Effects of multi-frequency acoustic waves on the agglomeration of fog droplets

Effects of multi-frequency acoustic waves on the agglomeration of fog droplets | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Effects of multi-frequency acoustic waves on the agglomeration of fog droplets M. Y. Ibrahim, Reyad El-Khazali, Diana Francis, Narendra Nelli This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4835869/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract This work focuses on using multi-frequency sound waves to dissipate fog. It is a promising fog-dissipation technique due to its ease of control, flexibility, environmental friendliness, and no interference with traffic flow. This study introduces a novel approach to dissipate artificial fog generated inside an experimental setup utilizing harmonically related multi-frequency acoustic waves. Fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz, along with their 9th, 11th, and 40th harmonics were tested at a maintained Sound Pressure Level (SPL) of 112 dB. Many combinations were found to increase fragmentation of large droplets, which reduces the condensation efficiency. The main mechanism for acoustic condensation seems to be the collision and merging of fog droplets. Most harmonics tested did not improve agglomeration, with the notable exception of the 400 Hz paired with its 9th-harmonic. This combination resulted in a 61.06% reduction in Liquid Water Content (LWC) for large droplets and a 90% condensation effect achieved quicker than all the other cases. These findings highlight the potential of using harmonics for acoustic fog dissipation. Earth and environmental sciences/Hydrology Physical sciences/Engineering Physical sciences/Physics acoustic coalescence fog dissipation fog droplets droplet agglomeration harmonics optimal frequency Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction Fog is a frequent phenomenon in the United Arab Emirates (UAE), located on the northeastern coast of the Arabian Peninsula. Despite its desert landscape, the UAE experiences numerous low visibility events during winter, primarily caused by haze and fog [ 1 – 7 ], leading to severe disruptions in road transportation and aviation, causing delays and accidents due to reduced visibility. In particular, Abu Dhabi's international airport records up to 13 fog days per month and 51 fog days annually during this season [ 2 ]. To address these visibility issues, researchers have suggested various techniques to artificially clear fog, each designed for specific fog types. Fog can be categorized into three types in the context of artificial dissipation: ice fog, warm fog, and supercooled fog. Ice fog, occurring at temperatures below − 30°C, which consists of airborne ice particles [ 8 ]. There is no method that has proven effective for operationally dispersing this type of fog [ 9 ]. Warm fogs occur at temperatures above 0°C, whereas supercooled fogs develop at temperatures below 0°C [ 8 ]. Dissipating supercooled fog involves triggering the freezing of certain droplets using substances like dry ice or silver iodide [ 10 ]. Warm fog lacks a standardized operational dispersal mechanism, unlike supercooled fog. Nevertheless, various approaches have been devised, each showing varying levels of efficacy [ 9 ]. This investigation will center on tackling warm fog elimination, given its limited success to date and its prevalence in an arid environment such as that of the UAE. The traditional methods have not been implemented operationally due to their environmental impact, inefficiency, or high cost [ 9 , 11 , 12 ]. In recent years, there has been a growing interest in research involving acoustic and ultrasonic waves [ 13 – 15 ], particularly for fog elimination [ 11 ]. The potential of utilizing sound waves in this regard is promising due to their controllability, flexibility, environmental friendliness, and minimal impact on traffic [ 15 ]. The technique of using acoustic waves for fog dispersal employs sound vibrations to facilitate the merging of fog particles into larger droplets, leading to the efficient dissipation of fog. However, thorough investigations into the effectiveness of this method, especially in typical fog conditions, are currently lacking [ 13 ]. Research on acoustic fog dispersion has primarily focused on single frequencies, neglecting the potential advantages of utilizing a combination of frequencies [ 13 – 15 ]. Low-frequency waves have a greater influence on condensing larger particles, whereas high-frequency waves are more effective in condensing smaller particles [ 13 ]. This indicates that different frequencies affect droplet sizes differently, suggesting that combining multiple frequencies, or their harmonics, could lead to superior outcomes. Patterson et al.'s work marked the pioneering effort in agglomeration via sound waves [ 16 ]. Since then, many researchers have delved into its applications across diverse domains [ 13 ]. A simulation investigating the condensation impact of ultrasonic waves revealed that the optimal frequency for coalescence is 20 kHz with more effective diminishing at higher frequencies [ 11 ]. This raises questions regarding the viability of ultrasonic waves for acoustic coagulation. A numerical simulation illustrated a notable enhancement of condensation efficiency achieved through acoustic fog dissipation [ 13 ]. Liu et al. performed an experimental study that identified the optimal frequency range for fog dispersion as being between 300 Hz and 500 Hz [ 15 ]. Moreover, it highlights the unique response of droplets of different sizes to varying frequencies, with higher frequencies amplifying condensation for smaller particles while yielding contrasting effects for larger ones. Qiu et al. examined the acoustic agglomeration of cloud particles subjected to sound waves at frequencies spanning from 35 Hz to 100 Hz and SPLs ranging between 112 and 122 dB [ 17 ]. Maintaining a constant SPL value revealed that the most efficient agglomeration took place within the frequency range of 50 Hz to 65 Hz. Zhang et al. investigated experimentally the dissipation of fog through acoustic means using frequencies ranging from 200 Hz to 700 Hz. Their work emphasized the significant role of frequency in the process of droplet merging. It specifically identified that a 300 Hz acoustic signal of 75 W had the best condensation effect [ 18 ]. A recent experimental study into the dissipation effects of frequencies below 100 Hz revealed notable dissipation effects for frequencies under 50 Hz at Sound Pressure Levels surpassing 125 dB [ 19 ]. Furthermore, the investigation undertook a comparative examination of acoustic dissipation techniques and hygroscopic salt seeding, ultimately establishing the former as the more efficacious approach. Determining the most effective frequencies for acoustic fog dissipation hinges on the specific properties of the fog under examination and the sizes of the particles present. As a result, ongoing debate surrounds the conclusive identification of the optimal frequency for efficient acoustic fog dissipation. Further research into fog dispersion via sound waves is believed imperative, as experimental evidence regarding the defogging efficacy of sound waves remains inadequate. Additionally, there is a pressing need to explore the influence of various parameters such as waveform types and their power, particle size distribution, and temperature [ 11 ]. This research will focus on the effects of frequencies and their harmonics on droplets agglomeration. As previously highlighted, a significant portion of research on acoustic fog dissipation has focused on single-frequency methodologies, with the objective of pinpointing an optimal frequency for fog dissipation. However, there exists untapped potential in exploring the effects of integrating harmonics to improve visibility, an area that has yet to be thoroughly investigated. This study seeks to present the first study in literature on the effect of harmonically related multi-frequency acoustic waves on the agglomeration of fog droplets. This paper is organized as follows: data and methodology are presented in Section 2 . Section 3 shows the main results and discussion, while the conclusions are summarized in Section 4 . 2. Data and Methodology Experimental setup Figure 1 shows an experimental setup of the fog agglomeration system. It consists of a high-pressure misting system, with a flow rate of approximately 6 Liters per minute, used to generate artificial fog withing the chamber. This system was integrated into the chamber through a network of pipes with evenly spaced nozzles, enabling uniform fog dispersal. The inlet of the machine is connected to a pump powered by a DC source, ensuring a continuous water supply. The fog chamber is a rectangular prism measuring 2 m × 2 m × 1.5 m (length × width × height), with supporting legs of 0.25 m in height. These dimensions were chosen to provide a more realistic simulation of foggy conditions. It features a glass front providing a clear view of fog during the experiment, while the remaining sides are constructed from High-Pressure Laminate (HPL) for cost-effectiveness and durability. The frame is made of Aluminum to ensure structural integrity. The glass panels are approximately 6 mm thick, and the HPL panels are about 2.5 mm thick. The chamber was properly insulated using silicone sealants and rubber strips. The Fog Monitor FM-120, manufactured by Droplet Measurement Technologies in the USA, was employed for real-time measurement of various parameters including the number concentration of fog droplets, Median Volume Diameter (MVD), Liquid Water Content (LWC), and other microphysical properties of the fog cloud. It has the capability to assess droplets ranging from 2 to 50 µm in diameter [ 4 ]. A compressor extracts a sample from the fog layer through a sampling tube. The instrument then quantifies the forward scattered light from particles as they traverse a laser beam. FM-120 has gained widespread acceptance in academic research, thereby bolstering the credibility and reliability of the obtained findings [ 20 – 22 ]. Prior to conducting the experiments, the apparatus underwent calibration procedures to guarantee the accuracy and reliability of the results. The sampling rate was set at 1 sample per second. A precise aperture was made at the rear side of the chamber to accommodate the inlet horn of the FM-120, which was securely fixed and properly insulated within the aperture. The speaker used in this work has an output frequency range of 33 Hz to 20 kHz. Temperature and humidity sensors were utilized to continuously monitor and record the temperature and humidity levels within the chamber throughout the experiments. The SPL was measured in dB using an SPL meter (Extech SL510). SPL measurements were taken 1 meter from the speakers before starting the experiments. Measures were taken to isolate the speakers from fog to prevent potential damage. To accommodate the speakers, the right side of the chamber featured an opening measuring 0.65 m × 0.45 m, which was properly covered with a plastic material known for its effective acoustic transmission. Similar techniques have been successfully applied in previous research [ 17 , 19 , 23 ]. Furthermore, sound dampening panels were placed on the interior sides of the chamber to reduce the impact of echo. Procedure Each experiment was conducted as follows: 1) Fog is generated for 4–5 minutes inside the chamber which is the time it takes for an object placed at the middle of the chamber to be completely invisible from outside. 2) The fog generating machine is turned off and the particle size analyzer and the speakers are turned on. The start time, temperature, and humidity inside and outside the chamber are recorded. 