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Article

Influence of Process Parameters on the Ultrasonic Atomization Efficiency and Possibility of Testing Properties of Liquid Metals

by
Rafał Szostak-Staropiętka
1,2,*,
Wojciech Presz
1,
Roksana Pawlic
2,
Anna Dziubińska
1 and
Katarzyna Kołacz
2
1
Faculty of Mechanical and Industrial Engineering, Warsaw University of Technology, Narbutta 85 Street, 02-524 Warsaw, Poland
2
Lukasiewicz Research Network—Tele and Radio Research Institute, Ratuszowa 11 Street, 03-450 Warsaw, Poland
*
Author to whom correspondence should be addressed.
Metrology 2025, 5(3), 39; https://doi.org/10.3390/metrology5030039
Submission received: 28 February 2025 / Revised: 2 May 2025 / Accepted: 19 June 2025 / Published: 2 July 2025

Abstract

Over recent years, ultrasonic atomization, especially with regard to liquid metals, has become an object of increased interest, mainly from industry, for additive manufacturing, but also from investigators, for research purposes. A strong correlation between the average particle size, distribution of particle sizes, and other process parameters like frequency and vibration amplitude was noted based on the analysis of available theoretical studies, simulations and experiments. The influence of parameters of the atomized fluid-like viscosity and surface tension on process parameters was also mentioned. The objective of this study is further research on the feasibility of using ultrasonic atomization to examine the properties of liquids, especially metals in liquid state. It attempts to close a gap in existing knowledge in searching for a new, possibly simple and cost-effective method to study the properties of liquid metals and further clarify the relationship between ultrasonic atomization parameters (amplitude, frequency, characteristics of metal being spilled on a vibrating surface) and obtained atomization results meant by average particle size and atomization time. Using numerical modeling (finite element method and computational fluid dynamics) as a methodology, combined with tests of using ultrasonic atomization as an instrument to determine properties of liquid metals, was considered as an introduction to a series of experiments. These tests were followed by real experiments that are also presented. At the first stage, numerical modeling was applied to a case of a specific liquid being spilled over a vibrating surface of different angles of inclination and specified, constant frequency and amplitude. The results of the simulation are in line with the current state of knowledge about ultrasonic atomization. Moreover, they can provide some more information on scalability, thus easing the comparison of the results of other experiments presented in the available literature. As a result, the relationship between fluid properties and the average size of atomized particles was demonstrated independently of the surface inclination angle. In the same way, the dependence of successful atomization on a sufficiently thin layer of a liquid was demonstrated. Thirdly, a correlation between the aforementioned layer thickness and the value of vibration amplitude has also been shown. Taking all the above into consideration, ultrasonic atomization can also be considered a research method and can be applied to study the properties of liquid metals. Further research, simulations and experimentation will be conducted to verify, develop and describe this method in full.

1. Introduction

The most important parameters that in various technological processes have an influence on the behavior of liquid materials, i.e., metals in the liquid state, are viscosity and surface tension. In metallurgical and foundry processes, factors like mold pouring, metal refining, degassing of the casting in the solidification process, as well as the metal solidification process in the mold itself, have been an object of interest in industry and science. Most properties of a metal (or alloy) are dependent on the primary structure of the casting or ingot. These final properties, mechanical and plastic, have an influence on further processing and final application of the material.
Viscosity is defined as the internal friction in a fluid and is described as the ability to carry tangential stresses by the fluid [1]. On the other hand, surface tension is defined as a physical phenomenon that occurs at the interface between the surface of a liquid and another medium, thanks to which this surface behaves like an elastic film. The cause of this phenomenon is believed to be the occurrence of attractive forces between the molecules of the liquid [2].
Since knowledge of the technological properties of liquid metals allows assessment of the quality of liquid metal and resulting solid, diagnosis of problems, and facilitation of the design of further processes, proper and accurate measurements have become a significant part of the metallurgical process.
Methods of testing the properties of liquid metals are known to be difficult, mainly due to the issues with keeping the liquid metal clean. Liquid metals have a tendency to be contaminated with other metals, surfactants, or even oxygen or nitrogen from the atmosphere. Many of the known methods that are commonly used to determine the properties of liquids are not applicable to the study of the properties of liquid metals, simply for this reason.
This article is the second step in an attempt to find the answer to the question of whether ultrasonic atomization can be an effective tool to study the properties of liquid metals, including impurities, and how effective it is. Although some conclusions are drawn, many other factors will be examined later, in detail, in the next experiments and simulations.
The objective of this article is to verify the hypothesis that ultrasonic atomization can be used to examine the properties of liquid metals. Ultrasonic atomization as a method of such measurement is being developed and investigated in this article. As mentioned before, this is a method in the early stage, and at this stage, it does not take into account factors like contamination, condition and amount of slag (important in the processing of steel), but there are strong reasons to use this method for testing such factors in the future. At this moment, basic hypotheses were tested and simulations were performed only for liquids (metals) of high purity and homogeneity. In the same manner, experiments were conducted in conditions allowing verification of theoretical predictions.

