The Development and Analysis of a Multistage Spraying Method for Liquids in an Ultrasonic Field

Abstract

Spraying various liquids (primarily aqueous solutions of various substances) is widely used in various technological processes. For most of them, high dispersibility and a narrow droplet size distribution are essential. Ultrasonic spraying allows these parameters to be achieved. However, the higher the dispersity of droplets produced by ultrasonic spraying, the lower the spray productivity. To solve this problem, we propose a method of multistage spraying, consisting of the generation of a large number of particles of large initial size (to ensure high productivity) and their subsequent destruction by propagation in a periodic ultrasonic field (to ensure small droplet sizes at high productivity). To experimentally determine the capabilities of this technique, a tubular emitter in the shape of a cylinder with a stepped-variable cross-section was designed. The configuration of the ultrasonic field inside the emitter (22.2 kHz; 182 dB) implements three-stage spraying (the number of sputtering stages corresponds to the number of anti-nodes along the emitter axis). The effectiveness of the proposed and developed technique, suitable for the generation of droplets smaller than 40 µm, with performance exceeding the known ultrasonic spray techniques by at least 10-fold, was confirmed in the course of the conducted research.

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 uniform penetration 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 µm 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 Taylor’s instability criteria [15]. Lang [16] measured surface disturbances by photographing capillary wave peaks on a vibrating surface. The apparent correlation between the median droplet diameter and the wavelength of capillary waves is considered to confirm the capillary wave theory. Cavitation bubbles are assumed to be generated within a liquid film when exposed to ultrasound, provided that the liquid film on the vibrating surface has a certain minimum thickness. High-intensity pressure surges are generated upon the implosive collapse of these cavities, especially with the implosion of cavities near the liquid surface. These pressure surges initiate the disintegration of the liquid film and cause the direct release of droplets. In this case, the size of the shaped droplets is also proportional to the size of the cavitation bubbles generated, i.e., the frequency of ultrasonic impact.

Buguslavsky and Eknadiosyants [17] combined these two theories and proposed the conjunctive theory. According to this theory, periodic pressure surges from cavitation disturbances generate and interact with capillary waves of finite amplitude and destroy and excite them with the generation of droplets. It should also be noted that cavitation shock (which is essentially a statistically random phenomenon) results in non-uniform random disintegration, and the observed non-uniformity of droplet distribution confirms this theory.

Since most droplets are formed through capillary wave generation, the droplet diameter can be estimated fairly accurately using Lang’s equation:

$$D_1=0.34\lambda =0.34\sqrt[3]{\frac{8\pi \sigma }{\rho f^2}}$$

(1)

The use of this equation is justified by the fact that the diameter of aerosol droplets is determined by the frequency of ultrasonic oscillations applied to the liquid film. As the frequency increases, the diameter of the generated droplets decreases [18,19]. Clearly, the spraying productivity decreases proportionally, which is described by the following well-known equation [20]:

$$P_1=2\frac{f}{{\lambda }^2}\pi \frac{D_1{}^3}{6}$$

(2)

It follows from the presented expressions that the productivity is inversely proportional to the spraying frequency. In practice, the dependence on frequency is not linear, which results in a more significant decrease in spraying productivity. So, a number of researchers have shown that with an increase in vibration frequency from 22 kHz to 80 kHz, the median droplet diameter decreases from 93 µm to 30 µm (by threefold). But the spraying productivity upon practical implementation of the process decreases by more than 12-fold (from 3 mL/s to 0.25 mL/s) [21].

Thus, the key challenge of the ultrasonic spraying technique in a liquid layer is the fundamental limitation of productivity with increasing dispersity of the generated aerosol. Since all existing ultrasonic spraying techniques do not facilitate the generation of finely dispersed aerosols with high productivity, this significantly limits the application scopes for solving many problems of contemporary high-tech industries.

In this connection, a need arises to develop new ways of implementation of ultrasonic spraying, providing an increase in the productivity of generating a finely dispersed liquid phase.

