Aerosol deposition on face masks in an open environment during inhalation

Respiratory droplets produced during exhalation, vocalization, coughing, and sneezing are carriers of infectious viruses.^1–3 These respiratory droplets can vary in size, and their travel ranges are often classified into different categories depending on their diameters.^4,5 Large respiratory droplets (⁠ $>5 μm$⁠) tend to settle on surfaces quickly within a short distance of about $1 m$ from the source.⁶ In contrast, small respiratory droplets, also known as water aerosols (⁠ $<5 μm$⁠), can remain suspended in the air for longer periods and may travel farther than larger droplets, contributing significantly to the transmission of respiratory infections.^1,7,8 For example, when water aerosols are ejected by a forceful cough, they can be dispersed over distances of up to 4 m, which exceeds the social distancing range, within a time span of 50 s.⁹ These dispersed aerosols then remain in the air for more than an hour while airborne, potentially infecting individuals who come into contact with them.¹⁰ Viral genomes are found in aerosols of various sizes, with the greatest concentration observed in aerosols smaller than $5 μm$ instead of larger respiratory droplets.¹¹ 

Reflecting growing concerns about the transmission of such respiratory droplets, the use of masks has become a ubiquitous practice in many communities worldwide.^12–14 Masks serve as effective barriers, reducing both the travel range and total amount of dispersed respiratory droplets, thereby mitigating the risk of transmission in crowded places such as hospitals.^15,16 Studies have shown that mask-wearing can substantially decrease the distance traveled by respiratory droplets and reduce the overall dispersion of infectious particles in the environment.^17–19 For instance, the distance traveled by respiratory droplets decreased by up to 92% as a result of mask-wearing in one study, with the masks preventing the ejection of droplets produced by respiratory activities.⁹ However, despite the effectiveness of masks in mitigating direct transmission through respiratory droplets, small airborne water aerosols remain a persistent concern because they can remain afloat in the air for a long time.

Due to the continuing use of masks and the associated risks of infection by airborne aerosols, numerous studies have investigated the effectiveness of masks during inhalation. Konda et al. tested the filtration performance of masks made of various fabrics and types of cotton.²⁰ Similarly, Drewnick et al. studied the influence of material properties and particle sizes on the filtration efficiency of masks.²¹ However, these previous studies are limited in that they did not sufficiently explore aerosol aerodynamics in an open environment. Closed environment studies make it hard to replicate aerosol movement in the real world, such as the dynamics of aerosol circumvention around a mask during inhalation. In the traditional mask performance measurement method, known as particle filtration efficiency (PFE), tests are conducted in a closed pipe setup, as illustrated in Fig. 1(a). In this configuration, all aerosols are forced to flow directly toward the mask surface due to the pressure-driven environment. In the PFE method, two different quantities of aerosols are measured: those deposited on and penetrating through masks in a closed environment. Here, only the penetrating aerosols were considered hazardous. However, deposited aerosols are also known to cause infection, as infectious viruses can survive on a mask surface and potentially be inhaled.^22–26 It is evident that, from the perspective of infection prevention, aerosols that are neither deposited on a mask nor penetrate through it are the only ones that are truly safe. However, this perspective could not be explored in the closed setups of previous studies.

In this work, we explore aerosol aerodynamics in an open environment to accurately represent the features of aerosol motion in human life. We then investigate their deposition on and penetration through a mask under varying inhalation pressures. We find that a water aerosol flow near a mask surface stagnates within the range of human inhalation. Additionally, we find that the amount of deposited aerosol can be predicted by modifying existing aerodynamic theory. Using this modified theory, we identify a critical inhalation pressure at which deposited aerosols start to penetrate through a mask and suggest a new metric for evaluating mask performance.