2. Phenomenon of Ultrasonic Atomization

Ultrasonic atomization is a phenomenon that occurs on the surface of a liquid being exposed to excitation with ultrasonic waves of high energy. Fine droplets of liquid are gradually generated at the gas–liquid interface [3]. The size of these droplets, depending on process parameters and properties of liquid can be even smaller than those produced by a spray nozzle. Moreover, they can diffuse into the gas phase without a significant change in their thermal state in comparison to other atomization methods [4]. Ultrasonic atomization does not need additional heat delivery; it uses only high-frequency ultrasonic excitation. Due to its relative simplicity, successful implementation of this technique has been proven in fuel delivery and combustion [5], drug delivery, including nebulization [6,7], air purification [8] and food processing [9]. The most recent applications of ultrasonic atomization are the production of metal powders for additive manufacturing [10,11,12] and testing properties of liquids, including liquid metals [13].
Although the phenomenon of ultrasonic atomization was described for the first time a long time ago [14], its mechanism is still not known and understood in full. The main hypotheses are still being discussed [15,16,17]. At the present moment, two main theories are used to describe it. These are cavitation theory and capillary wave theory; however, the authors in [18] point out the presence of a combination or cavitation-wave theory also.
Cavitation theory indicates cavitation as a main factor of atomization. When the liquid phase is excited with ultrasonic waves of sufficient energy, local implosions of bubbles (cavities) produce the droplets by rupture of the liquid–air interface. Repeatedly expanded and contracted cavities finally collapse when localized pressure in a liquid drops below the vapor pressure. This results in the formation and collapse of air/gas cavities and shock waves that are generated by cavity collapse. As a result, fine droplets are generated and ejected from the surface [19,20]. This phenomenon is dependent on surpassing a critical amplitude of ultrasonic vibrations, known as the Blake threshold. This theory, however, relies upon the atomizer parameters and geometry as well as upon the frequency used in the process (frequencies over 100 kHz and transducer power greater than 100 W) [18].
As per capillary wave theory, droplet generation occurs when unstable oscillations on the surface of the liquid have energy (expressed also as proportional to the amplitude of vibrations) sufficient to tear the surface of a liquid and to form the peaks of capillary waves. These waves, known also as Faraday waves, are standing wave patterns that occur on the surface of a fluid subjected to vibrations. These structured pattern ligaments appear due to the interplay between gravity, surface tension, and the periodic oscillations induced by the vibrating surface [15].
The droplet size of the generated mist highly depends on the wavelength of capillary waves. As observed, the capillary wavelength decreases with the increase in ultrasonic frequency, and smaller droplets are generated at higher frequencies. The wavelength of capillary waves can be estimated with the equation [21]:
λ = 8 π σ ρ f 2 1 3
where λ is the capillary wavelength, ρ and σ are, respectively, the density and surface tension of the atomized fluid, and f is a vibration frequency.
The median diameter of generated droplets within frequencies of 10–800 kHz [22] is proportional to the wavelength, as per correlation:
dp = 0.34·λ
where dp is the mean diameter of the atomized droplet.
Finally, the relation between the ultrasonic frequency and the mean diameter of a droplet is described by equation:
d = 0.34 8 π σ ρ f 2 1 3
Since the measurement method was based on the comparison of droplet sizes measured optically by use of a microscope and high-speed camera and the values were multiplied by a coefficient dependent on the capillary wavelength, droplets that could not be seen with the microscope were also taken into consideration. This leads to the conclusion that the true size of a droplet was in this case only estimated, not determined in detail. Evidence of such inaccuracy is present in [23], where the coefficient of 0.34 is shown not as a constant, but a variable that may range even from 0.17 to 0.65 (0.41 ± 0.24). Experiments and related calculations in [24] even led to the conclusion that the equation derived in [22] is valid only under specific experimental conditions. A lack of experimental results that can be compared both directly and indirectly, unfortunately, leaves all of the consideration still at the theoretical level only.

