Ultrasonic Nebulizer
Silvana Fleischacker
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In many applications where small, similar-sized droplets are needed, ultrasonic nebulizers are employed. Little is known about the mechanism of nebulization, for example about what determines the median droplet size. Even less understood, is the droplet size distribution, which is often simply fitted with a log-normal distribution or assumed to be very narrow. We perform the first systematic study of droplet size distributions for different nebulizer technologies, showing that these distributions can be very well fitted with distributions found for sprays, where the size distribution is completely determined by the corrugation of ligaments and the distribution of ligament sizes. In our case, breakup is believed to be due to pinch-off of Faraday instabilities. The droplet size distribution is then set by the distribution of wavelengths of the standing capillary waves and the roughness of the pinch-off ligaments. We show that different nebulizer technologies produce different size distributions, which we relate to (variation in) wavelengths of the waves that contribute to the droplet formation. We further show that the median droplet size scales with the capillary wavelength, with a proportionality constant that depends only slightly on the type of nebulizer, despite order-of-magnitude differences in other parameters.
Ultrasonic nebulizers or atomizers are very important due to their many applications such as drug delivery, mass spectrometry, humidity control, spray pyrolysis, coating, etc. In almost all cases, the distribution of droplet sizes is an important parameter. For example, in many drug delivery systems, droplets need to be sufficiently small to reach the lower parts of the pulmonary tract, as larger droplets are deposited predominantly at the start of the airways1. Despite extensive research2,3,4,5,6,7,8,9,10,11,12, many aspects of the nebulization process are still poorly understood, mainly because of the very complicated dynamics and the small length and time scales on which it takes place. This work is the first study that focusses primarily on the droplet size distribution for ultrasonic nebulization. We show that, where direct measurements are mostly inaccessible, the shape of the size distribution can be used as an indirect measure for the breakup mechanism. Depending on the type of nebulizer, the mechanism of nebulization can be very different. This is reflected in the droplet sizes, that unlike what is commonly observed, can be both narrowly or broadly distributed.
The process of ultrasonic nebulization is mostly explained by the capillary wave mechanism. The formation of capillary waves on the surface of a fluid supported by a vibrating solid was first described by Faraday in 1831, and are therefore also referred to as Faraday waves13. Later, Kelvin derived the formula for the capillary wavelength λ14, relating it to the surface tension σ, density of the fluid \(\rho \), fluid depth h and frequency f of the standing waves as follows:
In studies of ultrasonic nebulizers, the focus is mostly on the median droplet size. The spread around this median is however just as important, especially for their implementation in different applications. For sprays and jets, the shape of the droplet size distribution is well understood16,17,18,19,20,21. There, it is set by the ligament corrugation and the distribution of ligament sizes. Assuming that capillary waves are the droplet formation mechanism, the droplet sizes are determined by the initial size of the waves and the roughness of the pinch-off ligaments (Fig. 1), and would therefore be comparable with the breakup of sprays. In this case, waves can be more or less spread in size, giving more or less dispersion in droplet sizes (Fig. 1b). Similarly, ligaments can be very corrugated, leading to a broad distribution, or very smooth giving a narrow size distribution.
In this work we investigate three types of ultrasonic nebulizers, working at different frequencies. We find that for these devices the capillary wave hypothesis works well, with proportionality constants depending on the type of nebulizer. We further show that droplet size distributions also depend on the type of nebulizer. Distributions can be surprisingly broad, presumed to be due to large variability in wavelengths and rough pinch-off ligaments, but also very narrow as predicted by the classical picture of capillary wave breakup, where waves are similar sized with smooth pinch-offs.
The SAWN has many applications of which one of the most prominent ones is in mass spectrometry, where it has several advantages over more conventional nebulization methods22,23. The SAWN creates plumes of droplets with ionized molecules, which after the evaporation of the solvent, can be directly used by the mass spectrometer. The precise mechanism of the ionization is unknown, but is probably due to the high voltages present on the chip. It can also be a result of cavitation, which is known to produce sufficiently high temperatures and pressure24, but is considered unlikely to occur for the low power SAWN25. The droplet size distribution plays an important role for applications, as for example in mass spectrometry large droplets can lead to loss of sensitivity and if not properly desolvated may lead to vacuum fluctuations, while small droplets will not.
The breakup of droplets by Faraday waves is governed by the statistics of the interference of waves. An interesting large scale example of interference leading to very large amplitudes, are ocean freak waves or rogue waves. These waves that are much heigher than the average wave, pose a serious threat even to modern ships. Although the situation here is very different, extreme amplitudes do appear for which two examples are shown in Fig. 4b(I and II). Note that these are the larger surface waves, not the parametrically excited waves, which are too small to be observed.
All the droplet size distributions were measured by a laser diffraction method (Malvern Spraytec). Since the diffraction angle is inversely proportional to the droplet size, analysis of the scattered laser light intensity allows for the determination of the droplet size distribution, assuming a spherical droplet shape, an assumption easily met for such small droplets.
For the SAWN, we explored several waveforms such as pulsed, sinusoidal, square and AM-signals. There seems to be no affect of the waveform on the nebulization process. The only essential component seems to be the total power; certain waveforms give more power, resulting in better and quicker nebulization.
Figure 5 shows the rescaled size distributions for the different nebulizers for three consecutive measurements. The laser diffraction method does not allow for error bars on the data points, the setup averages hundreds of measurements per run, and the standard deviation between such measurements is typically small. The agreement between the three different runs shows however there is little variability between measurements. The droplet sizes are fitted with Eq. (3) to obtain the parameters m and n. Due to the form of Eq. (3), exponents can become large, leading to numerical problems in evaluating the distribution function. Standard minimization algorithms therefore do not work properly, since they are sensitive to the values of the initial guess. Fit parameters were therefore obtained by manually fitting the distribution function. This however does not affect the results, since minor changes of the parameters does not alter the conclusions in any way.
All distributions appear to be quite narrow, except for the smallest droplets of the SAWN. The values m and n for the SAWN distribution indicate large variations in wavelengths and rough ligaments. This is an expected result, considering that the smallest droplets of the SAWN are released by the rapid acceleration of the larger surface waves, thereby releasing small droplets in the form of jets as shown in Fig. 4a and schematically illustrated by Fig. 1c. Since this is a sudden and powerful ejection of droplets, there will be large variations in the ligament sizes with irregular pinch-offs.
The mist maker produces capillary waves on a free surface; its operation therefore bears the most resemblance to the classical Faraday wave scenario, where the breakup is smooth with similar-sized wavelengths (Fig. 1a). The distribution obtained experimentally is indeed the most narrow of all three nebulizers, with \(m=40\) and \(n=8\). Still, some randomness is expected; the mist maker creates a fountain of water at the center due to the driving force of the speaker, undoubtedly causing irregularities.
For the nebulizer chip, a layer of fluid is placed on the center of the transducer, where the nebulization takes place. The nebulizer only operates when the liquid layer is sufficiently thin, which can be associated with the shallow wave regime. We find that the size distribution is quite narrow with \(m=20\) and \(n=8\), which is somewhat surprising, considering that its operation appears to be similar to that of the SAWN. Still, what is distinctively different is that for the SAWN the smallest droplets are created by interaction with waves that are of a much larger length scale. Since the formation of the small and big droplets of the SAWN are interconnected, the lack of such bigger droplets implies that the nebulization mechanism for the nebulizer chip must be different.
Droplet size distribution of the SAWN including the larger droplets. These larger droplets are due to waves created by the direct interaction of the surface acoustic waves and the droplet. Three measurements are shown along with the fit (solid line) according to Eq. (3).
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