Inspiratory leakage flow fraction for surgical masks with varying gaps and filter materials Free

Appropriate fit is one of the most important aspects in ensuring a comfortable and protection-effective face mask. There has been tremendous advancement in the development of filter media with high aerosol filtration efficiency while maintaining appropriate pressure drop.^1–5 However, even the most effective filter media in a face mask cannot secure protection if the fit on the wearer's face is not appropriate. In other words, the mask works effectively only when the respiratory flow passes through it, not when the flow escapes via the gaps between the mask and skin. The mask protection efficiency is, therefore, directly correlated with the level of leakage.

A poor fit can significantly lower the overall protection efficiency of the mask. Unlike tight-fitting respirators, a disposable surgical mask often fits loosely to the wearer's face. The misfit can become even worse with incorrect wearing habits, prolonged uses, physical activities, or in certain places.^6–10 For instance, 99% of adults in Hong Kong reported wearing a mask in public; however, most large outbreaks have occurred in places where masks are often not appropriately worn or not worn at all, including bars, restaurants, gyms, etc.^11,12 Air leakages through the gaps between the mask and skin can affect the airflow and aerosol behaviors at varying degrees depending on the site and size of the gaps. Using a Schlieren optical system, Tang et al. demonstrated that a surgical mask could block the cough flow but also observed significant air leakages around the mask.¹³ Moreover, these leakages were mainly noted at the nose top where a loose fit between the mask and nose bridge often occurred.¹³ Su et al. investigated loose-fitting masks against ultrafine particles and reported similar decrease in the filtration efficiency among all loose-fitting masks tested (cloth, surgical KN95).¹⁴ Using an aerodynamic particle sizer, Cappa et al. experimentally showed that leakage flows due to imperfect sealing of a surgical mask significantly affected its efficacy in blocking expiratory particles during both talking and cough.¹⁵ Koh et al. demonstrated that a N95 respirator with a poor fit could provide less protections than a simple, well-fitted disposable mask.¹⁶ The practices of tucking in the mask or knotting the mask bands have been suggested to improve the mask–face fit, thus reducing the leak flow and improving protection efficiency.¹⁷ 

Current standard tests lack the ability to quantify the regional leakage fractions and their correlation with the mask-fit score. Even though there is leakage testing for tight-fitting respirators, leakage testing for loose-fitting masks such as disposable surgical masks has not been found.^18–24 Many factors contribute to this lack. First, the mask-fit testing apparatus was not designed for loose-fitting masks, which often gives a fit score close to zero for a surgical mask, if tested anyway. Second, even though the velocity of the leak flow from mask gaps can be measured using an anemometer, the areas of the mask–face gaps are difficult to measure. Moreover, the gaps can vary significantly depending on the physical activity, facial topology, or even the presence of facial hair. Wang et al. observed that some facial features, such as the height of the nose and the length of the chin, are key parameters that dictate the leakage extend and site from a loose-fitting face mask.²⁵ Similarly, Oestenstad et al. examined the location and shape of the leakages around a half-mask respirator and found that the facial dimension (size and shape) was an important factor in destemming the leak sites.²⁰ The mask fit can also be sex- or age-dependent. For instance, leakage is more likely from the bottom of the mask on female faces.²⁶ However, the actual leakage around the mask has been proven to be difficult to measure.¹⁵ None of the previous studies have quantified the leakage flow rate from varying regions around the face coverings.

The objective of this study is to numerically quantify the leakage fractions from surgical masks with varying gaps and filter materials in an integrated mask–face–airway model geometry. Specific aims include

1. to develop a computational model that consists of a 3D surgical mask, face, upper airway, and slit-like gaps of different sizes and at various sites around the mask;

2. to measure the resistance of surgical masks and determine the porous properties in the computational model;

3. to characterize the inspiratory flow dynamics and quantify leak fractions at the nose top, side, bottom, and all-around compared to those under perfect mask-fit conditions;

4. to evaluate the effects of mask resistance on gap leak fractions; and

5. to develop a correlation for the leakage fractions as a function of the gap area for two surgical masks.

The results of this study will provide insights into the actual performance that can be expected from a face covering (such as a surgical mask), which remains largely unexplored but can be highly relevant to the transmission control of respiratory infectious diseases.