3. Numerical Methods

Parallel to experimental methods in the study of physical phenomena, including atomization, numerical methods are being applied, analyzed and developed. The use of these methods allows firstly to verify existing theories and to draw conclusions about the further application and development of the process. On the other hand, the lack of complete understanding of the process limits the development of suitable numerical methods.
The use of numerical methods has the advantage that it allows an analysis of the studied phenomenon with significantly less effort and at much lower costs. In such studies, it is important to build a mathematical model with proper, sufficient accuracy, but the result should be treated in terms of an exact approximation, not a final result. The most advantageous case is when simulations are related to or are an introduction to real experiments.
Results and conclusions contained in [25] confirmed the validity of simulation results and the research methodology for concentrating power of cavitation in ultrasonic cleaning. Authors of [26] have proven the usefulness of the cavitation mathematical model in predicting erosive damage on surfaces of exposed material. As per [27], numerical simulation can successfully investigate the characteristics of a fluidic oscillator operating in quiescent air and a crossflow. Sufficient computational power even allows for the investigation of cavitation bubble dynamics and collapse [28] or even more demanding, coupled simulations like modeling of droplet impact on heat transfer during spray cooling under vibration environment [29] or atomization of a liquid under electrostatic charge [30]. Properly built and executed numerical simulation, even simplified into a two-dimensional domain, can give results accurate enough to be treated as a cross-section of a 3D domain and become serious guidance for further research.

4. Considerations on Ultrasonic Atomization as a Method to Investigate the Properties of Liquid Metals

Over recent years, ultrasonic atomization, despite applications mentioned earlier, has also been known as a method for the production of metal powders mainly for additive manufacturing. Being investigated and developed, it showed many advantages such as high predictability of average particle size and the possibility of obtaining a narrow distribution of powder particle sizes in comparison to other atomization techniques [11]. The high contribution of particles with the desired spherical shape in the total volume of the obtained powder is also an advantage of the process. Spherical shape is also a superior one for measurements, as spheres show the same shape regardless of orientation. This improves the accuracy of the size measurement results and thus, other properties measured based on the measurement of the atomized particle size. Other advantages, such as the possibility of carrying out the process in an atmosphere of different gases (inert or active), under both vacuum and pressure and the relatively low velocities of the atomized particles affecting the overall size of the atomization device, have led to interest in the ultrasonic atomization method not only for purely commercial purposes but also for research.
The process of ultrasonic atomization of liquids has been known for years and described in the literature; however, these descriptions concern the wave generation phenomenon itself [21] and the application of the ultrasonic atomization phenomenon to produce a mist or metal powders [31]. So far, no attempt has been made to investigate ultrasonic atomization for research purposes, and the following considerations and results are such an attempt.
By modification of Equation (3), the formula to obtain a surface tension can be found as:
σ = ρ f 2 d 3 0.314432   π
This assumption based on studies described, e.g., in [32], gives a good initial estimation, but ignores viscosity and assumes a small amplitude on a vibrating surface. In a similar manner, other theoretical analyses were performed and the results can be found in the literature [33,34].
Based on this theory, a practically comprehensive experiment was carried out and described [35]. It was aimed at verification and connection of existing dependencies, as well as concluding on the scalability of the derived formulas. One of its conclusions is the determination of the critical amplitude, which is necessary to start the process of wave excitation and thus, atomization:
A m = 2 μ ρ · ρ π σ f 3
where Am is the critical amplitude, µ is the viscosity, ρ is the density, σ is the surface tension of the liquid and f is the vibration frequency.
By modification of this equation, the viscosity can be found as:
μ = ρ · A m 2 · ρ π · σ · f 3
For the purpose of investigating the relation between viscosity and critical amplitude, the density of liquid metal can be considered constant. For liquid metal, i.e., aluminum, its density decreases linearly from 2357 to 2304 kg/m3 when the temperature changes from 973 to 1173 K [36]. The inaccuracy of liquid metal’s density can be kept smaller than 0.57%, provided temperature changes are allowed to vary only within the range of ±25 K. Inaccuracy can be even smaller when temperature variations are further decreased. With the assumption above, viscosity becomes proportional to the vibration amplitude, as well as the surface tension and vibrational frequency according to Equation (6); however, the last two factors have a smaller influence due to its occurrence under a third-degree root.
The research presented below is an attempt to verify the above assumptions, as well as the scale of the relationship between the material properties and the parameters of the atomization process.

