).  
In many publications, e.g., [11; 17; 18; 19], ultrasonic atomization of various liquids is described as an effect of cavitation phenomenon. High-power vibrations cause creation of the so-called cavitation bubbles. They break the surface tension of the liquid, allowing its atomization when it comes in contact with the surface of the sonotrode's working (vibrating) element [11; 17; 18; 19]. Depending on the process parameters, with the operating frequency as one of the most important one (see Figure 1), but also the kind of a liquid, it is possible to obtain droplets of various sizes and shapes. In the case of metal powder materials, the aim is to obtain powders with a spheroidal geometry and a narrow particle size distribution. This is the most influenced by two parameters of the ultrasonic system, i.e., the frequency and amplitude of the working tool vibrations. In addition, in this case,the physical properties of the liquid metal, such as viscosity, surface tension, temperature, and others, are important [18].  
According to the literature [17], the amplitude of vibrations should exceed a certain threshold value to initiate the atomization process. This level can be calculated using Equation (1) [17]  
\[A_{m}=\frac{2\mu}{\rho}\sqrt[3]{\frac{\rho}{\pi\sigma f}}\;\;, \tag{1}\]  
where: \(A_{m}\)--threshold value of the amplitude [\(\mu\)m], \(\mu\)--dynamic viscosity [Pa*s], \(\rho\)--liquid density [kg/m\({}^{3}\)], \(\sigma\)--surface tension [N/m] and \(f\)--vibrations frequency [Hz].  
On the ultrasonic system side, the vibration amplitude of the ultrasonic transducer can be adjusted by converting the excitation voltage value [17; 19; 20]. In addition, according to the assumptions of the surface wave model, increasing the frequency of the transducer's vibrations results in the formation of smaller droplets. This phenomenon is described by Equation (2) [11; 17]  
\[d=0.34\sqrt[3]{\frac{8\pi\sigma}{\rho f^{2}}}\;, \tag{2}\]  
where: \(d\)--droplets diameter [\(\mu\)m], \(\sigma\)--surface tension [N/m], \(\rho\)--metal density [kg/m\({}^{3}\)] and \(f\)--vibrations frequency [Hz].  
It can be found in the literature that the increase in the temperature of a liquid metal causes a decrease in particle size due to e.g., reduction of its surface tension [19]. In addition, the atomization process of liquid metals can be carried out in a protective atmosphere of argon, nitrogen or in the vacuum, which leads to the formation of spheroidal particles. The small presence of oxygen during the process usually leads to deviations of the particle geometry from the nodular shape [18; 19].  
Taking into account the above equations and literature data on material properties, it is possible to analytically determine the amplitude threshold values and droplet diameters for the two selected media, i.e., liquid metal and water. The material data, as well as the calculated values, are presented in Table 1[21].  
Figure 1: Diagram of the phenomenon of atomization of liquids: (**a**) a droplet on the surface of the plate, (**b**) formation of the capillary waves depending e.g., on the operating frequency, and (**c**) the appearance of liquid droplets in the atomization process (where the higher frequency should cause the release of finer droplets).