3) After 2 minutes, the speakers are turned off. 4) After 5 minutes, the particle size analyzer is turned off. Background noise was neglected as the measurements showed its minimal effect. Each case under investigation involved 3 experimental runs. Temperatures inside and outside the chamber were maintained at 24.65 ℃ ± 1.15 ℃ and 24.85 ℃ ± 1.05 ℃, respectively. The humidity inside the chamber was maintained at 98.85% ± 1.15%. Data representation Normalization ensures that particle concentrations are comparable across different bin sizes, incorporating a logarithmic scale. This scale allows for a more effective visualization of the distribution of particle sizes, particularly when dealing with particles spanning multiple orders of magnitude in size. The normalized particle concentration was calculated using the following formula [ 24 ]: $$\:\frac{dN}{dlog{D}_{p}}=\frac{dN}{log{D}_{p,u}-log{D}_{p,l}}$$ 1 Where, \(\:dN\) is the particle concentration within the specified size interval, while \(\:{D}_{p,u}\) and \(\:{D}_{p,l}\) represent the upper and lower bounds of the size interval, respectively. Moreover, \(\:dlog{D}_{p}\) quantifies the change in the logarithm scale of the particle diameter within the size interval. FM-120 can provide the overall LWC of a sample at a rate of one sample per second. However, it does not provide the LWC for each individual bin size. The LWC for each droplets size bin was estimated through the following expression [ 25 ]: $$\:{LWC}_{i}=({\rho\:}_{w}\times\:\frac{\pi\:}{6})\times\:{Nc}_{i}\times\:{D}_{p,\:i}^{3}$$ 2 Where, \(\:{\text{L}\text{W}\text{C}}_{\text{i}}\) is the LWC for each fog droplet bin size, \(\:{\rho\:}_{w}\) is the density of water, \(\:{Nc}_{i}\) is the number concentration of fog droplets at the ith-bin size, while \(\:{D}_{p,i}\) is the bin center diameter. The particle size analyzer also measures the total number concentration of droplets and the Median Volume Diameter (MVD). Earlier studies have opted to examine specific characteristic droplet diameters to explore the influence of sound waves, thereby simplifying the statistical analysis process [ 17 – 19 ]. The MVD essentially corresponds to a widely recognized characteristic droplet diameter known as D50, denoting the diameter at which 50% of the total volume is distributed among particles smaller and larger than that diameter. However, the MVD provided by the particle size analyzer pertains to each individual sample rather than an aggregate of all samples. To address this, D50 values are calculated for all samples using the following formula [ 26 ]: $$\:{D}_{50}={D}_{l}+\frac{0.5\sum\:_{i}^{m}{{n}_{i}V}_{i}-\sum\:_{i}^{l}{n}_{i}{V}_{i}}{\sum\:_{i}^{u}{{n}_{i}V}_{i}-\sum\:_{i}^{l}{n}_{i}{V}_{i}}({D}_{u}-{D}_{l})$$ 3 Where, i denotes the bin index, m is the total number of bins, \(\:{n}_{i}\) denotes the count of droplets in each bin, \(\:{V}_{i}\) refers to the volume corresponding to particles at the i-th bin, \(\:{D}_{u}\) and \(\:{D}_{l}\) denote the upper and the lower diameters to D50, respectively. To estimate the volume \(\:{V}_{i}\) in Eq. ( 3 ), it was assumed that the droplets are spherical with a radius \(\:{r}_{i}\) . The analysis of the experimental results includes D90, which represents the diameter at which 90% of the total volume is distributed among particles with smaller diameters. The D90 was obtained through a slight modification of Eq. ( 3 ). Input signal Various signal waveforms can be selected for the input signal to the speaker. The signal utilized in this research is a basic sine wave. Given that the maximum frequency the speakers can output is 20 kHz, a sampling frequency of 44.1 kHz was chosen to adhere to Nyquist theorem. The theorem asserts that to faithfully represent a signal, the sampling rate should be at least twice the maximum signal frequency [ 27 ]. However, in practice, a higher sampling rate is preferable to address quantization errors. The amplitude was consistently set to 1 for all experiments. The signal was normalized by dividing each sample by the maximum absolute value in the signal before sending it to the speakers to prevent clipping and distortion. The expression can be extended to account for the scenario of applying a sound wave with a fundamental frequency and one harmonic as follows: $$\:y=Asin\left(2\pi\:ft\right)+Asin\left(2\pi\:nft\right)$$ 4 Where, \(\:y\) is the output signal, \(\:A\) is the amplitude of the signal, t denotes time, \(\:f\) denotes the fundamental frequency and \(\:n\) signifies the harmonic number. For the sake of simplifying the investigation, there is no phase shift between the two signals. Data processing The examined frequencies were limited to 300 Hz, 400 Hz, and 500 Hz at a maintained SPL of 112 dB. During each experiment, sound was applied to the fog layer for 2 minutes. However, the initial four readings from the particle size analyzer had to be omitted as they yielded exceptionally small readings. To ensure the reliability of the findings, each experiment was repeated three times for every frequency and its harmonic combinations. The normalized size distribution plot displays the particle sizes in counts per cm³ per µm across each droplet diameter, which is represented by the bin midpoint. Plotting the normalized size distribution across the three runs demonstrated that the curves are remarkably close, with nearly identical peaks at all frequencies examined. A multiple comparison test was conducted via MATLAB using the LWC data obtained after sound application at each frequency across multiple runs. Subsequently, runs with significantly divergent means were excluded from the average measurements to mitigate the influence of varying initial fog amounts at the start of each experiment. 3. Results and Discussion The amplitude of the sine wave for both the fundamental frequency and its harmonic is maintained at an equal level. In the subsequent figures, \(\:h\) and \(\:{f}_{o}\) denote the harmonic level and the fundamental frequency, respectively. Several plots were generated for all cases across various parameters. The summarized results, including the D50 and the D90 data, are presented in Table 1 . Figure 2 (a) displays a plot of the median LWC, across the different cases. A noticeable trend appears in the curves for both the 300 Hz and 500 Hz waves, indicating that the median LWC increases with higher harmonic numbers. The lowest median LWC of 1.66 \(\:\text{g}/{\text{m}}^{3}\) was observed for the acoustic waveform of 400 Hz along with its 9th -harmonic signal. Figure 2 (b) depicts a plot of the median \(\:{N}_{c}\) , revealing a similar shape among the three curves, with each showing the minimum \(\:{N}_{c}\) at the 9th -harmonic. It is evident that the 300 Hz case with no additional harmonics has the highest normalized \(\:{N}_{c}\) (4073.25 counts/ \(\:{\text{c}\text{m}}^{3}\) /µm), whereas the lowest was observed for the same frequency with the addition of the 9th -harmonic (3144.55 counts/ \(\:{\text{c}\text{m}}^{3}\) /µm). The highest median MVD of 20.09 µm is observed for the no sound waves case, while the lowest median MVD of 15.03 µm is recorded for the 500 Hz case. The highest value for the D50 corresponds to the no-sound case, resembling D90, and is also observed in other instances of sound application. Conversely, the lowest values are observed in the case of sound application at 400 Hz with its 9th -harmonic. Table 1 D50, D90, and the medians for LWC, N c , and MVD of fog droplets when sound waves were applied at fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz. Harmonic number Median LWC ( \(\:\text{g}/{\text{m}}^{3}\) ) Median \(\:{\text{N}}_{\text{c}}\) (#/ \(\:\text{c}{\text{m}}^{3})\) Median MVD (µm) D50 (µm) D90 (µm) no sound - 3.13 3183.05 20.09 22.98 32.99 300 - 1.91 4073.25 15.03 18.97 26.98 9 1.97 3144.55 17.16 20.98 26.98 11 2.26 3816.65 17.25 20.98 26.98 40 2.51 3886.59 17.30 20.98 28.98 400 - 2.32 3598.60 17.60 20.98 28.98 9 1.66 3525.18 15.49 18.97 24.98 11 2.41 3846.15 17.13 20.98 26.98 40 2.29 3657.23 17.13 20.98 26.98 500 - 2.17 3913.15 16.38 20.98 26.98 9 2.48 3598.83 18.19 22.98 28.98 11 2.53 3859.32 17.55 22.98 28.98 40 2.82 3694.24 18.71 22.98 30.98 Table 2 Summary of results obtained from the normalized size distribution plots. Frequency (Hz) Harmonic number Peak diameter for small droplet sizes (µm) Normalized \(\:{\text{N}}_{\text{c}}\) at the peak diameter (#/ \(\:\text{c}{\text{m}}^{3}\) /µm) Normalized \(\:{\text{N}}_{\text{c}}\) at a diameter of 20.98 µm (#/ \(\:\text{c}{\text{m}}^{3}\) /µm) no sound - 8.49 5054 1997.92 300 - 6.48 7372.16 1182.15 9 6.48 5363.75 1358.12 11 6.48 6493.41 1738.55 40 6.48 6690.85 1658.9 400 - 5.48 6143.98 1499.82 9 6.48 6193.06 1086.86 11 6.48 6618.8 1629.29 40 6.48 6303.66 1520.03 500 - 6.48 6928.38 1372.33 9 6.48 5901.9 1824.36 11 6.48 6485.32 1888.86 40 6.48 6019.95 1908.46 Figure 2 (c) shows the normalized size distribution of fog droplets when subjected to sound waves at a fundamental frequency of 300 Hz. Similar plots were generated for the scenarios involving sound application at fundamental frequencies of 400 Hz and 500 Hz. Table 2 summarizes the results obtained from these figures. At all instances of sound application, a lower peak diameter was observed compared to the no sound case (8.49 µm). Additionally, the normalized \(\:{N}_{c}\) at the peak diameter for small droplets was lowest in the no sound case (5054 counts/ \(\:{\text{c}\text{m}}^{3}\) /µm) and highest in the 300 Hz case (7372.16 counts/ \(\:{\text{c}\text{m}}^{3}/\) µm). Figure 2 (d) presents plots for the normalized \(\:{N}_{c}\) at the peak diameter for small droplets and the median \(\:{N}_{c}\) when sound waves were applied at a fundamental frequency of 300 Hz. Similar plots were generated for the other scenarios, indicating that the curves exhibit close congruence and comparable shapes, in line with the observations detailed in the preceding section. This supports the conclusion that the application of sound waves causes the fragmentation of some large droplets, consequently increasing the number of small droplets. This effect appears to be different across various frequency and harmonic combinations as shown previously in Fig. 2 (b). The normalized \(\:{N}_{c}\) for droplet diameter of 20.98 µm is the highest for the no sound case (1997.92 counts/ \(\:{\text{c}\text{m}}^{3}\) /µm) and the lowest when sound waves were applied at 400 Hz and its 9th -harmonic (1086.86 counts/ \(\:{\text{c}\text{m}}^{3}\) /µm). Table 3 presents the percentage increase in the sum of LWC for small and large droplets after the application of sound waves. It is noticeable that the application of sound waves at 400 Hz with its 9th -harmonic results in the second lowest increase in LWC for small droplets at 0.19%. This effect is only exceeded by sound applied at 300 Hz with its 9th -harmonic, which uniquely induces a reduction in the overall sum of LWC. This highlights the significance of specific harmonic frequencies in influencing LWC dynamics in small droplets and demonstrates that it can result in reduced fragmentation of large droplets. Table 3 Percentage increase in LWC for small and large droplets when sound waves were applied at fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz. Frequency (Hz) Harmonic number Percentage increase in LWC for small droplets Percentage increase in LWC for large droplets 300 - 16.34% -56.22% 9 -4.82% -47.76% 11 16.44% -31.69% 40 17.81% -32.76% 400 - 4.14% -37.9% 9 0.19% -61.06% 11 17.63% -36.81% 40 9.67% -40.27% 500 - 11.89% -45.93% 9 8.91% -22.31% 11 20.41% -22.31% 40 10.66% -14.46% Moreover, it is evident that subjecting fog to sound at 400 Hz with its 9th -harmonic leads to the largest reduction in LWC for large droplets (61.06%). Remarkably, when sound wave was applied at 400 Hz, both its 9th - and 40th -harmonics emerged as the only instances where introducing