5. Assumptions for the Experiment

Since numerical verification of the hypothesis on the dependence of the size of the atomized particle on the properties of the liquid metal was found to be sufficient [13,37], the volume of fluid (VOF) method was chosen and used for modeling multiphase flows using computer-aided design methods in the field of computational fluid dynamics (CFD).
VOF is a multiphase model that is considered to be simple but predictable and highly accurate [38]. Its advantage is that it uses only a single momentum equation [37,38]. The vibrating motion of the base, causing vibrations in the liquid, is applied according to the continuity equation. The surface tension is assumed to be a constant value corresponding to the value for the liquid to be tested.
In the planned experiment, this method was used to check the relationship between the angle of inclination of the vibrating surface and the rate of atomization of the liquid sample. Such an approach is designed to simplify the practical part of the task by directing the atomized stream in one direction and making it easier for the droplets to spill over the vibrating surface. Due to the fact that different liquids have different contact angles, it is advisable to minimize this factor. Although it is possible to place a portion of the liquid on a horizontal vibrating surface and the results of studies carried out in this way are known [18,24], in practice, a greater effect of heat transfer from the portion of liquid metal to the vibrating surface would be expected. Greater heat transfer, in turn, would affect the characteristics of the vibrating stack. On the other hand, easier spillage of liquid metal affects the efficiency of the atomization process; in extreme cases, excessive accumulation of liquid metal can stop the atomization process [39].

6. Numerical Model of Ultrasonic Atomization

In order to verify theoretical considerations and assumptions, a model based on a similar one described in [37] was created. The same homogeneous quadrilateral mesh with a size of 0.002 mm was used to minimize the influence of the mesh on the calculations. Since a droplet of 2 mm in diameter was analyzed and sufficient space has to be assured for the spillage of a droplet within the domain, the modeling space dimensions were set to 30 mm in length and 2.05 mm in height. The model constructed on the basis of these criteria consisted of 3,820,000 elements. Calculations were performed using the Fluent solver included in the ANSYS R19 Package [40]. A diagram of the model used for calculations is shown in Figure 1.
The inclination angle of the vibrating surface was taken into account as the breakdown of the gravitational force and the velocity of the droplet impact into the tangential and normal components to the surface. Schematically, it is shown in Figure 1 with arrows. This approach ensured that the number of elements used for the analysis was minimized and allowed the use of the same homogeneous quadrilateral mesh for each case. Three cases of inclination were analyzed: 30, 45 and 60 degrees, with the following values of gravity acceleration and fall velocity corresponding to the fall of a drop from a height of 0.3 m, as shown in Table 1.
At this stage, water with the following parameters was used as a liquid in order to check the adopted simplifications in the model:
  • density: 998 kg/m3;
  • viscosity: 1.003 mPa·s;
  • surface tension: 0.0728 N/m.
The model is based on the equation of motion of the ground defined as:
y(t) = A·sin(2π·f·t)
where y(t) is the deflection as a function of time, A is the amplitude, f is the frequency and t is the time.
A frequency of 50 kHz was used in the simulation as a reference to the results presented in the aforementioned studies. This frequency was also chosen for the reason of significantly smaller atomization time and calculation time (approximately 25%) than for lower frequencies [37].