The computational model consisted of four parts, with each part being a separate volume [Fig. 1(a)]. These include the ambient air, a three-layer surgical mask, the airspace between the mask and face, and an upper airway model consisting of the nose, mouth, pharynx, and larynx. The mask geometry was developed using the graphics software Blender (Blender Foundation, Amsterdam, Netherlands) based on images of a disposable three-ply surgical mask on a subject's face taken at different angles. Mask shape details, such as the three pleats (or folds) on the front when tucked in to fit the face contour, were retained. The mask covered the lower face. When there was no leak, the mask–face interface was a close-loop strip that snuggly bordered with the nose top, two cheeks, and the chin. The face outside the loop was exposed to the environment. The face airway model was developed in our previous studies based on MRI scans of a 53-year-old male subject.^27–30 To connect the mask and face-airway, the geometrical volume of the mask was extended backward and intersected with the human face. By removing the components of the mask that fell behind the face, a seamless seal between the mask and face was obtained [Fig. 1(a)]. To perform numerical analyses, a computational mesh was generated [Fig. 1(b)] with sufficiently fine mesh size [Fig. 1(c)]. The mask was modeled as a porous material with the resistance obtained from measurements using a TSI mask tester [Fig. 1(d)]. Details of experimental and numerical methods were described in more detail in Secs. II B and II C.

To quantitatively evaluate the leakages from surgical masks, the gaps between the mask and face should be considered of different sizes at various locations of the mask–face interface. Following our observation and other studies,^19,25 individual volumes were created along the mask–face interface, as denoted by the bounding boxes in Fig. 2(a). Each volume represented a gap when specified as air and represented part of a mask when specified as a porous media.

There were eight gaps on the nose top, with four on the right side (i.e., R1–4) and four on the left (L1–4), as illustrated in Fig. 2(b). To study the effects of small gaps, the gap R1 was further divided into four parts (i.e., A, B, C, and D) with A (green color) touching the face and D touching the mask front [Fig. 2(b)]. Four combinations, A, AB, ABC, and ABCD, were simulated that represented the progressively worsening scenarios of the mask fit.

To simulate large gaps, both individual gaps (R1–R4–4, L1–L4) and their combinations (R1–L1, R12–L12, R123–L123, and R1234–L1234) were computed. Likewise, there are three gaps (i.e., upper, middle, and lower) on both the right and left cheeks and seven gaps in the chin (middle, three in the right, and three in the left), as illustrated in Fig. 2(c). Model validation was also conducted by comparing the measured and predicted leak flow velocities from the left middle check [Figs. 2(d)–2(f)], which will be detailed in later sections.

The area of each gap is shown in Fig. 3, with the total gap area at each side of the mask presented in Fig. 3(a), the areas of individual gaps on the nose top in Fig. 3(b), on the right and left cheeks in Fig. 3(c), and on the chin in Fig. 3(d).

Two types of disposable three-layer surgical masks were tested using TSI Automated Filter Tester 8130A (TSI, Shoreview, MN), as shown in Fig. 1(d). The fixture that held the mask is also shown in the right panel in Fig. 1(d), which had a circular hole with a diameter of 7.62 cm (or 3 in.) and an area of 45.6 cm². The test flow rate was specified at 85 L/min. The measured pressure drop was 14.6 mmH₂O for Mask 1 and 4.86 mmH₂O for Mask 2. The filtration efficiency was 90.5% and 81.5%, respectively.

When there was no leak, there were three fluid bodies: the ambient air, the mask, and the airspace behind the mask that included the upper airway [Fig. 1(a)]. The mask was modeled as a porous media in Ansys Fluent under cell zone conditions. The resistance of the masks was computed from Darcy's law using the standard mask-testing flow rate of 85 l/min and the pressure drop measured using TSI 8130A, as follows:^31,32

Based on a TSI-test flow rate of 85 L/min, a sampling area A = 45.6 cm², a dynamic viscosity μ = 1.825 × 10⁻⁵kg/m s, and an overall mask thickness L = 2.3 mm, the mask resistance was calculated as 1.120 × 10¹⁰ 1/m² and 3.727 × 10⁹ for the two masks with a TSI-tested pressure drop of 14.6 and 4.86 mmH₂O, respectively.

To study the leak flows from a gap, the volume that occupied the gap was switched from the porous media to air under the “cell zone conditions” in Ansys Fluent. Note that both the mask front and the mask–face interface were the two parts of the mask; there would be airflows passing through both parts even without any leak. Opening a gap at the mask–face interface would divert a large fraction of inhaled airflow from the mask to the gap due to its low resistance until the flow resistance through the gap became equivalent to the flow resistance through the mask.