We quantified the dynamics of aerosols that circumvent a face mask under the dynamic conditions of inhalation in an open environment using a breath simulator, as illustrated in Fig. 2(a). The breath simulator was connected to a linear stage (SL1-2020-4S, ST1 Inc.) to simulate human inhalation. The linear stage was set to gradually move back and forth, mimicking the human breath cycle. The simulated breath flow rate was measured using a velocimeter (MiniAir 20, Schiltknecht Inc.) and was found to closely approximate the human breath cycle models for both normal and heavy inhalation conditions, respectively, as plotted in Fig. 3. Note that the terms “normal inhalation” and “heavy inhalation” refer to human breathing during daily activities (⁠ $8–40 L/min$⁠)²⁷ and during exercise (⁠ $58−72 L/min$⁠),²⁸ respectively. The linear stage was operated in a 2 s inhalation cycle, which is representative of a normal respiratory rate.²⁹ The nose of mannequin head was then connected to the breath simulator to replicate nasal breathing. We used single-layer polypropylene (PP) masks with three different fabric densities of 50 g/m² (coarse PP mask), 100 g/m² (medium PP mask), and 150 g/m² (dense PP mask), as well as two representative commercial masks: a surgical mask (3M surgical, 3M Inc.) and an N95 mask (3M 9210, 3M Inc.). The detailed properties of these masks are listed in Table I. The masks were then worn tightly on a mannequin head and sealed to minimize any gaps. Gaps can vary significantly depending on factors such as face shape, mask type, and fit, affecting airflow differently across various areas of the face, particularly around the nose, cheeks, and chin. Although these gaps are a critical factor influencing aerosol flow, this study focuses on near-ideal conditions with minimal gaps in order to isolate and analyze the key mechanisms of aerosol deposition.

The aerosol deposition experiment was designed to replicate the aerosol flow that a walking individual would encounter. In this context, the aerosol jet was expelled at a speed of $1.5 m/s$⁠, which corresponds to the average walking speed of a healthy adult.³² The humidifier was positioned 1 m away from the mask to fully expose the mask and mannequin head to the aerosol jet. This distance also aligns with the social distancing guidelines during the COVID-19 pandemic, which recommended maintaining a minimum distance of 1 m or more between individuals.³³ Additionally, the average speed of water aerosols expelled during conversation between individuals is generally in the range of $1−5 m/s$ at the moment of expulsion.^34,35 The aerosol weights deposited on and penetrating through the mask were then measured using an electronic scale (GF-603A, AND Inc.) with 1 mg resolution. The pressure difference across the mask was measured using a pressure meter (FCO560, Furness Controls Inc.) in the flow rate range of $8–72 L/min$⁠.

The average diameter of the water aerosols (⁠ $dw$⁠) ejected from the humidifier was measured to be 4.5  $μ$m, which closely matches the size range of human respiratory aerosols, as shown in Fig. 4.^36,37 The size of water aerosols plays an important role in determining whether they settle on surfaces or travel a long distance while remaining airborne. We used a high-speed camera (Fastcam Mini UX50, Photron Inc.) attached to an optical microscope (BX53M, Olympus Inc.) equipped with a 50  $×$ objective lens to assess the size distribution of the water aerosols. The water aerosols suspended in the air were recorded at a frame rate of $12 000 Hz$⁠, resulting in a spatial resolution of 0.4  $μm$ per pixel, as shown in Fig. 4(a). During the recording of 4000 frames, we detected a total of 7800 water aerosols within a field of view of 512 × 96  $μm$². To determine the size distribution of these water aerosols in our recordings, we used an in-house MATLAB code built upon the imfindcircles function, which is widely used for cell detection in various contexts.^38–40  Figure 4(a) shows that the MATLAB code detected water aerosols when they were optically focused and hence measurable in size, as indicated by the red dotted circles. Moreover, our in-house MATLAB code was enhanced to prevent duplicate counting of these water aerosols in consecutive frames, ensuring an accurate size distribution analysis. Figure 4(b) shows that the water aerosol size distribution had its highest peak in the range of $2–4 μm$ and the average size of the aerosols was calculated to be $4.5 μm$⁠. This size distribution is similar to that of small respiratory droplets (⁠ $<5 μm$⁠), which can remain airborne for a long time.^1,7,8