7. Simulation Results

In the first phase, the overall behavior of a spilled droplet was analyzed over time of atomization. Results for the inclination angle of 30 degrees are presented in Figure 2.
The time of simulation for every case was limited to 0.004 s as sufficient to make conclusions about the process principles, formation of droplets, the influence of inclination angle on speed of atomization and the speed of the process in general. The evaluation of physical, chemical and thermodynamic properties by simulation is also possible, but it has not been performed at this stage due to the proportionally longer simulation time for each additional degree of freedom.
Results have confirmed previous observations [13] and evidence [12] of atomized particles’ mean size (measured as 37 μm) and the dependence of starting the atomization process on the thickness of the liquid layer. The atomization process is the fastest in areas of the thinnest liquid layer, as shown in Figure 3, although some evidence of atomization occurred in different areas, like the crests of waves of much larger length shown in Figure 4 (the enlarged area marked as a yellow rectangle in Figure 2), or areas close to the wavefront, as shown in Figure 5.
The vast majority of particles have the same size as theoretically predicted; however, a significant number of particles of larger diameter have also been noticed. As an example, the evolution of large particle formation on a moving wavefront over time is shown in Figure 5.
Comparing the progress of atomization, its effect in relation to the inclination angle of the vibrating surface is presented in Figure 6. It shows the result of the atomization process in 0.004 s for angles of 30, 45 and 60 degrees, respectively, from top to bottom. For reference, the initial stage (t = 0) of the simulation was added to the results table.
The results of this comparison are presented in Table 2. The efficiency of the atomization process was estimated by measuring the amount (area) of a liquid remaining on the vibrating surface. For reference, the area of a 2 mm droplet was also presented.
The difference between extreme cases is 2.7%, and the atomization of a single droplet can be considered insignificant. The analyzed case is a simplified two-dimensional one, and slope angles in the third dimension are smaller than the nominal one. However, with increased feed rate or for purposes of constructing a research or production stand, it may prove important as it has an impact on the overall geometry of a stand and heat transfer of the used vibrating stack.

8. The Experiment

For further investigation of the atomization process of the liquid metals, a simple test stand was built. It consists of a frame that allows adjustment of the inclination of the vibrating surface relative to the horizontal. The vibrating system itself consists of an available ultrasonic transducer (Sonic Converter) and a number of available acoustic signal amplifiers (boosters). A stainless-steel plate with dimensions of 160 mm × 30 mm × 1 mm was used as the vibrating surface. The system was powered by a digital ultrasonic generator, Sonic Blaster Plus. All elements were designed and manufactured at the Tele- and Radio Research Institute, which is part of the Łukasiewicz Research Network. The devices are shown in Figure 7.
Since the output amplitude of an available converter was initially estimated as 6 μm, acoustic amplification was set to 2:1 in order to obtain a 12 μm amplitude of the vibrating surface. This assumption was based on the available data on the viscosities of liquid metals. Refs. [41,42,43,44,45,46] and the necessary minimal amplitude was based on Equation (5). The viscosity of the liquid metal is typically in the range of 1.05 (Aluminum alloys) to 7.50 mPa·s (low-carbon steel alloys); however, for specific grades of steel, this value can even reach 18 mPa·s. For the worst-case scenario, the minimal theoretical amplitude necessary to start the process atomization for liquid metals was estimated as less than 2 μm; however, a specially prepared liquid used for the experiment has a viscosity of 5.5 mPa·s, a density of 995 kg/m3 and surface tension of 0.047 N/m. For such liquid, the minimal theoretical amplitude of atomization is 6.08 μm. In order to compensate for all unknown factors and uncertainties, a so-called safety factor of 2 was adopted to reach the mentioned necessary output amplitude at 100% power from the generator.
To supply the system with liquid, a calibrated orifice of 2 mm in diameter was used. The frequency of liquid delivery was varied from 1 droplet per second to a continuous stream.