In this study, quiet breathing was simulated with a flow rate of 15 l/min.³³ The airflow was assumed isothermal (20 °C) and incompressible (ρ = 1.204 kg/m³). The boundary conditions included a zero pressure at the far-field of the ambient airspace and a negative flow rate at the trachea opening to simulate the inspiratory flows. The standard k-ω turbulence model with low Reynolds number (LRN) corrections was used in the airflow zone to resolve the multiple flow regimes that might occur in the ambient airspace and respiratory tract, while laminar zone was activated in the porous media to disable the turbulence production.^34,35 The LRN k-ω turbulence model has been demonstrated to accurately simulate the velocity and pressure for both turbulent and transitional flows.³⁶ Furthermore, it also yields a reliable approximation to laminar flows when the turbulent viscosity decreases to zero.^34,37 Further details regarding this turbulence model are referred to Wilcox.³⁴ 

In this study, the flow dynamics were visualized in several ways, including vorticity, helicity, and Q-criterion. Briefly, vorticity is the curl of the velocity and depicts the fluid's spinning motion near certain points. Helicity is the inner product of the velocity and measures the knottiness and/or linkage of vortex lines. Q-criterion is defined as

where S denotes the strain rate and Ω denotes the vorticity tensor. Therefore, Q > 0 means the dominance of the vorticity, and Q < 0 means the dominance of the strain rate or viscous stress.³⁸ 

Before the quantification of gap-induced leakage, two points should be clarified: (1) only flows that pass through the gap were termed as leakage, while flows that pass through the mask (front or interface) were termed filtered flow and (2) even if the gap was replaced by the mask, there was still airflow passing through it, only with a much lower flow rate. Therefore, the flow rates through the blocks along the mask–face interface were quantified, even when they were not specified as gaps. In doing so, the leakage enhancement ratio could be quantified by comparing the flow rates before and after opening the gap. To facilitate the comparison of gap-leakages among different cases, the leakage was qualified as either the leakage fraction (normalized by the inhalation flow rate, %) or leakage intensity (leakage fraction per unit area, %/cm²). The least squares method was used to develop the correlations.

Ansys Fluent 21 (Canonsburg, PA) was used to solve the flow governing equations. Ansys ICEMCFD was used to generate the computational mesh. Multi-scale meshes were used to resolve the ambient air (coarse), mask (ultrafine fine), face (normal), and airway (fine), in order to achieve both prediction accuracy and numerical efficiency [Fig. 1(b), upper panel].³⁹ To consider the boundary flow effect, body-fitted prismatic cells were generated in the near-wall regions on both the face and airway [Fig. 1(b), lower panel]. Mesh sensitivity analysis was conducted by comparing the leakage fractions at Gap A of six mesh sizes (i.e., 1, 1.5, 2.0, 2.6, 3.2, and 4.0 × 10⁶), where the grid-independent result was attained at 3.2 × 10⁶ [Fig. 1(c)].

To validate the computational model, the leak flow velocities were measured for Mask 1 from a gap at the left middle check of a life-size head manikin [Fig. 2(d)]. Tapes were used applied along the mask–face interface to ensure no leak except the left middle check. A rectangular duct of 17 × 6.5 mm² was inserted between the mask and skin at the left middle cheek to create a gap of a known size. The head manikin was connected to a Robinair vacuum (Warren, MI) that generated a steady inhalation flow rate of 15 l/min. A TSI 9565 VelociCalc ventilation meter (Shoreview, MN) was used to measure the velocity at the gap.^40,41 Measurements were taken five times to obtain the average and its standard deviation and were compared to complementary CFD predictions.

The CFD predicted flow dynamics from a gap at the left middle check for Mask 1 is shown in Fig. 2(e), with the front and lateral views. The gap flow velocity was sampled right at the gap [black cross in Fig. 2(e)]. A good agreement was achieved between the measured and predicted flow velocities from the gap [Fig. 2(e)], indicating that the computational model hereof adequately captured the mask flow dynamics.