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 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]:

$$I_t=2W_l{\left(\frac{{\sigma }_{stp}}{D\omega {\rho }_l}\right)}^2$$

(3)

where σ_stp is the strength of the particle, ω is the frequency of emission, ρ_l is the density of the fluid, W_l = ρ_l c is the wave resistance, and c is the speed of sound.

It should be borne in mind that the strength of water σ_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):

$$D_{\min }=\frac{{\sigma }_{stp}}{\omega {\rho }_l}\sqrt{\frac{2W_l}{I}}$$

(4)

The intensity of exposure is related to the sound pressure level p by a known relationship:

$$I=\frac{p^2}{2W_l}$$

(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. In such a case, the primary droplets generated with high productivity (e.g., 100 µm) will be exposed to ultrasonic vibrations (standing ultrasonic wave) on the gas side, for example, 3...5 times (stages) when moving in the direction of gravity (or the gas flow transporting the droplets), which will ensure the generation of particles with an average size of less than 40 µm. The number of stages will be determined by the number of anti-nodes in the path of the droplet.

3. Ultrasonic Emitter

An ultrasonic emitter in the form of a hollow bending–oscillating cylinder (tubular emitter) was developed for the practical implementation of the proposed multistage ultrasonic spraying technique. The emitter is a cylinder with a stepped-variable cross-section, which generates bending–diametral vibrations at a frequency above 20 kHz. The hollow shape of the cylinder was chosen for this emitter in order to ensure the self-focusing of ultrasonic vibrations in the internal cavity on the axis of the cylinder. The application of this type of emitter enables the generation of a regular structure of vibrations of great length. Liquid droplets consistently passing the maximums of standing wave velocity inside the cylindrical emitter will deform and collapse until they reach the minimum possible particle size for the sound pressure level generated by the emitter.

To ensure sufficient ultrasonic vibration intensity at high ultrasonic frequencies, a multi-package transducer with radially spaced Langevin transducers can be used as the piezoelectric transducer [26]. An estimation of acoustic and geometric parameters and calculation of the emitter vibration waveform were performed using modal analysis in the finite element modeling system (ANSYS package, ver. 19.2).

The tetrahedral type of finite element was used for the estimation and analysis of the performance of an ultrasonic emitter exposed to a volumetric stress state. When the modal analysis was performed, the convergence of numerical results for different emitter designs was analyzed. A modeling result that corresponded to a finite element model with a minimized number of finite elements, the increase in which results in a change in the main values of the design parameters (e.g., the natural frequency of vibrations) by no more than 0.2–0.5%, was considered satisfactory.

Figure 2 shows a drawing of the tubular emitter and the waveform of its vibrations obtained from the results of the estimations.

The ultrasonic field generated by the tubular emitter was estimated by finite element analysis in ANSYS. The harmonic acoustics module of harmonic acoustic analysis was used. During modeling, the boundary conditions were set on the basis of the obtained design data specifying cylindrical emitter parameters (the frequency of vibrations and distribution of the vibration amplitudes of the emitting surface). The scope of the calculation domain was limited by the inner surface of the tubular emitter. The boundary conditions were set at the ends of the estimated area: radiation boundary. During the estimations of the acoustic field, the iterative variation of tubular emitter dimensions was carried out to ensure the standing wave mode in the inner space of the emitter. Figure 3 shows the results of the estimations of distribution of the sound pressure generated in the emitter and a picture of the manufactured emitter.

The results of estimations show that conditions and a sufficient sound pressure level in the volume of the multistage spraying chamber (more than 190 dB) are available for the implementation of multistage spraying. Three sound pressure maxima were formed along the emitter axis. Thus, a droplet moving inside the emitter will undergo up to three stages of disintegration. The sound pressure level was measured inside the fabricated emitter to confirm the estimations. The measurements were carried out with a noise meter/vibro-meter Ekofizika-110A (OKTAVA-ElektronDizayn, Moscow, Russia) with a microphone VMK-401 (Vibropribor, Yaroslavl, Russia). The measurements showed that the sound pressure level formed inside the tubular emitter was within 170...182 dB. The measurements were carried out at maximum power consumption.