9. The Results

The first run of the experiment revealed unexpected difficulties in successful atomization. Although some of the liquid has been atomized, the residue formed a characteristic pattern corresponding to the arrangement of nodes and antinodes on the vibrating surface, as shown in Figure 8.
With the addition of subsequent drops, the thickness of the remaining layer increased, the power absorbed by the vibrating system also increased, but the liquid did not flow off the surface. This showed that the energy of vibrations was not sufficient to start the atomization process, so the real amplitude of the vibrating surface and the available ultrasonic converter was measured, as shown in Figure 9. The device for amplitude measurements that contained an optical laser sensor of distance was designed and developed in Łukasiewicz Tele- and Radio Research Institute, Warsaw, Poland.
Surprisingly, the measured maximum amplitude was only about 2.8 μm. Measurements were made using the mentioned laser sensor and verified using a standard micrometer gauge. Although many points on a graph show smaller or larger values, this is due to the fact that the measured surface was not perfectly even and caused reflections. Measurements have also shown limited linear dependency in the relationship between the amplitude set by the generator and the output amplitude available at the converter. Within the range of 5 to 60%, the output amplitude of the converter increased linearly to 2.4 μm. At 70%, it reached 2.8 μm. For higher values set by the generator, the amplitude increase was within the measurement error, despite the increased power consumption measured by the generator.
After rearranging the setting of the waveguiding signal amplifiers, an amplitude of 8 μm was reached, and the experiment was continued. With sufficiently large amplitude, the conducted atomization process went smoothly, showing the strongest atomization at the nodes of the vibrating plate, as shown in Figure 10.
At the next stage of the experiment, the viscosity of the liquid was gradually increased to find the correlation between the viscosity of the liquid itself and the magnitude of the amplitude necessary to initiate the atomization. The results have confirmed the assumptions for the liquid with a viscosity of 7.5 mPa·s, density of 997 kg/m3 and surface tension of 0.055 N/m. Such a liquid required an amplitude not lower than 8 μm.
In the last stage of the experiment, a liquid of very high viscosity (by two orders of magnitude) was used to examine its behavior when excited with vibrations. The same behavior of the equipment was examined during an increasing amount of liquid being atomized. Subsequent steps of the experiment are shown in Figure 11.
As subsequent drops were fed onto the vibrating surface, the formation of a characteristic pattern similar to the pattern in Figure 8 was observed first, and then the thickness of the formed buildup layer increased. Atomization was not started despite the increase in the power drawn from the generator (a). Despite the increasing thickness of the layer, the liquid did not tend to flow off the vibrating surface. However, an increasing amount of liquid caused a minimal change in the frequency of the process and increased power consumption from the generator. After switching off the ultrasound (b), the existing pattern spread over the plate and flowed evenly downwards, creating a stream. After the first drop dripped and the ultrasound was switched on again, the pattern was recreated. The subsequent stages of pattern formation are shown in steps (c–f).

10. Conclusions

The aim of the study was to evaluate in more detail the applicability of ultrasonic atomization to study the properties of liquids, including metals. The second aim was to study the possibility of using numerical simulations as approximations of real ultrasonic atomization experiments. Simulation experiments shown within this study are consistent with real experiments in terms of the behavior of a liquid droplet dropped onto a vibrating surface and the initiation (or not) of the ultrasonic atomization process. This confirms the correctness and sufficient accuracy of the numerical model as an alternative to challenging real experiments or observations. Models used for the purpose of this study clearly confirmed capillary wave theory; however, this theory can dominate over cavitation theory for lower ultrasonic frequencies. It is also possible that the parameters and accuracy of the model were not sufficient to show the generation of a cavitation bubble, but this was not a goal of this study. Simulations are also proven to be valuable tests for planned experiments, as unexpected factors like overestimated output amplitude can lead to wrong conclusions or make the experiment unsuccessful. An interesting result of the observation is also the fact that the liquid does not atomize until its spreading speed drops below a certain value. The liquid atomizes firstly from the wavefront when its speed drops to the minimum speed, secondly—from the center of the spreading droplet surface, when the layer thickness decreases below a certain value. In both cases, it is in the direction perpendicular to the liquid surface.
The presented results can be a subject for further discussion, showing the need to adopt uniform indicators during the experiments. As a result, it can be clearly stated that ultrasonic atomization can be an alternative in testing properties of liquids, including liquid metals, provided proper conditions for the process are assured. The amplitude of vibrations was found to be a decisive factor in measuring liquid properties: primarily viscosity, but also surface tension. However, for more detailed research, the distribution of amplitude for the vibrating surface shall be taken into consideration; as for detailed measurements, an evenly distributed amplitude is preferred. In the same way, an accurate value given in units of length is necessary for measurement as well as for comparison purposes. Since the inclination angle value within the specified range has been found as an insignificant factor for the process of atomization, other research results can be compared without the precise determination of this factor. However, the inclination angle can have an influence on the overall geometry of the vibrating stack (size of the vibrating surface) and thus on the overall geometry (size and volume) of the atomization stand.
Results of the experiment have confirmed the fact that parameters of ultrasonic atomization and liquid properties correlated in the wrong way can even stop the process of ultrasonic atomization, as mentioned to be possible in [13] and reported in [39]. Excessive feeding resulted in the formation of a considerable amount of molten metal on the sonotrode platform. As a result, the thickness of the liquid layer was increased, and this phenomenon prevented the ultrasound system from working properly. Taking into account all the above-described results, it is possible to confirm the thesis given at the beginning—that ultrasonic atomization can be an effective tool to study the properties of liquid metals, including impurities understood as deviations from nominal values. These cases, as well as various cases of changing fugacity and wettability, will be examined later, during the next set of experiments. At the present moment, the objective of this research and article has been met in the range of verification of the method for simple cases.
The proposed method, although in the verification and testing phase, was submitted for patent protection in October 2024.