The inhalation airflow dynamics with perfect mask fit (i.e., no gap, no leak) is shown in Fig. 4 in terms of different manifestations. Figure 4(a) shows the pressure distribution in the mid-plane. The total pressure drop between the ambient (zero gauge pressure) and the throat (vacuum pressure) was around 16 Pa. There are two major sites of abrupt pressure drops, with one across the mask (due to the resistance of the porous media) and the one in the throat (due to the flow-limiting glottis). A noticeable pressure drop is also observed between the mask and mouth. This, however, is because of a wall at the mouth opening (close mouth); no inspiratory flow enters the mouth, and only nose breathing has been considered in this study [Fig. 4(a)].

The pressure gradient in the midplane is shown in Fig. 4(b). As expected from Fig. 4(a), large gradients are observed across the mask and in the throat. In addition, large gradients are also noted in the nostril and the nasal valve, reflecting the contra vena effect before the air enters the nose and the flow-limiting effect of the nasal valve. A careful examination of the mask pressure gradient in Fig. 4(b) also reveals a heterogeneous pattern within the mask, which is due to the flow heterogeneity through the mask for a given mask-filter resistance (standard TSI test: 146 pa). This heterogeneity is also evident in Fig. 4(a), where more concentrated iso-pressure contour lines are spotted in the corners of the mask pleats than in other regions of the mask.

The streamlines around the mask are shown in Fig. 4(c) in both the 2D mid-plane and 3D space. Multi-scale airflow speeds around the mask are captured, with only around 0.02 m/s across the mask while 1.5 m/s in the nostril. With a color scale of 0–0.25 m/s, the airflow within the mask–face space shows a highly heterogeneous velocity distribution, as well as a quick increase in magnitude from the mask to the nose [Fig. 4(c), first panel]. With no gap at the mask–face interface and, therefore, no obvious preferential ventilation through specific regions of the mask, all inspiratory streamlines exhibit blue color before the mask (low velocities) and blue-to-red colors after the mask. Another salient feature in Fig. 4(c) (second and third panels) is the distorted streamlines across the mask, indicating that the computational model hereof has captured the effects of mask morphology on airflows.

The coherent flow structures are shown in Fig. 4(d) in terms of the iso-surfaces of the Q-criterion, which vividly captured the morphological details of the surgical mask. The iso-surfaces of flow velocities are shown in Fig. 4(e). At 20 mm/s (0.02 m/s), the flow iso-surface resembles the mask shape; at a lower velocity (8 mm/s), we observed airflows just ahead of the mask and around the mask–face interface; at an even lower velocity (2 mm//s), we saw a hemisphere in front of the face, which can be considered as the inhalation zone when airborne aerosols/organisms are of concern.

Figure 5 shows the flow dynamics when there is an enlarging gap on the right top nose (i.e., A, AB, ABC, and ABCD) in terms of streamline, helicity, and pressure gradient, respectively. More airflow diverts to the gap as the gap becomes larger, as demonstrated by the increasingly red color of the streamlines around the nose [Fig. 5(a), upper panel]. The inertia of these streamlines also significantly increases, with no apparent flow recirculation in A, to an intensifying recirculation in AB, ABC, and ABCD, as illustrated by both the streamlines (upper panel) and helicity (middle panel) in Figs. 5(a)–5(d). Considering the pressure gradient [lower panel in Figs. 5(a)–5(d)], two variations are noted with a growing gap: (1) a decrease in $∇P$ across the mask and (2) an increase in $∇P$ at the nostril. The former is due to the decrease in flow through the mask as more airflow diverts to the gap, while the latter is presumably caused by the increasing level of contra vena effect before entering the nostril.

The leakage fractions from the enlarging gaps, as well as the flow partitions among the mask–face interface and mask front, are shown in Fig. 6. The inhalation flow rate is 15 l/min, and the mask has a resistance of 146 Pa under TSI standard test. Switching from the porous media to air in Gap A increased the flow partition 55 times [i.e., from 0.17% to 9.3%, Fig. 6(a)]. The leakage fraction per unit gap area was 18.2%/cm² (i.e., 9.3%/0.511 cm²), which was defined as the leakage intensity (LI) hereof. Increasing the gap (from A to AB, ABC, and ABCD) further increased the gap leakage from 9.3% to 17.4%, 24.8%, and 32.4% [Figs. 6(a)–6(d)]. However, the leak fraction from the individual gap decreased somewhat, i.e., from 9.3% to 7.4% through the A gap. The leak intensity also decreased slightly as the gap grew [i.e., LI from 18.2%/cm², to 17.1%/cm², 16.0%/cm², and 15.7%/cm², Figs. 6(a)–6(d)]. Taking the four cases together, switching a filter to a gap at the nose top increased the leakage 50–60 times than otherwise. A gap of 2.07 cm² (vs a mask surface area of 115 cm²) led to 32.4% inhalation flow passing through the gap, with 55.7% passing through the mask front and 11.9% through the interface around the mask (Table I).