harmonics led to a notable reduction in LWC for large droplets compared to that of the fundamental frequency. The table demonstrates that the application of sound at 400 Hz with its 9th -harmonic gave superior results compared to the 400 Hz waveform alone, with a difference of 3.95% for small droplets and 23.16% for large droplets. To gain more insight into the dynamics at each time interval, the full 116-second duration was divided into 6 segments of 19 seconds each. Figure 3 illustrates the LWC plots across each droplet diameter in the scenario of applying 400 Hz with various harmonics. The plots are arranged from (a) to (f) corresponding to their sequential occurrence, with each plot representing a 19-second segment of the original duration. The figure reveals that the curve for 400 Hz with its 9th -harmonic displayed the lowest values for the majority of the period across most plots. Similar plots were generated for sound waves applied at fundamental frequencies of 300 Hz and 500 Hz. The plots indicated that the fundamental frequency resulted in the lowest values for large droplets, while the results for the 9th -harmonic showed the lowest values for small droplets across almost the whole period. This observation is in line with the results obtained in Tables 2 and 3 . This is consistent across almost all cases, where the LWC for large droplets exhibits a decreasing trend, hinting at a potential continuation with continuous application of sound. Figure 4 (a) illustrates the results of Table 3 , showing the LWC for each droplet size in the cases that led to the highest reduction in LWC for large droplets. It is observed that the case of using the 400 Hz sound wave along with its 9th -harmonic exhibits the lowest LWC for large droplets, followed by the 300 Hz one. Figure 4 (b), however, displays the LWC for the same cases over a period of 345 seconds, confirming the previous results and indicating that the results when using a 400 Hz signal with its 9th -harmonic remain the lowest for most of the duration. Figure 4 (c) captures the evolution of fog droplet sizes throughout a natural dissipation process, spanning a duration of 400 seconds. The y -axis of the graph is depicted on a logarithmic scale, representing the particle diameter, while the color gradient at each data point indicates the number density (normalized \(\:{N}_{c}\) ) of fog droplets. It also shows a gradual rise in the count of small particles, accompanied by a corresponding decline in the count of larger particles over time. Figure 4 (d) displays a similar visualization when using the 300 Hz sound waves. The observation period spans 400 seconds, during which the sound waves were only applied for the first 120 seconds. The application of sound waves at 300 Hz led to a rapid increase in the number of tiny particles, particularly evident around the midpoint of the period, as indicated by the intensified red color. This observation aligns with the previous findings where the 300 Hz case exhibited a very high number of tiny particles. It is hypothesized that this effect delays the condensation of fog droplets into larger droplets, as evidenced by comparing the final segments of Fig. 4 (c) and Fig. 4 (d). The plot for the case of applying 400 Hz sound wave with its 9th -harmonic at 112 dB is displayed in Fig. 4 (e). It shows a similar visualization with no red-colored points observed, and the condensation process appears to occur more rapidly compared to the previous two cases. The time required for fog to achieve 90% condensation, or in other words, for 10% of the original \(\:{N}_{c}\:\) of particles to remain suspended in the air was investigated for various cases involving the application of sound at the selected fundamental frequencies with different harmonics. The initial five readings of the scenario involving no sound application were averaged and employed as a baseline to determine the timing at which 90% condensation occurred. This methodology is conducted under the assumption that a nearly equivalent quantity of fog was introduced at the onset of each experiment. Table 4 presents the outcomes of this investigation, showcasing the time taken for each case to reach 90% condensation. Only the case of applying a sound wave of 400 Hz with its 9th -harmonic exhibits a faster attainment of 90% condensation compared to the natural dissipation (no sound case). It also has the shortest duration among all the other cases of around 318 seconds. This marks a difference of 23 seconds from the no sound case and a difference of 49 seconds from the scenario where sound waves were applied at only the fundamental frequency of 400 Hz. Table 4 Time taken to reach 90% condensation effect for different scenarios. Frequency (Hz) Harmonic Number Time (s) no sound - 341 300 - 358 9 364 11 379 40 383 400 - 367 9 318 11 408 40 388 500 - 389 9 348 11 419 40 368 These findings highlight the potential of utilizing harmonics in improving visibility. Based on the observations thus far, the primary mechanism for acoustic condensation appears to be the collision and coalescence of fog droplets, resulting in their descent and consequent reduction of LWC. However, certain frequencies increased fragmentation of large droplets, thus impairing condensation efficiency. Clearly, the initial investigation revealed deviations from findings in similar studies [ 18 , 19 ]. Prior research noted that sound waves at specific frequencies increase droplet size, facilitating growth rate comparisons. Additionally, one study indicated that application of sound waves increased the number of large particles and decreased the number of small particles [ 18 ]. In this work, the median MVD, D50, and D90 either decreased or remained constant with sound application. There was an observed decrease in large particles and an increase in smaller particles due to differences in experimental setups. Unlike previous studies that used smaller chambers with sound generators positioned at the top or bottom [ 17 , 18 ], this work employed a larger, rectangular prism chamber with a centrally located speaker. The particle size analyzer was positioned at the center rear, which caused it to miss descending large droplets and led to observed discrepancies. While this does not invalidate the results or conclusions, it limits comparisons with other studies. Moreover, the study's results may differ from real-life applications. During fog events in the UAE, fog droplets range from 80 to 700 counts per cm³, with a median diameter of 25 µm and LWC between 0.06 and 0.58 \(\:\text{g}\:{\text{m}}^{-3}\) [ 28 ]. In contrast, the study observed a median number concentration of 3183.05 droplets per \(\:{\text{c}\text{m}}^{3}\) , a median diameter of 20.09 µm, and a LWC of 3.13 \(\:\text{g}\:{\text{m}}^{-3}\) for the case involving no sound application. These differences highlight variations in fog microphysics, with the latter scenario demonstrating more particle collisions due to the greater number of suspended droplets. 4. Conclusion Experiments were conducted within a controlled environment of a fog chamber. The study investigated how different frequencies of sound waves contribute to visibility enhancement using single and multi-frequency sound waves. The impact of harmonics was investigated for fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz. The primary focus was on the 9th -, the 11th -, and the 40th -harmonics. The findings revealed that: All instances of sound application resulted in a lower median LWC, median MVD, D90 figure, peak diameter for small droplet sizes, and normalized \(\:{N}_{c}\) for large droplets. The results suggest that extended exposure to sound waves beyond two minutes may further reduce the LWC of fog. The application of sound waves can fragment large droplets, with the effect varying across different combinations, potentially impairing condensation efficiency. The primary mechanism for acoustic condensation appears to be the collision and coalescence of droplets, resulting in their descent and a consequent reduction of LWC. In nearly all instances of adding harmonics, there was no enhancement observed in the parameters associated with visibility. Employing 400 Hz with its 9th -harmonic yielded a significantly enhanced effect on visibility compared to all other cases. It resulted in a reduction of 61.06% in the LWC for large droplets, showed minimal increase in LWC for smaller droplets, and achieved a 90% condensation effect in less time compared to all the other cases. These observations highlight the significance of investigating the impact of harmonics on improving the efficacy of the acoustic fog dissipation technique, suggesting promising avenues for further research. Future research avenues include examining the impact across a wider spectrum of frequencies and harmonics, evaluating the influence of non-harmonically related frequencies on fog agglomeration, and investigating the effects of varying SPL, waveform, duration of acoustic exposure, and signal phase. Declarations Competing interests The authors declare no competing interests. Author Contribution R.E. developed the initial problem statement, directed the work, and collaboratively designed the study with M.Y.I. who built the setup, conducted the experiments, analyzed the data, and wrote the manuscript. D.F. and N.N provided the particle size analyzer and assisted in data representation and interpretation. The authors collectively offered crucial editorial input for this article. Data Availability The dataset utilized in this research is accessible through the corresponding author upon request. References Fonseca, R., Francis, D., Nelli, N. & Cherif, C. Regional atmospheric circulation patterns driving consecutive fog events in the united arab emirates. Atmospheric Research 282, 106506 (2023). Mohan, T. et al. On the investigation of the typology of fog events in an arid environment and the link with climate patterns. Monthly Weather Review 148, 3181–3202 (2020). Nelli, N. et al. First measurements of electric field variability during fog events in the united arab emirates. Journal of Arid Environments 220, 105096 (2024). Nelli, N. et al. In-situ measurements of fog microphysics: Visibility parameterization and estimation of fog droplet sedimentation velocity. Atmospheric Research 107570 (2024). Nelli, N. et al. The wind-blown sand experiment in the empty quarter desert: Roughness length and saltation characteristics. Earth and Space Science 11, e2024EA003512 (2024). Nelli, N. et al. Characterization of the atmospheric circulation near the empty quarter desert during major weather events. Frontiers in Environmental Science 10, 972380 (2022). Temimi, M. et al. On the analysis of ground-based microwave radiometer data during fog conditions. Atmospheric Research 231, 104652 (2020). Weinstein, A. I. Fog dispersal-a technology assessment. Journal of Aircraft 14, 38–43 (1977). Fletcher, R. D. Progress in the dissipation of fog. In The Space Congress® Proceedings (1971). Hicks, J. R. Improving visibility during periods of supercooled fog, vol.181 (US Army Materiel Command, Cold Regions Research & Engineering Laboratory, 1966). Liu, C., Tian, Z., Zhao, Y. & Zeng, X. Review and prospect of fog elimination technology based on acoustic condensation. In IOP Conference Series: Earth and Environmental Science, vol. 514, 032011 (IOP Publishing, 2020). Christensen, L. S. & Frost, W. Fog dispersion. Tech. Rep., NASA (1980). Liu, C., Zhao, Y., Tian, Z., Zhou, H. et al. Numerical simulation of condensation of natural fog aerosol under acoustic wave action. Aerosol and Air Quality Research 21, 200361 (2021). Chou, K., Lee, P. S. & Shaw, D. Aerosol agglomeration in high-intensity acoustic fields. Journal of Colloid and Interface Science 83, 335–353 (1981). Liu, C., Tian, Z., Zhao, Y. & Zhou, H. Experimental study on acoustic condensation fog elimination in traveling wave tube. In IOP Conference Series: Earth and Environmental Science, vol. 714, 022048 (IOP Publishing, 2021). Patterson, H. S. & Cawood, W. Phenomena in a sounding tube. Nature 127, 667–667 (1931). Qiu, J., Tang, L.