The acoustic power of the developed emitter was determined. It was determined as the difference between the total electrical power consumed by the emitter and the emitter’s own loss power. The measurement methodology was as follows. The total electrical power consumed by the ultrasonic emitter from the generator was determined as the sum of the acoustic power emitted into the gaseous environment and the power of its own losses in the emitter. The acoustic power emitted into a gaseous medium is proportional to the density of the gas multiplied by the speed of sound in the gas. Accordingly, if the gas density is reduced to values close to zero (by pumping gas out of the volume in which the emitter is installed), then the acoustic power will also become zero. In this case, the electrical power consumed from the generator will decrease and become equal to the power of its own losses in the emitter material. Thus, the acoustic power of the emitter can be defined as the difference between the electrical power consumed by the emitter from the generator at normal pressure and the electrical power consumed from the generator when the emitter is operating in a vacuum. The loss of power was estimated by measuring the power consumed by the emitter when operating without a load. For this purpose, the emitter was placed in a vacuum chamber [27]. The air was evacuated from the vacuum chamber to a residual pressure not exceeding 1000 Pa. The electric power consumed by the emitter was measured using the MT-1010 measuring instrument (Motech Industries Inc., Taiwan).

The performed calculations and measurements enabled an estimation of the main technical parameters of the developed tubular emitter (

Table 1. Lists the main parameters of the developed tubular emitter.

Parameter	Value
Dimensions of the tubular emitter, mm	D2 = 92 D1 = 52 L = 96
Vibration frequency, kHz	22.2
Electric power consumption, W	50
Amplitude (sweep) of the surface vibrations, max–min	51–40
Acoustic power, W	35

).

A test bench was developed in order to experimentally assess the feasibility and efficiency of the proposed method for the multistage spraying of liquids. The design diagram of the test bench and its image are shown in Figure 4. The test bench allows carrying out high-speed video recording of the droplet-breaking process and estimating the dispersion characteristics of the generated aerosol depending on the sound pressure level and liquid properties.

The test bench consists of an ultrasonic tubular emitter (3) with a piezoelectric transducer powered by an electronic ultrasonic frequency generator (4), a dispenser (1) with mounted nozzle (2), and an optical aerosol analyzer (6) from Malvern SprayTec. The operation principle of the analyzer is based on laser diffraction. The Spraytec analyzer enables the measurement of particle dispersity with a frequency up to 10 kHz in the range from 0.1 to 2000 μm. During the experiments, the sprayed liquid was fed by a peristaltic pump (1) into the nozzle (2) installed at the end of the tubular emitter.

The nozzle generated liquid droplets of 1500...2000 µm in size (initial droplet size) with productivity up to 20 mL/s. The dispersion characteristics were measured at two points shown in Figure 4:

(1)

At a distance of approximately 1/3 from the upper end of the tubular emitter, after the droplets passed the first standing wave vibration’s anti-node inside the emitter. A vacuum aspirator was used to collect the aerosol droplets. The selected droplets corresponded to the aerosol after the first stage of spraying.

(2)

At a distance of 50 mm from the lower end of the tubular emitter, to determine the dispersion characteristics of the aerosol generated as a result of the multistage spraying of liquids.

Since three ultrasonic vibration anti-nodes are formed along the axis of the developed emitter, it will provide three stages of droplet breakdown.

Visual observation and analysis of the dynamics of deformation and destruction of the liquid droplets in the sound field were performed using a “VideoSprint” high-speed video camera. The frame rate was 5000 frames/s.

Water, aqueous solutions of glycerol (of different viscosity), and alcohol (of different surface tension) were used as sprayed liquids.

4. Results and discussion

4.1. Droplet Disintegration Dynamics

To study the dynamics of the first stage of liquid droplet disintegration, the video camera was focused on the area on the tubular emitter axis located 20 mm below the upper end of the emitter (the first stage of droplet disintegration). The records of the deformation and disintegration of the droplet with indicated time marks are shown in Figure 5. The sound pressure level inside the tubular emitter was 175 dB.