In typical daily environments, where the ambient temperature is around 20–25 °C and the relative humidity is generally between 40% and 60%,³⁵ water aerosols evaporate at a rate that can alter their size and mass during transit. According to Fick's law of diffusion,⁴¹ the rate of evaporation is proportional to the vapor pressure difference between the water aerosol and the surrounding air. For aerosols with an average size of $4.5 μm$⁠, the evaporation time $tevap$ can be estimated as $tevap∼d02/8α(RH)$⁠,⁴² where $d0$ is the initial aerosol diameter, and $α(RH)$ is the evaporation rate constant that depends on relative humidity (RH). At 50% RH, the evaporation time for a $4.5 μm$ water aerosol is on the order of seconds, and research shows that under this condition, such aerosols can lose up to 50% of their mass within seconds of being airborne.^43,44 This indicates that, during interpersonal communication, while a portion of the aerosol's mass can evaporate before it reaches the other person's mask, a considerable fraction still can reach the mask within typical conversation distances. In our experimental setup, we maintained a controlled environment with a temperature of $20±2 °C$ and a relative humidity of $80±5%$ to minimize such evaporation effects. Under these conditions, the evaporation rate was significantly reduced due to the smaller vapor pressure difference between the aerosol and the surrounding air. To be specific, at 80% relative humidity (RH), a $4.5 μm$ aerosol would experience only about 10% mass loss over the same time and distance.⁴⁵ This allowed us to focus on the aerosol flow and deposition mechanisms themselves, which is the main focus of this study, with less influence from changes in aerosol size or mass.

A particle image velocimetry (PIV) experiment was performed to analyze the velocity field of the aerosol flow around a mask, as shown in Fig. 5. A 10 W, 532 nm continuous wave DPSS laser system (GL532T9, Shanghai Laser & Optics Century) was used in conjunction with a Powell lens (Thorlabs) to create the laser sheet and illuminate the water aerosols. To minimize 3D effects, the laser sheet was made as thin as feasible, with a thickness less than 1 mm. A high-speed camera (FASTCAM Nova S9, Photron) with a resolution of 1024  $×$ 1024 pixels and a frame rate of 6000 Hz was used to capture the aerosol flow. Here, it is worth noting that the water aerosols themselves were used as seeding particles in the PIV measurements, allowing us to directly capture their flow. While the main focus of this study is on aerosol flow, the very low Stokes number near the mask surface (⁠ $St=9.3×10−5$⁠) indicates that the aerosol flow in this region closely followed the air flow. Here, the Stokes number is known to serve as an indicator of how well the seeding particles align with the fluid flow.⁴⁶ The images were then post-processed using PIVlab,⁴⁷ a MATLAB-based open-source software, to determine the velocity field of the aerosol flow. The image pairs were analyzed using the fast Fourier transform window deformation algorithm, with a final interrogation window size of 4  $×$ 4 pixels and 50% window overlap during four-step passes, resulting in a spatial resolution of 130  $μm$ $×$ 130  $μm$⁠. The subpixel displacement was estimated through a 2  $×$ 3 Gaussian point fit. Spurious vectors were eliminated using our in-house MATLAB code built upon a median filter with 5  $×$ 5 vectors per 3 frames and universal outlier detection and replaced through interpolation. The filtered vectors were then averaged within 3  $×$ 3 vectors. The velocity fields in Figs. 2(c) and 2(d), as well as Figs. 7(c) and 7(d), were obtained by averaging the instantaneous flow fields over 12 000 frames, which corresponds to one cycle of 2 s at 6000 Hz.

The velocity fields obtained from the PIV experiment near the masks were compared under normal inhalation conditions (⁠ $8−40 L/min$⁠)²⁷ and heavy inhalation conditions (⁠ $58−72 L/min$⁠),²⁸ as shown in Figs. 2(c) and 2(d), respectively. In these figures, the colors represent the absolute value of the ratio of the vertical components to the horizontal components of the aerosol velocity (⁠ $|uy/ux|$⁠) toward the mask surface. A reduced $ux$⁠, represented by the decreased size of the vector arrows, was observed under normal inhalation conditions. This flow pattern resembles the well-known pattern of flow stagnation near a solid wall^48,49 and is more clearly shown in the magnified images of Figs. 2(c) and 2(d). This flow stagnation weakened as the inhalation strength increased under heavy inhalation conditions, under which aerosols were pulled more directly toward the mask.