11. Future Work

In the next stage of this work, a test stand with the ability to atomize liquids with temperatures of over 700 °C will be constructed, taking into account all the conclusions from this set of experiments. The temperature of 700 °C is sufficient to melt alloys of aluminum, a metal sensitive to oxidation and thus to changes in viscosity and surface tension as well as fugacity and wettability. In parallel with the construction of the test stand, a number of other simulations will be carried out as an attempt to determine the influence of the condition (understood as roughness and flatness) of the atomizing surface on the atomization process and the accuracy of properties’ testing. Research is planned in the following steps:
(a)
Numerical verification of heat exchange during the atomization process and development of the ultrasonic device in its final shape.
(b)
Design of an ultrasonic device that can provide sufficient amplitude and is non-sensitive to excessive buildup of a liquid metal, as this can disturb or even stop the process.
(c)
Investigation (separately) of the influence of the amplitude, frequency, liquid feed rate, and surface conditions on the time of the atomization process and the size of particles.
(d)
Investigation (separately) of the influence of the parameters of the atomized liquid (density, viscosity, surface tension and purity) on the time, efficiency and accuracy of the atomization process.
(e)
Verification of the results with available data on liquid metals.
The results will be used for further development of research methodologies for ultrasonic atomization in testing properties of liquids and ultrasonic systems for use in research work on the atomization of liquids, including liquid metals. In parallel, results are planned for the development of ultrasonic atomization for the powder metallurgy industry. With developed methods and equipment, industrial research on powder metallurgy, including research on impurities, oxidation and slag conditions, is also planned.