The presented sequence of high-speed video frames indicates that the droplet undergoes a series of deformations while in the ultrasonic field before breaking into smaller droplets. The following phases of deformation and disintegration of the droplet can be distinguished in the first stage:

• First phase: The initial droplet possessing initial momentum (obtained by crushing the liquid jet at the nozzle outlet) deforms as it approaches the region of the velocity anti-node in the standing wave. The droplet impacted by radiation pressure assumes the shape of a concave membrane (disk).
• Second phase: As the diameter of the liquid membrane increases and its concavity degree increases, the liquid film thickness decreases. Faraday capillary waves [28] are generated on the surface of the liquid disk under the impact of ultrasonic vibrations. These waves reach the highest amplitude at the edges of the disk. When the Faraday waves reach their critical amplitude, disintegration of the liquid disk begins, starting from the outer edge. The smallest droplets are generated owing to the implementation of this mechanism.
• Third phase: The instability of the liquid film increases due to a further increase in the disk size and decrease in its thickness. When the liquid membrane reaches a certain limiting size, the liquid film thickness decreases below the critical value. This results in the structural destruction of the liquid disk with the formation of large droplets.

This completes the first stage of droplet breakdown. The formed polydisperse droplets are subjected to the structuring effect of secondary nonlinear effects arising in the ultrasonic field. Large droplets (formed at the first stage), possessing, as a rule, a lower emission rate (upon liquid film destruction), move in the direction of the next vibration velocity anti-node in the standing wave. This motion originates from the impact of the resultant radiation force, which is proportional to the squared droplet radius.

Thus, sufficiently large (more than 100 µm) liquid droplets formed at the first stage of spraying, with a higher velocity (because the force effecting the droplet is proportional to the squared droplet diameter), move into the vibration velocity anti-node, where they undergo secondary and subsequent disintegration.

Accordingly, the smallest droplets move in the direction of the vibration velocity nodes, where the ultrasonic vibrations do not have a significant effect on them. Further, such drops leave the ultrasonic exposure domain (in this case, from the internal volume of the tubular emitter) via the action of gravity or with the flow of transporting air. In this case, due to the arrangement of small droplets in the nodes of vibrational velocity, their coagulation under the impact of ultrasonic vibrations does not, in fact, occur. Thus, in the proposed technique of multistage spraying, ultrasonic vibrations have not only a dispersing effect (the breakdown of liquid droplets) but also a structuring effect (the selective breakdown of the largest droplets) [29,30,31]. The recorded images of deformation and disintegration of the droplet at the second and subsequent stages are shown in Figure 6.

As can be seen from the images presented in Figure 6, the secondary and subsequent breakdowns also deform the droplets into a flat disk. However, a meniscus is not formed due to the smaller diameter of the droplet. Owing to this, Faraday waves are excited all over the surface of the disk. As a result, the disk collapses into small droplets whose diameters are proportional to the wavelength of the excited capillary waves. At the same time, since the capillary waves excited closer to edge of the disk have a shorter wavelength, the droplets formed from the edges of the disk will also have a smaller diameter. This explains the scattering of droplet diameters relative to the median diameter.

4.2. The Dispersion Characteristics of the Formed Droplets

To confirm the applicability of the proposed spraying technique, the disperse composition of droplets formed by spraying water (settled, tap water, temperature of 23 °C) was analyzed. The sound pressure level was 182 dB. The water supply capacity was equal to 5 mL/s. The initial size of the droplets injected into the tubular emitter was equal to 2000 µm. Histograms of the droplet distribution, after the first stage of spraying and at the outlet of the tubular emitter, are shown in Figure 7. Statistical processing of the obtained data was carried out using the Malvern SprayTech laser meter software v3.20. The measurements were carried out in long-term measurement mode with data averaging for 1 s.

As can be seen from the histograms presented in Figure 7a, a bimodal aerosol consisting of small droplets (the first peak formed by the capillary mechanism of liquid film breakdown) and large droplets (the second peak consisting of droplets formed after the structural breakdown of the liquid film) is generated at the first stage of dispersion of the initial droplets. The median droplet diameter (hereinafter referred to as Sauter’s diameter) of the first peak is 89 μm.