The inhalation flow distribution was also visualized as the subsurface of velocity (8 mm/s) in Figs. 6(a)–6(d) for the growing gap. In Fig. 6(a), there is an appreciable portion of flow passing through the mask front (74%). A significantly higher portion of airflow occurs at the left nose top than any other interfacial region around the mask. A larger gap enhanced the flow portion at the nose top; meanwhile, it also reduced the flow portion through the mask front. It is also noted that higher flow speeds occur around the three pleats of the mask [Fig. 6(d)], indicating an important effect of the mask topology on airflow dynamics around the mask.

The effects of the mask resistance on flow partition are shown in Fig. 7 by comparing a new mask (Mask 2) with a standard TSI resistance of 48.6 Pa (green bar) to the control case (Mask 1: 146 Pa, hollow bar). Due to better breathability, more airflow passes through the mask filtration in Mask 2, which includes both the mask front and the mask interfacing with the face. On the other hand, about one-third less airflow passes through the gaps in Mask 2 than in Mask 1. For instance, the gap leak fraction between Mask 1 and 2 is 5.6% vs 9.3% through A (39% reduction), and 21.5% vs 32.4% through ABCD (33% reduction) (Table I).

The responses of the two masks to an enlarging gap were also different. Even though the filtered flow decreases with the gap area in both masks, this decrease is quicker in Mask 1. Conversely, the gap-leak increases faster with gap area in Mask 1 (i.e., from 9.3% to 50.4% in A to ABCD) than in Mask 2 (i.e., from 5.6% to 35.2%), as shown in both Figs. 7(a)–7(d) and Table I. Both observations can be explained by the fact that the gap-flow resistance decreases faster with gap area in Mask 1, thereby diverting more inhaled air to the growing gaps that should pass through the mask filtration otherwise.

A comparison of inhalation flows through gaps at different locations of Mask 1 is shown in Fig. 8. The area is also listed for the gap at the nose top (R1_L1: 4.27 cm²), left cheek (middle: 3.48 cm²), chin (middle: 2.96 cm²), as well as with all gaps open (33.0 cm²). Note that a larger velocity scale (0–0.5 m/s) was used herein than that in Fig. 5 (0–0.25 m/s) in order to better visualize the differences among cases. Significantly different flow patterns were observed around the mask, especially in the airspace between the mask and face. As expected, high-speed airflows were inhaled through the gaps at the nose bridge, left cheek, and chin [Figs. 8(a)–8(c)], leading to strong recirculation behind the mask. By contrast, the airflow speed was much lower when all gaps were open, even though 96.5% air was inhaled through the gaps [Fig. 8(d) and Table I). As a result, no apparent recirculation was observed behind the mask. It is emphasized that only 3.5% inhalation was filtered by the mask in this case, leaving a strong warning that a misfit mask can provide very limited protection to the wearer.

The aerodynamic differences among the cases are further compared in Fig. 9 in terms of $∇P$⁠, Q-criterion, vorticity, and velocity iso-surfaces. Considering $∇P$⁠, a clear difference was seen in Fig. 9(a) (R1_L1) at the nose bridge and in Fig. 9(c) at the chin. In the case of all gaps open [Fig. 9(d)], the $∇P$ across the mask was too small to be visible, which was somewhat expected considering that there was only 3.5% inhaled air passed through the mask.

Considering the coherent flow structures (second and third columns), common patterns around the mask were predicted among the four cases. For instance, there were vortex filaments outside the mask that resembled the mask pleats in both Q-criterion and vorticity. Unique patterns were also predicted for each of the four leak conditions. With gaps at the nose top [Figs. 9(a) and 9(d)], we observed vortex filaments of Q-criterion and vortex-patches of vorticity on the eyebrows and eyes. In Figs. 9(b) and 9(d), the gap at the left cheek was coincident with a vorticity patch thereof. Similarly, in Fig. 9(c) and 9(d), the gap in the middle of the chin was coincident with a vorticity bubble thereof. Compared to local gaps around the mask in Figs. 9(a)–9(c), opening all gaps substantially decreased the intensity of coherent structures outside the mask in both Q-criterion and vorticity [Fig. 9(d)].