Author Contributions

Conceptualization, R.S.-S., W.P., and A.D.; methodology, W.P., R.S.-S., and R.P.; software, R.S.-S. and R.P.; validation, W.P., R.S.-S., A.D., and K.K.; formal analysis, W.P., R.S.-S., K.K., and A.D.; investigation, R.S.-S.; resources, W.P. and K.K.; writing—original draft preparation, R.S.-S. and A.D.; writing—review and editing, R.P. and A.D.; visualization, R.S.-S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Ultrasonic atomization domain model and its representation for simulation.
Figure 1. Ultrasonic atomization domain model and its representation for simulation.
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Figure 2. The process of droplet spreading on the vibrating surface and the evolution of ultrasonic atomization over time (time in seconds; air—blue, liquid—red).
Figure 2. The process of droplet spreading on the vibrating surface and the evolution of ultrasonic atomization over time (time in seconds; air—blue, liquid—red).
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Figure 3. Evolution of atomization from a sufficiently thin layer of liquid over time (time in microseconds; air—blue, liquid—red, flow direction from right to left).
Figure 3. Evolution of atomization from a sufficiently thin layer of liquid over time (time in microseconds; air—blue, liquid—red, flow direction from right to left).
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Figure 4. Example of atomization starting from a wavefront (air—blue, liquid—red).
Figure 4. Example of atomization starting from a wavefront (air—blue, liquid—red).
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Figure 5. Evolution of the moving wavefront over time and an example of large particle formation. (no timescale; air—blue, liquid—red).
Figure 5. Evolution of the moving wavefront over time and an example of large particle formation. (no timescale; air—blue, liquid—red).
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Figure 6. Comparison of atomization results after time 0.004 s for various inclination angles (air—blue, liquid—red).
Figure 6. Comparison of atomization results after time 0.004 s for various inclination angles (air—blue, liquid—red).
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Figure 7. Equipment used for the experiment: Left—ultrasonic generator, Right—ultrasonic stack mounted in a test stand.
Figure 7. Equipment used for the experiment: Left—ultrasonic generator, Right—ultrasonic stack mounted in a test stand.
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Figure 8. Pattern of a liquid formed on a vibrating surface (left) and corresponding vibration nodes determined on the basis of FE analysis (right).
Figure 8. Pattern of a liquid formed on a vibrating surface (left) and corresponding vibration nodes determined on the basis of FE analysis (right).
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Figure 9. Ultrasonic converter on a test stand (left) and results of amplitude measurements (right). Axis designations: horizontal: X and Y, mm; vertical: amplitude, μm. Colors of the dots are used to show the deviation from the mean value (yellow).
Figure 9. Ultrasonic converter on a test stand (left) and results of amplitude measurements (right). Axis designations: horizontal: X and Y, mm; vertical: amplitude, μm. Colors of the dots are used to show the deviation from the mean value (yellow).
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Figure 10. Achieved atomization, strongest at the nodes of the vibrating plate.
Figure 10. Achieved atomization, strongest at the nodes of the vibrating plate.
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Figure 11. Subsequent steps of high viscosity liquid behavior being excited with too small amplitude, description in the text.
Figure 11. Subsequent steps of high viscosity liquid behavior being excited with too small amplitude, description in the text.
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Table 1. The x and y component values used in the simulation.
Table 1. The x and y component values used in the simulation.
Inclination Angle [°]Gravity Acceleration X [m/s2]Gravity Acceleration Y [m/s2]Velocity X [m/s]Velocity Y [m/s]
304.9058.4962.1221.225
456.9376.9371.7321.732
608.4964.9051.2252.122
Table 2. Results of the remaining liquid amount measurement for various inclination angles.
Table 2. Results of the remaining liquid amount measurement for various inclination angles.
CaseArea (Total) [mm2]Area (Downstream) [mm2]Area (Upstream) [mm2][%] of Initial Area
Initial61,144.6--100
30° slope29,717.912,187.117,530.848.2
45° slope30,631.211,669.318,961,949.7
60° slope31,433.611,108.220,325.650.9
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Szostak-Staropiętka, R.; Presz, W.; Pawlic, R.; Dziubińska, A.; Kołacz, K. Influence of Process Parameters on the Ultrasonic Atomization Efficiency and Possibility of Testing Properties of Liquid Metals. Metrology 2025, 5, 39. https://doi.org/10.3390/metrology5030039

AMA Style

Szostak-Staropiętka R, Presz W, Pawlic R, Dziubińska A, Kołacz K. Influence of Process Parameters on the Ultrasonic Atomization Efficiency and Possibility of Testing Properties of Liquid Metals. Metrology. 2025; 5(3):39. https://doi.org/10.3390/metrology5030039

Chicago/Turabian Style

Szostak-Staropiętka, Rafał, Wojciech Presz, Roksana Pawlic, Anna Dziubińska, and Katarzyna Kołacz. 2025. "Influence of Process Parameters on the Ultrasonic Atomization Efficiency and Possibility of Testing Properties of Liquid Metals" Metrology 5, no. 3: 39. https://doi.org/10.3390/metrology5030039

APA Style

Szostak-Staropiętka, R., Presz, W., Pawlic, R., Dziubińska, A., & Kołacz, K. (2025). Influence of Process Parameters on the Ultrasonic Atomization Efficiency and Possibility of Testing Properties of Liquid Metals. Metrology, 5(3), 39. https://doi.org/10.3390/metrology5030039

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