The largest droplets formed at the first stage are subjected to subsequent stages of breakdown. As a result, the distribution of aerosol droplets at the tubular emitter outlet takes the shape shown in Figure 7b. The median (Sauter) diameter equals 34 µm. It can be concluded from a comparison of the obtained distributions that the median diameter of the resulting droplets (Figure 7b) is smaller than the median diameter of small droplets after the first breakdown stage (the first peak in Figure 7a). This indicates that coagulation processes have almost no effect on the disperse composition of the formed droplets. This is due to the fact that the ultrasonic frequency used (22.2 kHz) is significantly higher than that required for the coagulation of the formed liquid droplets and does not grant them oscillatory motion [32,33]. This fact will be the subject of future studies.

It was established that the droplets formed have a smaller diameter than the same obtained by the known method of ultrasonic spraying of the liquid in a layer at the same frequency of exposure. The proposed multistage spraying technique provides a median (Sauter) diameter of 120 µm vs. 34 µm for ultrasonic spraying in a layer of liquid. This provides significantly higher (by more than 10-fold) spraying productivity than in the known ultrasonic spraying techniques [34,35].

4.3. 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.

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 µm). The increase in the median diameter was not more than 5 µm. 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.

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.

4.4. Dependence on the Sound pressure Level

Figure 10 shows a sequence of histograms characterizing the evolution of the disperse composition of the formed droplets (at the outlet of the tubular emitter) depending on the sound pressure level. The liquid supply rate is 5 mL/s.

It follows from the presented histograms that the sound pressure level was the main parameter of the process, which significantly affected the dispersion characteristics of the generated aerosol. At the same time, hydrodynamic parameters (the flow rate of the sprayed liquid) and physical properties of the liquid (will be shown below) had much less influence.

This makes the proposed technique invariant to the conditions of the process (flow rate and physical properties of the liquid), but at the same time, it can be configured through the selection of ultrasonic exposure modes (sound pressure level). All this ensures adjustability in the disperse characteristics of the generated aerosol. Figure 11 shows the dependence of the median diameter of the formed droplets on the sound pressure level to identify the limits of controllability of the disperse composition of the formed droplets. Each experimental point in Figure 11 was obtained by averaging 10 Sauter diameter measurements (determined using Malvern SprayTech). The experimental data satisfactorily correspond to linear regression. The error bars indicate standard deviation.

It can be seen that changing the sound pressure level in the range of 160–182 dB enables an adjustment of the median diameter of the formed droplets in the range of 170–34 µm.

4.5. Dependence on Liquid Viscosity

As mentioned above, viscosity is one of the main physical properties of the liquid that influences the disperse characteristics of the formed liquid droplets. To analyze the effect of liquid viscosity on the disperse composition of the resulting aerosol, an aqueous solution with a volume content of glycerol of 20%; 30%; 40%; 50%; and 60% was used. The viscosities of the liquid were, respectively: 1.8; 2.5; 3.7; 6.0; and 10.8 mPa·s. The sound pressure level was 182 dB, and the liquid flow rate was 5 mL/s.

Histograms of the droplet diameter distribution upon the spraying of liquids with different viscosities are presented in Figure 12.

As can be seen from the histograms, with the increasing viscosity of the liquid, the droplet diameters tend to migrate to the large-diameter domain. The spread of drops relative to the median diameter increases likewise. For example, at a liquid viscosity of 1.8 mPa·s, the median diameter of the formed droplets is 34 μm, and with increasing viscosity up to 10.8 mPa·s, the median diameter increases to 57 μm.

The dependence of the median diameter of the formed droplets on the viscosity of the liquid is presented in Figure 13. Each experimental point in Figure 13 was obtained by averaging 10 Sauter diameter measurements (determined using Malvern SprayTech). The experimental data satisfactorily correspond to polynomial regression. The error bars indicate standard deviation.

The presented dependence shows that liquid viscosity had a poor effect on the diameter of the formed droplets. In the range of viscosities from 1 mPa·s (water) to 3.7 mPa·s (40% aqueous glycerol solution), a weak increase in the median diameter of the formed droplets (no more than 2 μm) was observed. A further increase in the viscosity of the liquid resulted in an increase in the median diameter of the resulting droplets, up to 57 µm. Apparently, this is explained by the fact that the forces of viscous friction prevent the development of Faraday waves and generation of smaller droplets. At the same time, the majority of droplets are formed by the mechanism of the structural breakdown of a liquid droplet (large droplets larger than 100 µm are formed).