Similar patterns were also observed in the velocity iso-surfaces (20 mm/s), with a clear velocity bubble at the nose bridge, left cheek, and chin in Figs. 9(a)–9(c), respectively. Plotting the velocity iso-surfaces at 2 mm/s reveals remarkable differences between cases with and without nose top gaps. With a good fit at the nose top, the inhalation flow was mostly from the ambient air below the eyes [Figs. 9(b) and 9(c)]. By contrast, a gap at the nose bridge, which is the most frequent misfit when wearing a surgical mask, significantly lifted the inhalation zone [Figs. 9(a) and 9(d)], and meanwhile increased the chances of eye deposition of ambient aerosols.

The flow partition among the gaps, mask front, and mask–face interface is shown in Fig. 10 for two masks (Mask 1: 146 Pa vs Mask 2: 48.6 pa) under different leak conditions. For the gap R1, the flow partitions through the four parts (A–D) were calculated [Fig. 10(a)]. The same data are also listed in Table I. With a gap area of 4.27 cm² at the nose bridge (R1_L1, Table I), the leakage fraction was predicted to be 59.3% for Mask 1 and 41.7% for Mask 2. By comparison, a gap area of 3.48 cm² at the left cheek led to similar leakage factions, i.e., 60.4% for Mask 1 and 42.8% for Mask 2, suggesting that the leakage fraction may also depend on the site of the leakage [Side_L_M, Table I and Fig. 10(b)].

Considering the mask resistance (R) effects, for a given gap, the leakage fraction is higher for the high-R mask (Mask 1) than the low-R mask (Mask 2), regardless of the gap site and area [Figs. 10(a)–10(d)]. This leaves a smaller fraction of inhaled air being filtered by the high-R mask. For both masks, opening all gaps around the mask (with a total gap area of 33.0 cm²) led to a leakage fraction of 96.5%, with only 3.5% being filtered by the mask. Note that in this study, the mask filtration included both the mask front and the mask interfacing with the face. For comparison purposes, the flow partition between the mask front (∼82%) and interface (18%) is also presented in Fig. 10(e) and Table I.

The predicted leakage fractions for all combination of gaps were plotted in Fig. 11(a), with the blue symbols for Mask 1 and brown symbols for Mask 2. A correlation between the leakage fraction vs gap area was developed for Mask 1 and 2, separately, with a R-squared value of 96.4% and 97.9%, respectively, and is shown in Eqs. (3) and (4),

where L.F. is the leakage fraction (%) and A is the gap area (cm²). The same data and correlations were replotted in Fig. 11(b) in a semi-algorithm (x-coordinate). A good fit was also obtained between the predicted data points and correlation for both masks.

Using the experiment-based mask resistances, we conducted a numerical quantification of the leakages from slit-like gaps of varying sizes and at different sites around surgical masks. It is observed that for a typical 3-ply surgical mask (TSI-measured resistance: 14.6 mmH₂O) with a typical misfit (a nose top gap of 4.2 cm²), the leakage fraction was around 60%. This leakage is alarmingly high and causes cautions in health risk assessment with face coverings. Only the airflow passing through the mask will be filtered to capture the bacteria and viruses in the airflow. Thus, the actual mask protection efficiency can be significantly lower than the filtration efficiency of the filter media that the mask was made of. For instance, an N95 mask means a 95% filtration efficiency for aerosols 0.3 μm and above that was measured using a standardized mask tester (e.g., TSI 8130A) under a flow rate of 85 L/min. In other words, N95 can only have 95% filtration deficiency when there is no leakage. A poorly fitted N95 will lead to leakage flows, which can perform poorly in protecting the wearer because the mask only filters the airflow passing through it. The filtration efficiency of a surgical mask often ranges from 80% to 95%, as measured in this and other studies.^42,43 A leakage fraction of 60% leaves only 40% of inhaled air being filtered and, thus, can considerably decrease the mask's protection efficiency to the wearer. However, we also wish to warn against a simple interpretation of a 60% increase in exposure risk to the wearer for two reasons. First, even with gap-leakages, a misfitted mask can still lower the velocities of inhaled air, thereby delaying the viral transmission from an infected host. Second, a loose-fitting surgical mask also reduces the viral emission from the host by filtering out exhaled virus and lowering exhaled air velocities, despite a compromised efficiency.