-J., Cheng, L., Wang, G.-Q. & Li, F.-F. Interaction between strong sound waves and cloud droplets: Cloud chamber experiment. Applied Acoustics 176, 107891 (2021). Zhang, M. et al. Experimental study on coalescence of fog droplets in cloud chamber under low-frequency sound waves. Journal of Physics D: Applied Physics 54, 395301 (2021). Cheng, L., Jia, Y.-H., Li, F.-F. & Qiu, J. Cloud chamber experimental study for acoustic fog elimination technology. Applied Acoustics 219, 109885 (2024). Boudala, F. S., Wu, D., Isaac, G. A. & Gultepe, I. Seasonal and microphysical characteristics of fog at a northern airport in alberta, canada. Remote Sensing 14, 4865 (2022). Du, P. et al. Design and evaluation of ACFC—an automatic cloud/fog collector. Atmosphere 14, 563 (2023). Kim, S., Rickard, C., Hernandez-Vazquez, J. & Fernandez, D. Early night fog prediction using liquid water content measurement in the monterey bay area. Atmosphere 13, 1332 (2022). Bai, W., Wei, J., Shi, Y., Zhao, Z. & Li, Q. Microphysical characteristics and environmental isotope effects of the micro-droplet groups under the action of acoustic waves. Atmosphere 12, 1488 (2021). Wu, T. S. Comparing Bulk Aerosol Profiles in the Mixed Layer in Coastal Los Angeles and the Inland Empire. Bachelor’s thesis, Scripps College (2015). Spiegel, J. K. et al. Evaluating the capabilities and uncertainties of droplet measurements for the fog droplet spectrometer (fm-100). Atmospheric Measurement Techniques 5, 2237–2260 (2012). Alivio, M. B., Bezak, N. & Mikoš, M. The size distribution metrics and kinetic energy of raindrops above and below an isolated tree canopy in urban environment. Urban Forestry & Urban Greening 85, 127971 (2023). Oshana, R. DSP software development techniques for embedded and real-time systems (Elsevier, 2006). Weston, M. et al. The first characterization of fog microphysics in the united arab emirates, an arid region on the arabian peninsula. Earth and Space Science 9, e2021EA002032 (2022) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 16 Apr, 2025 Reviews received at journal 15 Apr, 2025 Reviewers agreed at journal 13 Apr, 2025 Reviewers agreed at journal 12 Apr, 2025 Reviewers agreed at journal 11 Apr, 2025 Reviewers agreed at journal 11 Apr, 2025 Reviews received at journal 21 Nov, 2024 Reviewers agreed at journal 12 Nov, 2024 Reviewers invited by journal 11 Nov, 2024 Editor assigned by journal 06 Nov, 2024 Editor invited by journal 08 Aug, 2024 Submission checks completed at journal 08 Aug, 2024 First submitted to journal 31 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4835869","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":348291575,"identity":"c74b8233-1894-4333-a015-1b0d1405f03e","order_by":0,"name":"M. Y. Ibrahim","email":"","orcid":"","institution":"Khalifa University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"Y.","lastName":"Ibrahim","suffix":""},{"id":348291576,"identity":"d4433876-8dd2-429d-b695-7b8540e8731c","order_by":1,"name":"Reyad El-Khazali","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVRIie2RT0rDQBSHfyVgXbwDvJCQXOGFgFqQnmVKoNlEEAQJCLZQ0E0OkNLiJXoBJWA3PUCWitss4i5QQae4kcL4Z+divtVjZj6+BwNYLP8VAnzm3XTOAf9WoU9FOP6zglH50+vj2yJqG5ySu5i9tJ2cpPNS9doOw8Ck+JtN7C4xJs9/lKgQPluwctwCSWxSmDPxCBUFrESRVu5YwQOc0dSkhE28JbxrJW0f3oRT7TpbYDIxKkxHunJPHmfRTFeUx+pAVyplXIzGl4OlJOSW2YXjC0fz4vlmUMg6Mlb61apu8mHAdbp6bfLrkNdJVXf5VWiqAIey+46v9Kb7J3v0n767tVgsFgvwAbYlRsDI2g93AAAAAElFTkSuQmCC","orcid":"","institution":"Khalifa University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Reyad","middleName":"","lastName":"El-Khazali","suffix":""},{"id":348291577,"identity":"c04ffad7-d4f8-46cc-b100-8eb0dfa77e6b","order_by":2,"name":"Diana Francis","email":"","orcid":"","institution":"Khalifa University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Diana","middleName":"","lastName":"Francis","suffix":""},{"id":348291578,"identity":"cfbe8118-ce5a-422e-8be1-c7304cce99c3","order_by":3,"name":"Narendra Nelli","email":"","orcid":"","institution":"Khalifa University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Narendra","middleName":"","lastName":"Nelli","suffix":""}],"badges":[],"createdAt":"2024-07-31 13:21:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4835869/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4835869/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":64604145,"identity":"970b81fb-a9f2-4c85-91ba-0857c00747b6","added_by":"auto","created_at":"2024-09-16 12:44:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":996121,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental setup’s (a) schematic diagram (b) lab photo.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4835869/v1/1ae6b54132da73be81bde206.png"},{"id":64604144,"identity":"12b50247-efa1-4463-a10f-c691a42bef4e","added_by":"auto","created_at":"2024-09-16 12:44:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":295552,"visible":true,"origin":"","legend":"\u003cp\u003ePlots for (a) median LWC, (b) median N\u003csub\u003ec\u003c/sub\u003e of fog droplets when sound waves were applied at fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz, (c) normalized size distribution of fog droplets when sound waves were applied at a fundamental frequency of 300 Hz, (d) normalized N\u003csub\u003ec\u003c/sub\u003e at the peak diameter for small droplet sizes and median N\u003csub\u003ec\u003c/sub\u003e when sound waves were applied at 300 Hz.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4835869/v1/ce07c39f9bd9cb02c9af6f1f.png"},{"id":64604147,"identity":"5e42961e-ee70-406d-826c-7ce6a4115902","added_by":"auto","created_at":"2024-09-16 12:44:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":392425,"visible":true,"origin":"","legend":"\u003cp\u003eLWC plots for each droplet diameter in the scenario of applying sound at a fundamental frequency of 400 Hz. These plots are organized from (a) to (f), aligning with their sequential occurrence, with each plot representing a 19-second segment of the original duration.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4835869/v1/b70b2c432da39f52cfe2821a.png"},{"id":64604146,"identity":"965b6b08-5ed6-43ee-b547-7689c06c803e","added_by":"auto","created_at":"2024-09-16 12:44:21","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":446822,"visible":true,"origin":"","legend":"\u003cp\u003eLWC of fog during the application of sound waves at 300 Hz, 300 Hz with its 9th harmonic, and 400 Hz with its 9th harmonic (a) across each droplet size (b) across 345 seconds. Evolution of fog droplet sizes (c) throughout a natural dissipation process, during and after the application of sound waves (d) at 300 Hz and (e) at 400 Hz with its 9th harmonic for 400 seconds.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4835869/v1/fb7c3d5aff4b3babe286d972.png"},{"id":64605471,"identity":"dcde3f9f-922b-431c-9d65-3c135c5fff89","added_by":"auto","created_at":"2024-09-16 12:52:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3344852,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4835869/v1/f6ad6ee1-b537-4802-af42-d350a7d9016e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Effects of multi-frequency acoustic waves on the agglomeration of fog droplets","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFog is a frequent phenomenon in the United Arab Emirates (UAE), located on the northeastern coast of the Arabian Peninsula. Despite its desert landscape, the UAE experiences numerous low visibility events during winter, primarily caused by haze and fog [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], leading to severe disruptions in road transportation and aviation, causing delays and accidents due to reduced visibility. In particular, Abu Dhabi's international airport records up to 13 fog days per month and 51 fog days annually during this season [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo address these visibility issues, researchers have suggested various techniques to artificially clear fog, each designed for specific fog types. Fog can be categorized into three types in the context of artificial dissipation: ice fog, warm fog, and supercooled fog. Ice fog, occurring at temperatures below \u0026minus;\u0026thinsp;30\u0026deg;C, which consists of airborne ice particles [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. There is no method that has proven effective for operationally dispersing this type of fog [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Warm fogs occur at temperatures above 0\u0026deg;C, whereas supercooled fogs develop at temperatures below 0\u0026deg;C [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Dissipating supercooled fog involves triggering the freezing of certain droplets using substances like dry ice or silver iodide [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Warm fog lacks a standardized operational dispersal mechanism, unlike supercooled fog. Nevertheless, various approaches have been devised, each showing varying levels of efficacy [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. This investigation will center on tackling warm fog elimination, given its limited success to date and its prevalence in an arid environment such as that of the UAE. The traditional methods have not been implemented operationally due to their environmental impact, inefficiency, or high cost [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn recent years, there has been a growing interest in research involving acoustic and ultrasonic waves [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], particularly for fog elimination [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The potential of utilizing sound waves in this regard is promising due to their controllability, flexibility, environmental friendliness, and minimal impact on traffic [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. The technique of using acoustic waves for fog dispersal employs sound vibrations to facilitate the merging of fog particles into larger droplets, leading to the efficient dissipation of fog. However, thorough investigations into the effectiveness of this method, especially in typical fog conditions, are currently lacking [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Research on acoustic fog dispersion has primarily focused on single frequencies, neglecting the potential advantages of utilizing a combination of frequencies [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Low-frequency waves have a greater influence on condensing larger particles, whereas high-frequency waves are more effective in condensing smaller particles [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. This indicates that different frequencies affect droplet sizes differently, suggesting that combining multiple frequencies, or their harmonics, could lead to superior outcomes.