To theoretically explore the relationship between the flow stagnation, inhalation pressure, and surface curvature $κ$⁠, we conducted an experiment with a curvature-controllable mask head (CC head) mounted on the breath simulator, as shown in Fig. 6. As shown in Fig. 6(b), face masks, particularly around the nose area, tend to exhibit significantly larger horizontal curvature (⁠ $κh$⁠) compared to vertical curvature (⁠ $κv$⁠). Specifically, masks like the N95, as depicted in Fig. 6(a), typically have near-zero vertical curvature.^50,51 In this regard, we simplified the analysis of the complex curvature of face masks using the CC heads [Fig. 6(c)], which allowed us to independently test the effects of horizontal and vertical curvatures. The horizontal curvature was set at 0.08 mm⁻¹ based on the measurement from a mannequin wearing an N95 mask. This CC head setup provided a simplified geometry in which both the flow stagnation and aerosol circumvention could be more clearly identified. The CC head had a 25 mm diameter to approximate the size of the human nose and mouth region.⁵² 

In addition to the aerosol deposition, the temporal evolution of the impact speeds of the aerosols was studied for different types of masks and inhalation conditions, as plotted in Fig. 10. The impact speed was calculated by averaging $ux$ over a field of view measuring 10  $×$ 10 mm² near the mask surface. The black curves are included in the plots as reference data for comparison, as the experiment was conducted without a mask. Note that the experiments were conducted under the same operating conditions in the linear stage for each plot. The beginning and end of the plot (⁠ $t=0$ s and $t=2$ s) represent the moments at which the linear stage began operating and stopped, respectively. After $t=0$ s, the impact speed rapidly increased when the water aerosols influenced by inhalation reached the mask. The arrival time was delayed with a lower $p¯$⁠, as can be seen by comparing Figs. 10(a) and 10(b). In each panel of this figure, it can also be observed that denser masks delayed the moment at which the impact speed rapidly increased. This indicates that the onset of the impact speed was delayed by the thickening of the mask. In addition, the plots show that as the mask thickened, the inhalation time span also decreased. These trends were consistently observed across all inhalation conditions.

As the ACE accounts for aerosols not deposited on the mask surface, it is a more challenging metric to use than the conventional PFE. Table II suggests that PFE measurements may underestimate the performance of surgical masks for use in an open environment. According to the ACE, $92.5 %$ of water aerosols failed to reach the surface of the surgical mask, meaning that only $7.5 %$ of the aerosols were deposited on it. In contrast, the PFE data show that, within the closed setup where $100 %$ of water aerosols were deposited, $13.0 %−53.0 %$ ended up penetrating through the mask. For the N95 mask, both the ACE and the PFE measures showed a high mask performance of over $95 %$⁠, owing to its excellent circumvention capability and penetration resistance. The ACE data also show that, compared to surgical masks, only $1.7 %$ of aerosols were deposited on the N95 mask. This is because the curvature of the N95 mask was larger than that of the surgical mask, facilitating aerosol circumvention. This suggests that geometric factors may influence mask performance in addition to filtration capabilities. Recent studies have explored various modifications to mask shapes to enhance infection prevention,^65,66 including duckbill and axe-shaped masks.⁶⁷ Thus, the use of wires or frames to keep masks in a circumvention-favorable shape is encouraged.

In this study, we have examined the aerodynamics of water aerosols and their deposition on a mask under varying inhalation pressures in an open environment. Particle image velocimetry (PIV) data showed that a water aerosol flow near a mask surface exhibits characteristics similar to a viscous flow, leading to stagnation within the range of typical human inhalation. A stagnation-based theory showed that the rate of aerosol deposition on a face mask can be described using the inhalation pressure and mask properties. A critical inhalation pressure of $p¯c=34 g/m2·s$ was also identified at which the deposited aerosols begin to penetrate the mask. Finally, we introduced a new metric, the aerosol circumvention efficiency (ACE), to estimate mask performance in an open environment, which is a better reflection of real-life conditions.

This work was supported by a KIST internal project (2E33202). S.C. also acknowledges support from the Samsung Research Funding & Incubation Center of Samsung Electronics under Project No. SRFC-IT1901-51.

The authors have no conflicts to disclose.

Y. J. Lee: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). M. W. Moon: Funding acquisition (lead); Project administration (equal); Validation (supporting); Writing – review & editing (supporting). S. Chung: Funding acquisition (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). S. J. Kim: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.