The large variations in mask leakage observed in this study may reconcile, at least partially, the debates on whether mask-wearing protects us from viral infection. In the past two years, there have been seemingly contradicting reports of mask effectiveness on COVID control from large-scale randomized studies, ranging from highly effective to not effective at all.^{11,17,44–46} As a public health measure, the effectiveness of mask-wearing in migrating viral transmission at a population scale can be affected by many factors, but mainly by the level of adherence to mask-wearing rules (i.e., all the time when close to a viral source and with a good fit). Despite that 99% of adults in Hong Kong reported wearing mask in public, large outbreaks still occurred in places such as bars, restaurants, or gyms, where mask-wearing rules were difficult to adhere too strictly.^11,12 Moreover, SARS-CoV-2 and its mutants have been proven to be highly transmissible, and inter-personal infection can occur within a short time window.^47,48 The observation of a 60% in led flow escaping the filtration of the most used surgical mask may partially explain the large variations in these large-scale mask-protection results, where adherence to mask-wearing rules (when and how) could have significantly varied.

Considering that the mask fit may vary significantly, we have considered slit-like gaps ranging from very small (0.5 cm²) to very large (33.0 cm², with all gaps open) and at different locations around the mask. Only a gap of 0.5 cm² gap area (0.4% of the mask area) at the nose top area can cause 9% leakage. Increasing the gap magnifies the leakage fraction; however, it does not follow a linear profile, but rather an asymptotic profile. This is expected considering that the maximal leakage fraction can only be 100%. The leakage intensity (i.e., leakage fraction per unit area) appeared relatively insensitive to the gap location.

The effect of mask resistance on leakages were evaluated by comparing two masks, one with a TSI-measured resistance of 14.6 cmH₂O (Mask 1) and the other 4.86 cmH₂O (Mask 2). For a given gap, the leakage fraction is 30%–40% lower in Mask 2 than Mask 1 with 40% for the smallest gap (0.5 cm²) and 30% for the largest (33.0 cm²), as shown in Table I.

Airflow will naturally go wherever it has the least resistance. The airflow that attempts to cross a high-resistance filter is more predisposed to divert to the gap that has a much lower resistance. Take gap A as an example, the flow rate through the gap is 60 times higher than when the gap was occupied by the mask. However, as more air is diverted toward the gap, the flow speed rises, and the flow resistance increases until a balance is reached between flow resistances in the gap and across the mask.

The correlations of leakage fraction for surgical masks developed in this study can provide a practical estimation of the leakage of the surgical masks. We know that face mask wearing can provide us protections, but we may not realize how large the leakage can be from a misfit mask and how this leakage compromises the mask protection. By establishing a quantification method for leakage flows, a more accurate evaluation of the actual PPE protection efficiency can be obtained. This quantification will offer an additional dimension when selecting the right mask from many options. Additionally, the mask regional leakage estimation will provide practical information for mask design improvement. The results of this study can serve as a reminder to the public to wear the mask properly in high-risk regions to obtain the designed mask protection.

In summary, the leakages from varying gaps around surgical masks were numerically assessed in a physiologically realistic mask–face-airway model implemented using measured properties of the surgical masks. A better understanding of the factors involved in determining the dosimetry of ambient aerosols on the face and in the respiratory tract was obtained. Specific findings are

1. A small gap could lead to a high leakage: i.e., a 0.5-cm² gap caused 9% leakage.

2. The leakage fraction increased asymptotically with the gap area and was relatively insensitive to the gap location.

3. For a surgical mask, a 60% leakage fraction was expected during regular use, i.e., with a gap area of 4.3 cm² at the nose top.

4. For a given gap, the leakage was lower for the mask with lower resistance. For all gaps considered, the leakage fraction was 30%–40% lower for the 4.86-mmH₂O mask than the 14.6-mmH₂O mask.

5. Correlations were developed for the leakage fraction vs gap area for two surgical masks.

This study was partially supported by the Advanced Functional Fabrics of America (No. AFFOA CARES ACT 119452). We thank Professor Ramaswamy Nagarajan for insightful discussions. Ms. Claire Lepont is gratefully acknowledged for the project management.

The authors have no conflicts to disclose.

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