\u003c/p\u003e \u003cp\u003ePatterson et al.'s work marked the pioneering effort in agglomeration via sound waves [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Since then, many researchers have delved into its applications across diverse domains [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. A simulation investigating the condensation impact of ultrasonic waves revealed that the optimal frequency for coalescence is 20 kHz with more effective diminishing at higher frequencies [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. This raises questions regarding the viability of ultrasonic waves for acoustic coagulation. A numerical simulation illustrated a notable enhancement of condensation efficiency achieved through acoustic fog dissipation [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Liu et al. performed an experimental study that identified the optimal frequency range for fog dispersion as being between 300 Hz and 500 Hz [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Moreover, it highlights the unique response of droplets of different sizes to varying frequencies, with higher frequencies amplifying condensation for smaller particles while yielding contrasting effects for larger ones. Qiu et al. examined the acoustic agglomeration of cloud particles subjected to sound waves at frequencies spanning from 35 Hz to 100 Hz and SPLs ranging between 112 and 122 dB [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Maintaining a constant SPL value revealed that the most efficient agglomeration took place within the frequency range of 50 Hz to 65 Hz. Zhang et al. investigated experimentally the dissipation of fog through acoustic means using frequencies ranging from 200 Hz to 700 Hz. Their work emphasized the significant role of frequency in the process of droplet merging. It specifically identified that a 300 Hz acoustic signal of 75 W had the best condensation effect [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA recent experimental study into the dissipation effects of frequencies below 100 Hz revealed notable dissipation effects for frequencies under 50 Hz at Sound Pressure Levels surpassing 125 dB [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Furthermore, the investigation undertook a comparative examination of acoustic dissipation techniques and hygroscopic salt seeding, ultimately establishing the former as the more efficacious approach.\u003c/p\u003e \u003cp\u003eDetermining the most effective frequencies for acoustic fog dissipation hinges on the specific properties of the fog under examination and the sizes of the particles present. As a result, ongoing debate surrounds the conclusive identification of the optimal frequency for efficient acoustic fog dissipation. Further research into fog dispersion via sound waves is believed imperative, as experimental evidence regarding the defogging efficacy of sound waves remains inadequate. Additionally, there is a pressing need to explore the influence of various parameters such as waveform types and their power, particle size distribution, and temperature [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis research will focus on the effects of frequencies and their harmonics on droplets agglomeration. As previously highlighted, a significant portion of research on acoustic fog dissipation has focused on single-frequency methodologies, with the objective of pinpointing an optimal frequency for fog dissipation. However, there exists untapped potential in exploring the effects of integrating harmonics to improve visibility, an area that has yet to be thoroughly investigated. This study seeks to present the first study in literature on the effect of harmonically related multi-frequency acoustic waves on the agglomeration of fog droplets.\u003c/p\u003e \u003cp\u003eThis paper is organized as follows: data and methodology are presented in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the main results and discussion, while the conclusions are summarized in Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e"},{"header":"2. Data and Methodology","content":"\u003cp\u003e \u003cb\u003eExperimental setup\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows an experimental setup of the fog agglomeration system. It consists of a high-pressure misting system, with a flow rate of approximately 6 Liters per minute, used to generate artificial fog withing the chamber. This system was integrated into the chamber through a network of pipes with evenly spaced nozzles, enabling uniform fog dispersal. The inlet of the machine is connected to a pump powered by a DC source, ensuring a continuous water supply. The fog chamber is a rectangular prism measuring 2 m \u0026times; 2 m \u0026times; 1.5 m (length \u0026times; width \u0026times; height), with supporting legs of 0.25 m in height. These dimensions were chosen to provide a more realistic simulation of foggy conditions. It features a glass front providing a clear view of fog during the experiment, while the remaining sides are constructed from High-Pressure Laminate (HPL) for cost-effectiveness and durability. The frame is made of Aluminum to ensure structural integrity. The glass panels are approximately 6 mm thick, and the HPL panels are about 2.5 mm thick. The chamber was properly insulated using silicone sealants and rubber strips. The Fog Monitor FM-120, manufactured by Droplet Measurement Technologies in the USA, was employed for real-time measurement of various parameters including the number concentration of fog droplets, Median Volume Diameter (MVD), Liquid Water Content (LWC), and other microphysical properties of the fog cloud. It has the capability to assess droplets ranging from 2 to 50 \u0026micro;m in diameter [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. A compressor extracts a sample from the fog layer through a sampling tube. The instrument then quantifies the forward scattered light from particles as they traverse a laser beam. FM-120 has gained widespread acceptance in academic research, thereby bolstering the credibility and reliability of the obtained findings [\u003cspan additionalcitationids=\"CR21\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePrior to conducting the experiments, the apparatus underwent calibration procedures to guarantee the accuracy and reliability of the results. The sampling rate was set at 1 sample per second. A precise aperture was made at the rear side of the chamber to accommodate the inlet horn of the FM-120, which was securely fixed and properly insulated within the aperture. The speaker used in this work has an output frequency range of 33 Hz to 20 kHz. Temperature and humidity sensors were utilized to continuously monitor and record the temperature and humidity levels within the chamber throughout the experiments. The SPL was measured in dB using an SPL meter (Extech SL510). SPL measurements were taken 1 meter from the speakers before starting the experiments. Measures were taken to isolate the speakers from fog to prevent potential damage. To accommodate the speakers, the right side of the chamber featured an opening measuring 0.65 m \u0026times; 0.45 m, which was properly covered with a plastic material known for its effective acoustic transmission. Similar techniques have been successfully applied in previous research [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Furthermore, sound dampening panels were placed on the interior sides of the chamber to reduce the impact of echo.\u003c/p\u003e \u003cp\u003e \u003cb\u003eProcedure\u003c/b\u003e \u003c/p\u003e \u003cp\u003eEach experiment was conducted as follows: 1) Fog is generated for 4\u0026ndash;5 minutes inside the chamber which is the time it takes for an object placed at the middle of the chamber to be completely invisible from outside. 2) The fog generating machine is turned off and the particle size analyzer and the speakers are turned on. The start time, temperature, and humidity inside and outside the chamber are recorded. 3) After 2 minutes, the speakers are turned off. 4) After 5 minutes, the particle size analyzer is turned off. Background noise was neglected as the measurements showed its minimal effect. Each case under investigation involved 3 experimental runs. Temperatures inside and outside the chamber were maintained at 24.65 ℃ \u0026plusmn; 1.15 ℃ and 24.85 ℃ \u0026plusmn; 1.05 ℃, respectively. The humidity inside the chamber was maintained at 98.85% \u0026plusmn; 1.15%.\u003c/p\u003e \u003cp\u003e \u003cb\u003eData representation\u003c/b\u003e \u003c/p\u003e \u003cp\u003eNormalization ensures that particle concentrations are comparable across different bin sizes, incorporating a logarithmic scale. This scale allows for a more effective visualization of the distribution of particle sizes, particularly when dealing with particles spanning multiple orders of magnitude in size. The normalized particle concentration was calculated using the following formula [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\frac{dN}{dlog{D}_{p}}=\\frac{dN}{log{D}_{p,u}-log{D}_{p,l}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:dN\\)\u003c/span\u003e\u003c/span\u003e is the particle concentration within the specified size interval, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{p,u}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{p,l}\\)\u003c/span\u003e\u003c/span\u003e represent the upper and lower bounds of the size interval, respectively. Moreover, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:dlog{D}_{p}\\)\u003c/span\u003e\u003c/span\u003e quantifies the change in the logarithm scale of the particle diameter within the size interval. FM-120 can provide the overall LWC of a sample at a rate of one sample per second. However, it does not provide the LWC for each individual bin size. The LWC for each droplets size bin was estimated through the following expression [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{LWC}_{i}=({\\rho\\:}_{w}\\times\\:\\frac{\\pi\\:}{6})\\times\\:{Nc}_{i}\\times\\:{D}_{p,\\:i}^{3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{L}\\text{W}\\text{C}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the LWC for each fog droplet bin size, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{w}\\)\u003c/span\u003e\u003c/span\u003e is the density of water, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Nc}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the number concentration of fog droplets at the ith-bin size, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{p,i}\\)\u003c/span\u003e\u003c/span\u003e is the bin center diameter. The particle size analyzer also measures the total number concentration of droplets and the Median Volume Diameter (MVD). Earlier studies have opted to examine specific characteristic droplet diameters to explore the influence of sound waves, thereby simplifying the statistical analysis process [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The MVD essentially corresponds to a widely recognized characteristic droplet diameter known as D50, denoting the diameter at which 50% of the total volume is distributed among particles smaller and larger than that diameter. However, the MVD provided by the particle size analyzer pertains to each individual sample rather than an aggregate of all samples. To address this, D50 values are calculated for all samples using the following formula [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{D}_{50}={D}_{l}+\\frac{0.5\\sum\\:_{i}^{m}{{n}_{i}V}_{i}-\\sum\\:_{i}^{l}{n}_{i}{V}_{i}}{\\sum\\:_{i}^{u}{{n}_{i}V}_{i}-\\sum\\:_{i}^{l}{n}_{i}{V}_{i}}({D}_{u}-{D}_{l})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cem\u003ei\u003c/em\u003e denotes the bin index, \u003cem\u003em\u003c/em\u003e is the total number of bins, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{n}_{i}\\)\u003c/span\u003e\u003c/span\u003e denotes the count of droplets in each bin, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{i}\\)\u003c/span\u003e\u003c/span\u003e refers to the volume corresponding to particles at the i-th bin, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{u}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{l}\\)\u003c/span\u003e\u003c/span\u003e denote the upper and the lower diameters to D50, respectively. To estimate the volume \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{i}\\)\u003c/span\u003e\u003c/span\u003e in Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), it was assumed that the droplets are spherical with a radius \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{r}_{i}\\)\u003c/span\u003e\u003c/span\u003e. The