4.6. Dependence on Liquid Surface Tension

It is known that surface tension is the key factor affecting the wavelength of generated Faraday capillary waves and, consequently, the diameter of generated liquid droplets [16]. A solution of ethyl alcohol in water in proportions of 20%, 30%, 40%, 60%, and 80% was used as the spray liquid. The respective surface tensions of the solutions were equal: 40.9 mN/m, 36 mN/m, 32.1 mN/m, 28.8 mN/m, and 25.6 mN/m [36]. The sound pressure level was 182 dB, and the liquid flow rate was 5 mL/s. Figure 14 shows comparative histograms of droplet distribution formed at minimum and maximum ethyl alcohol content in solution.

It follows from the presented histograms that a decrease in the surface tension (higher alcohol content in the solution) contributed to a decrease in the diameter of the formed droplets. This was caused by a decrease in the wavelength of the generated Faraday capillary waves (see Equation (1)). In addition, the spread of the formed droplets’ diameters also decreased. The histogram in Figure 14b becomes narrower.

Figure 15 shows the dependence of the median diameter of the formed droplets on the surface tension of the liquid. Each experimental point in Figure 15 was obtained by averaging 10 Sauter diameter measurements (determined using Malvern SprayTech). The experimental data correspond to polynomial regression. The error bars indicate standard deviation.

Figure 15 shows that the median diameter of the formed droplets monotonically decreased with the decreasing surface tension of the liquid. However, the dependence (a decrease by 8 µm) of the median droplet size on the surface tension was not as significant as that on the sound pressure level.

Thus, a multistage spraying technique, consisting of the generation of a large number of large-initial-diameter particles (to ensure high productivity) and their subsequent breakdown during propagation in an ultrasonic field, was proposed. The disperse characteristics of the formed droplets, from the modes of ultrasonic exposure and the properties of the liquid, were studied. It was shown that the method of multistage spraying of a liquid enables the generation of liquid droplets of smaller diameters and with higher productivity than other commonly used techniques of ultrasonic spraying (spraying in a layer and spraying in a fountain).

5. Conclusions

The development of new liquid atomization devices and methods that can produce a fine spray at high throughput is of significant interest for various technological applications. For example, high dispersion, together with high productivity in aerosol creation, are required in the technological processes of aerosol drying, aerosol coating, surface treatment, and the spraying of drugs.

In this study, a method of multistage spraying was proposed, consisting of the generation of a large number of particles of large initial diameter (to ensure high productivity) and their subsequent destruction in a periodic ultrasonic field (to ensure small droplet sizes at high productivity). For the practical implementation of the method, an ultrasonic emitter was developed in the form of a cylinder with a stepped-variable cross-section for the formation of bending–diametrical vibrations. The shape of this emitter in the form of a hollow cylinder was chosen to ensure the self-focusing of ultrasonic vibrations in the internal cavity on the cylinder axis. The developed emitter provides the generation of a periodic ultrasonic field with a frequency of 22.2 kHz and sound pressure level of up to 182 dB. The configuration of the ultrasonic field inside the emitter enables three-stage spraying.

It was shown that the disperse characteristics of the formed droplets mainly depend on the sound pressure level at which the droplets break down. So, the increase in the sound pressure level from 160 dB to 182 dB changes the average diameter of the formed droplets in the range of 34–170 µm, while the spraying productivity is not changed. The physical properties of liquids have a much smaller effect on the diameter of the formed droplets. In this way, an increase in viscosity from 1 mPa·s (water) to 3.7 mPa·s (40% aqueous solution of glycerin) indicates a weak increase in the median diameter of the formed droplets (no more than 2 μm). A further increase in the viscosity of the liquid results in an increase in the median diameter of the resulting droplets, up to 57 µm. In turn, the result of decreasing the surface tension of the liquid from 72.8 mN/m to 25.6 mN/m is a further decrease in the droplet size by 8 μm.