analysis of the experimental results includes D90, which represents the diameter at which 90% of the total volume is distributed among particles with smaller diameters. The D90 was obtained through a slight modification of Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cb\u003eInput signal\u003c/b\u003e \u003c/p\u003e \u003cp\u003eVarious signal waveforms can be selected for the input signal to the speaker. The signal utilized in this research is a basic sine wave. Given that the maximum frequency the speakers can output is 20 kHz, a sampling frequency of 44.1 kHz was chosen to adhere to Nyquist theorem. The theorem asserts that to faithfully represent a signal, the sampling rate should be at least twice the maximum signal frequency [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. However, in practice, a higher sampling rate is preferable to address quantization errors. The amplitude was consistently set to 1 for all experiments. The signal was normalized by dividing each sample by the maximum absolute value in the signal before sending it to the speakers to prevent clipping and distortion. The expression can be extended to account for the scenario of applying a sound wave with a fundamental frequency and one harmonic as follows:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:y=Asin\\left(2\\pi\\:ft\\right)+Asin\\left(2\\pi\\:nft\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:y\\)\u003c/span\u003e\u003c/span\u003e is the output signal, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e is the amplitude of the signal, \u003cem\u003et\u003c/em\u003e denotes time, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\)\u003c/span\u003e\u003c/span\u003e denotes the fundamental frequency and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e signifies the harmonic number. For the sake of simplifying the investigation, there is no phase shift between the two signals.\u003c/p\u003e \u003cp\u003e \u003cb\u003eData processing\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe examined frequencies were limited to 300 Hz, 400 Hz, and 500 Hz at a maintained SPL of 112 dB. During each experiment, sound was applied to the fog layer for 2 minutes. However, the initial four readings from the particle size analyzer had to be omitted as they yielded exceptionally small readings. To ensure the reliability of the findings, each experiment was repeated three times for every frequency and its harmonic combinations. The normalized size distribution plot displays the particle sizes in counts per cm\u0026sup3; per \u0026micro;m across each droplet diameter, which is represented by the bin midpoint. Plotting the normalized size distribution across the three runs demonstrated that the curves are remarkably close, with nearly identical peaks at all frequencies examined. A multiple comparison test was conducted via MATLAB using the LWC data obtained after sound application at each frequency across multiple runs. Subsequently, runs with significantly divergent means were excluded from the average measurements to mitigate the influence of varying initial fog amounts at the start of each experiment.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eThe amplitude of the sine wave for both the fundamental frequency and its harmonic is maintained at an equal level. In the subsequent figures, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:h\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{o}\\)\u003c/span\u003e\u003c/span\u003e denote the harmonic level and the fundamental frequency, respectively. Several plots were generated for all cases across various parameters. The summarized results, including the D50 and the D90 data, are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a) displays a plot of the median LWC, across the different cases. A noticeable trend appears in the curves for both the 300 Hz and 500 Hz waves, indicating that the median LWC increases with higher harmonic numbers. The lowest median LWC of 1.66 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{g}/{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e was observed for the acoustic waveform of 400 Hz along with its 9th -harmonic signal. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b) depicts a plot of the median \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e, revealing a similar shape among the three curves, with each showing the minimum \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e at the 9th -harmonic. It is evident that the 300 Hz case with no additional harmonics has the highest normalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e (4073.25 counts/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e/\u0026micro;m), whereas the lowest was observed for the same frequency with the addition of the 9th -harmonic (3144.55 counts/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e/\u0026micro;m). The highest median MVD of 20.09 \u0026micro;m is observed for the no sound waves case, while the lowest median MVD of 15.03 \u0026micro;m is recorded for the 500 Hz case. The highest value for the D50 corresponds to the no-sound case, resembling D90, and is also observed in other instances of sound application. Conversely, the lowest values are observed in the case of sound application at 400 Hz with its 9th -harmonic.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eD50, D90, and the medians for LWC, N\u003csub\u003ec\u003c/sub\u003e, and MVD of fog droplets when sound waves were applied at fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHarmonic number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMedian LWC\u003c/p\u003e \u003cp\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{g}/{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMedian \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{c}}\\)\u003c/span\u003e\u003c/span\u003e (#/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{c}{\\text{m}}^{3})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMedian MVD (\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eD50\u003c/p\u003e \u003cp\u003e(\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eD90 (\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eno sound\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3183.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e22.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e32.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4073.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e18.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e26.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3144.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e26.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3816.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e26.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3886.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3598.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3525.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e18.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e24.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3846.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e26.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3657.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e26.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3913.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e16.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e26.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3598.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e22.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3859.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e22.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3694.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e22.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e30.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of results obtained from the normalized size distribution plots.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrequency (Hz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHarmonic number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeak diameter for small droplet sizes (\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNormalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{c}}\\)\u003c/span\u003e\u003c/span\u003e at the peak diameter (#/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{c}{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e/\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNormalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{c}}\\)\u003c/span\u003e\u003c/span\u003e at a diameter of 20.98 \u0026micro;m (#/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{c}{\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e/\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eno sound\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1997.92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7372.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1182.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5363.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1358.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6493.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1738.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6690.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1658.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6143.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1499.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6193.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1086.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6618.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1629.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6303.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1520.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6928.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1372.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5901.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1824.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6485.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1888.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6019.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1908.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (c) shows the normalized size distribution of fog droplets when subjected to sound waves at a fundamental frequency of 300 Hz. Similar plots were generated for the scenarios involving sound application at fundamental frequencies of 400 Hz and 500 Hz. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes the results obtained from these figures. At all instances of sound application, a lower peak diameter was observed compared to the no sound case (8.49 \u0026micro;m). Additionally, the normalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e at the peak diameter for small droplets was lowest in the no sound case (5054 counts/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e/\u0026micro;m) and highest in the 300 Hz case (7372.16 counts/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}\\text{m}}^{3}/\\)\u003c/span\u003e\u003c/span\u003e\u0026micro;m). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (d) presents plots for the normalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e at the peak diameter for small droplets and the median \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e when sound waves were applied at a fundamental frequency of 300 Hz. Similar plots were generated for the other scenarios, indicating that the curves exhibit close congruence and comparable shapes, in line with the observations detailed in the preceding section. This supports the conclusion that the application of sound waves causes the fragmentation of some large droplets, consequently increasing the number of small droplets. This effect appears to be different across various frequency and harmonic combinations as shown previously in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b). The normalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e for droplet diameter of 20.98 \u0026micro;m is the highest for the no sound case (1997.92 counts/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e/\u0026micro;m) and the lowest when sound waves were applied at 400 Hz and its 9th -harmonic (1086.86 counts/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e/\u0026micro;m). Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the percentage increase in the sum of LWC for small and large droplets after the application of sound waves. It is noticeable that the application of sound waves at 400 Hz with its 9th -harmonic results in the second lowest increase in LWC for small droplets at 0.19%. This effect is only exceeded by sound applied at 300 Hz with its 9th -harmonic, which uniquely induces a reduction in the overall sum of LWC. This highlights the significance of specific harmonic frequencies in influencing LWC dynamics in small droplets and demonstrates that it can result in reduced fragmentation of large droplets.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePercentage increase in LWC for small and large droplets when sound waves were applied at fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrequency (Hz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHarmonic number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePercentage increase in LWC for small droplets\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePercentage increase in LWC for large droplets\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16.34%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-56.22%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-4.82%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-47.76%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16.44%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-31.69%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17.81%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-32.76%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.14%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-37.9%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.19%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-61.06%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17.63%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-36.81%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.67%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-40.27%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.89%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-45.93%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.91%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-22.31%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.41%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-22.31%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.66%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-14.46%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eMoreover, it is evident that subjecting fog to sound at 400 Hz with its 9th -harmonic leads to the largest reduction in LWC for large droplets (61.06%). Remarkably, when sound wave was applied at 400 Hz, both its 9th - and 40th -harmonics emerged as the only instances where introducing harmonics led to a notable reduction in LWC for large droplets compared to that of the fundamental frequency. The table demonstrates that the application of sound at 400 Hz with its 9th -harmonic gave superior results compared to the 400 Hz waveform alone, with a difference of 3.95% for small droplets and 23.16% for large droplets.\u003c/p\u003e \u003cp\u003eTo gain more insight into the dynamics at each time interval, the full 116-second duration was divided into 6 segments of 19 seconds each. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the LWC plots across each droplet diameter in the scenario of applying 400 Hz with various harmonics. The plots are arranged from (a) to (f) corresponding to their sequential occurrence, with each plot representing a 19-second segment of the original duration. The figure reveals that the curve for 400 Hz with its 9th -harmonic displayed the lowest values for the majority of the period across most plots. Similar plots were generated for sound waves applied at fundamental frequencies of 300 Hz and 500 Hz. The plots indicated that the fundamental frequency resulted in the lowest values for large droplets, while the results for the 9th -harmonic showed the lowest values for small droplets across almost the whole period. This observation is in line with the results obtained in Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. This is consistent across almost all cases, where the LWC for large\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003edroplets exhibits a decreasing trend, hinting at a potential continuation with continuous application of sound. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (a) illustrates the results of Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, showing the LWC for each droplet size in the cases that led to the highest reduction in LWC for large droplets. It is observed that the case of using the 400 Hz sound wave along with its 9th -harmonic exhibits the lowest LWC for large droplets, followed by the 300 Hz one. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (b), however, displays the LWC for the same cases over a period of 345 seconds, confirming the previous results and indicating that the results when using a 400 Hz signal with its 9th -harmonic remain the lowest for most of the duration. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (c) captures the evolution of fog droplet sizes throughout a natural dissipation process, spanning a duration of 400 seconds. The \u003cem\u003ey\u003c/em\u003e-axis of the graph is depicted on a logarithmic scale, representing the particle diameter, while the color gradient at each data point indicates the number density (normalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e) of fog droplets. It also shows a gradual rise in the count of small particles, accompanied by a corresponding decline in the count of larger particles over time. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (d) displays a similar visualization when using the 300 Hz sound waves. The observation period spans 400 seconds, during which the sound waves were only applied for the first 120 seconds. The application of sound waves at 300 Hz led to a rapid increase in the number of tiny particles, particularly evident around the midpoint of the period, as indicated by the intensified red color. This observation aligns with the previous findings where the 300 Hz case exhibited a very high number of tiny particles. It is hypothesized that this effect delays the condensation of fog droplets into larger droplets, as evidenced by comparing the final segments of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (c) and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (d). The plot for the case of applying 400 Hz sound wave with its 9th -harmonic at 112 dB is displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (e). It shows a similar visualization with no red-colored points observed, and the condensation process appears to occur more rapidly compared to the previous two cases.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe time required for fog to achieve 90% condensation, or in other words, for 10% of the original \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\:\\)\u003c/span\u003e\u003c/span\u003eof particles to remain suspended in the air was investigated for various cases involving the application of sound at the selected fundamental frequencies with different harmonics. The initial five readings of the scenario involving no sound application were averaged and employed as a baseline to determine the timing at which 90% condensation occurred. This methodology is conducted under the assumption that a nearly equivalent quantity of fog was introduced at the onset of each experiment. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the outcomes of this investigation, showcasing the time taken for each case to reach 90% condensation. Only the case of applying a sound wave of 400 Hz with its 9th -harmonic exhibits a faster attainment of 90% condensation compared to the natural dissipation (no sound case). It also has the shortest duration among all the other cases of around 318 seconds. This marks a difference of 23 seconds from the no sound case and a difference of 49 seconds from the scenario where sound waves were applied at only the fundamental frequency of 400 Hz.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTime taken to reach 90% condensation effect for different scenarios.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrequency (Hz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHarmonic Number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTime (s)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eno sound\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e341\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e358\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e364\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e379\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e383\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e367\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e318\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e408\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e388\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e389\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e348\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e419\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e368\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThese findings highlight the potential of utilizing harmonics in improving visibility. Based on the observations thus far, the primary mechanism for acoustic condensation appears to be the collision and coalescence of fog droplets, resulting in their descent and consequent reduction of LWC. However, certain frequencies increased fragmentation of large droplets, thus impairing condensation efficiency.\u003c/p\u003e \u003cp\u003eClearly, the initial investigation revealed deviations from findings in similar studies [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Prior research noted that sound waves at specific frequencies increase droplet size, facilitating growth rate comparisons. Additionally, one study indicated that application of sound waves increased the number of large particles and decreased the number of small particles [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. In this work, the median MVD, D50, and D90 either decreased or remained constant with sound application. There was an observed decrease in large particles and an increase in smaller particles due to differences in experimental setups. Unlike previous studies that used smaller chambers with sound generators positioned at the top or bottom [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], this work employed a larger, rectangular prism chamber with a centrally located speaker. The particle size analyzer was positioned at the center rear, which caused it to miss descending large droplets and led to observed discrepancies. While this does not invalidate the results or conclusions, it limits comparisons with other studies. Moreover, the study's results may differ from real-life applications. During fog events in the UAE, fog droplets range from 80 to 700 counts per cm\u0026sup3;, with a median diameter of 25 \u0026micro;m and LWC between 0.06 and 0.58 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{g}\\:{\\text{m}}^{-3}\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. In contrast, the study observed a median number concentration of 3183.05 droplets per \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{c}\\text{m}}^{3}\\)\u003c/span\u003e\u003c/span\u003e, a median diameter of 20.09 \u0026micro;m, and a LWC of 3.13 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{g}\\:{\\text{m}}^{-3}\\)\u003c/span\u003e\u003c/span\u003e for the case involving no sound application. These differences highlight variations in fog microphysics, with the latter scenario demonstrating more particle collisions due to the greater number of suspended droplets.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eExperiments were conducted within a controlled environment of a fog chamber. The study investigated how different frequencies of sound waves contribute to visibility enhancement using single and multi-frequency sound waves. The impact of harmonics was investigated for fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz. The primary focus was on the 9th -, the 11th -, and the 40th -harmonics. The findings revealed that:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eAll instances of sound application resulted in a lower median LWC, median MVD, D90 figure, peak diameter for small droplet sizes, and normalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{c}\\)\u003c/span\u003e\u003c/span\u003e for large droplets.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe results suggest that extended exposure to sound waves beyond two minutes may further reduce the LWC of fog.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe application of sound waves can fragment large droplets, with the effect varying across different combinations, potentially impairing condensation efficiency.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe primary mechanism for acoustic condensation appears to be the collision and coalescence of droplets, resulting in their descent and a consequent reduction of LWC.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eIn nearly all instances of adding harmonics, there was no enhancement observed in the parameters associated with visibility. Employing 400 Hz with its 9th -harmonic yielded a significantly enhanced effect on visibility compared to all other cases. It resulted in a reduction of 61.06% in the LWC for large droplets, showed minimal increase in LWC for smaller droplets, and achieved a 90% condensation effect in less time compared to all the other cases.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThese observations highlight the significance of investigating the impact of harmonics on improving the efficacy of the acoustic fog dissipation technique, suggesting promising avenues for further research. Future research avenues include examining the impact across a wider spectrum of frequencies and harmonics, evaluating the influence of non-harmonically related frequencies on fog agglomeration, and investigating the effects of varying SPL, waveform, duration of acoustic exposure, and signal phase.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eR.E. developed the initial problem statement, directed the work, and collaboratively designed the study with M.Y.I. who built the setup, conducted the experiments, analyzed the data, and wrote the manuscript. D.F. and N.N provided the particle size analyzer and assisted in data representation and interpretation. The authors collectively offered crucial editorial input for this article.\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe dataset utilized in this research is accessible through the corresponding author upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eFonseca, R., Francis, D., Nelli, N. \u0026amp; Cherif, C. Regional atmospheric circulation patterns driving consecutive fog events in the united arab emirates. Atmospheric Research 282, 106506 (2023).\u003c/li\u003e\n\u003cli\u003eMohan, T. et al. On the investigation of the typology of fog events in an arid environment and the link with climate patterns. Monthly Weather Review 148, 3181\u0026ndash;3202 (2020).\u003c/li\u003e\n\u003cli\u003eNelli, N. et al. First measurements of electric field variability during fog events in the united arab emirates. Journal of Arid Environments 220, 105096 (2024).\u003c/li\u003e\n\u003cli\u003eNelli, N. et al. In-situ measurements of fog microphysics: Visibility parameterization and estimation of fog droplet sedimentation velocity. Atmospheric Research 107570 (2024).\u003c/li\u003e\n\u003cli\u003eNelli, N. et al. The wind-blown sand experiment in the empty quarter desert: Roughness length and saltation characteristics. Earth and Space Science 11, e2024EA003512 (2024).\u003c/li\u003e\n\u003cli\u003eNelli, N. et al. Characterization of the atmospheric circulation near the empty quarter desert during major weather events. Frontiers in Environmental Science 10, 972380 (2022).\u003c/li\u003e\n\u003cli\u003eTemimi, M. et al. On the analysis of ground-based microwave radiometer data during fog conditions. Atmospheric Research 231, 104652 (2020).\u003c/li\u003e\n\u003cli\u003eWeinstein, A. I. Fog dispersal-a technology assessment. Journal of Aircraft 14, 38\u0026ndash;43 (1977).\u003c/li\u003e\n\u003cli\u003eFletcher, R. D. Progress in the dissipation of fog. In The Space Congress\u0026reg; Proceedings (1971).\u003c/li\u003e\n\u003cli\u003eHicks, J. R. Improving visibility during periods of supercooled fog, vol.181 (US Army Materiel Command, Cold Regions Research \u0026amp; Engineering Laboratory, 1966).\u003c/li\u003e\n\u003cli\u003eLiu, C., Tian, Z., Zhao, Y. \u0026amp; Zeng, X. Review and prospect of fog elimination technology based on acoustic condensation. In IOP Conference Series: Earth and Environmental Science, vol. 514, 032011 (IOP Publishing, 2020).\u003c/li\u003e\n\u003cli\u003eChristensen, L. S. \u0026amp; Frost, W. Fog dispersion. Tech. Rep., NASA (1980).\u003c/li\u003e\n\u003cli\u003eLiu, C., Zhao, Y., Tian, Z., Zhou, H. et al. Numerical simulation of condensation of natural fog aerosol under acoustic wave action. Aerosol and Air Quality Research 21, 200361 (2021).\u003c/li\u003e\n\u003cli\u003eChou, K., Lee, P. S. \u0026amp; Shaw, D. Aerosol agglomeration in high-intensity acoustic fields. Journal of Colloid and Interface Science 83, 335\u0026ndash;353 (1981).\u003c/li\u003e\n\u003cli\u003eLiu, C., Tian, Z., Zhao, Y. \u0026amp; Zhou, H. Experimental study on acoustic condensation fog elimination in traveling wave tube. In IOP Conference Series: Earth and Environmental Science, vol. 714, 022048 (IOP Publishing, 2021).\u003c/li\u003e\n\u003cli\u003ePatterson, H. S. \u0026amp; Cawood, W. Phenomena in a sounding tube. Nature 127, 667\u0026ndash;667 (1931).\u003c/li\u003e\n\u003cli\u003eQiu, J., Tang, L.-J., Cheng, L., Wang, G.-Q. \u0026amp; Li, F.-F. Interaction between strong sound waves and cloud droplets: Cloud chamber experiment. Applied Acoustics 176, 107891 (2021).\u003c/li\u003e\n\u003cli\u003eZhang, M. et al. Experimental study on coalescence of fog droplets in cloud chamber under low-frequency sound waves. Journal of Physics D: Applied Physics 54, 395301 (2021).\u003c/li\u003e\n\u003cli\u003eCheng, L., Jia, Y.-H., Li, F.-F. \u0026amp; Qiu, J. 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Comparing Bulk Aerosol Profiles in the Mixed Layer in Coastal Los Angeles and the Inland Empire. Bachelor\u0026rsquo;s thesis, Scripps College (2015).\u003c/li\u003e\n\u003cli\u003eSpiegel, J. K. et al. Evaluating the capabilities and uncertainties of droplet measurements for the fog droplet spectrometer (fm-100). Atmospheric Measurement Techniques 5, 2237\u0026ndash;2260 (2012).\u003c/li\u003e\n\u003cli\u003eAlivio, M. B., Bezak, N. \u0026amp; Miko\u0026scaron;, M. The size distribution metrics and kinetic energy of raindrops above and below an isolated tree canopy in urban environment. Urban Forestry \u0026amp; Urban Greening 85, 127971 (2023).\u003c/li\u003e\n\u003cli\u003eOshana, R. DSP software development techniques for embedded and real-time systems (Elsevier, 2006).\u003c/li\u003e\n\u003cli\u003eWeston, M. et al. The first characterization of fog microphysics in the united arab emirates, an arid region on the arabian peninsula. Earth and Space Science 9, e2021EA002032 (2022)\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"acoustic coalescence, fog dissipation, fog droplets, droplet agglomeration, harmonics, optimal frequency","lastPublishedDoi":"10.21203/rs.3.rs-4835869/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4835869/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This work focuses on using multi-frequency sound waves to dissipate fog. It is a promising fog-dissipation technique due to its ease of control, flexibility, environmental friendliness, and no interference with traffic flow. This study introduces a novel approach to dissipate artificial fog generated inside an experimental setup utilizing harmonically related multi-frequency acoustic waves. Fundamental frequencies of 300 Hz, 400 Hz, and 500 Hz, along with their 9th, 11th, and 40th harmonics were tested at a maintained Sound Pressure Level (SPL) of 112 dB. Many combinations were found to increase fragmentation of large droplets, which reduces the condensation efficiency. The main mechanism for acoustic condensation seems to be the collision and merging of fog droplets. Most harmonics tested did not improve agglomeration, with the notable exception of the 400 Hz paired with its 9th-harmonic. This combination resulted in a 61.06% reduction in Liquid Water Content (LWC) for large droplets and a 90% condensation effect achieved quicker than all the other cases. These findings highlight the potential of using harmonics for acoustic fog dissipation.","manuscriptTitle":"Effects of multi-frequency acoustic waves on the agglomeration of fog droplets","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-16 12:44:16","doi":"10.21203/rs.3.rs-4835869/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-16T11:28:04+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-15T17:55:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"156109401872265054036360554030353280911","date":"2025-04-13T07:15:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"257405940299013089532209157192414531828","date":"2025-04-12T18:03:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"53001812297906282651945140112043442863","date":"2025-04-11T10:14:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"34709476345260466762312568070126053689","date":"2025-04-11T09:39:25+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-11-21T07:05:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"269557500629548254287707569231993022111","date":"2024-11-13T04:03:47+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-11-11T09:18:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-11-06T05:17:27+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-08-09T03:54:28+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-08-08T04:37:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-07-31T13:18:53+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8ae6b203-4a00-445e-9870-79dae1c2f18b","owner":[],"postedDate":"September 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":36947917,"name":"Earth and environmental sciences/Hydrology"},{"id":36947918,"name":"Physical sciences/Engineering"},{"id":36947919,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2025-08-28T08:53:13+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-16 12:44:16","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4835869","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4835869","identity":"rs-4835869","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}