## Introduction

It has been well established that diseases such as SARS-CoV-2 (COVID-19) are spread by airborne transmission, as respiratory expirations such as talking, coughing and sneezing produce small, virus-laden droplets [1, 2]. The airborne transmission of infectious particles is one of two primary methods for spreading infectious diseases (the other being Fomite transmission) [3]. The particles present in respiratory clouds generated by coughing are produced by the atomization of secretions that line the respiratory system as air travels from the lungs to the mouth, as well as the atomization of saliva at the mouth [4]. In particular, the particles present in respiratory clouds have been shown to originate in three primary locations: small droplets (<1–5 µm) originate via bronchiolar film rupture, 5–20 µm droplets via a laryngeal mode and droplets >50 µm in the oral cavity [5, 6]. It is the atomization of particles at the site of infection that causes droplets to contain infectious particles, and so the distribution of contagious particles in an expiratory event is dependent on the site of infection. Significant research is still required into the dispersion of droplets via respiratory expirations, due to a lack of universal agreement as to particulate sizes [7]. Small particles of $${{{{{{{\mathcal{O}}}}}}}}$$(1 µm) in the expiratory flow are quick to evaporate and aerosolize and these droplet nuclei remain suspended in continuum with the expiratory flow, becoming more buoyant as large particles fall from the cloud [8]. These small particles can stay airborne for hours, with the COVID-19 virus specifically having a half-life of more than an hour [9]. Furthermore, the extent of dispersion of these suspended aerosolized droplets depends on the fluid dynamics of the expiratory event and this has been previously studied both via experiment [10,11,12] and via computational fluid dynamics (CFD) [13, 14]. When an expiratory event such as a cough or sneeze occurs, the high-velocity flow from the mouth generates vortex ring structures [5, 15], with the size and strength of the vortex ring dependent on the expulsion process. As such, the human cough is often modeled as an impulsively started jet. In particular, it can be characterized as a two-stage jet consisting of a starting-jet stage (SJS) and an interrupted-jet stage (IJS): the streamwise penetration distance of a cough in the SJS scales with t1/2 and with t1/4 in the IJS [12].

In actuality, however, the human cough is normally characterized as a multi-pulsed event, referred to as cough epochs, with each pulse lasting ~0.3 s [10, 12]. It has been shown that the flow rate profiles of these multi-pulsed events are the same as single-pulsed events, with subsequent pulses having lower amplitudes than the original pulse [10]. Furthermore, regular speech can form a train of pulsatile jets, as different speech patterns in succession will continually produce different strength jets [16]. In contrast to the single impulsively started jet, this multi-pulsed jet results in the formation of multiple viscous vortex rings [12, 17]. Entrainment considerably increases for pulsing jet flow [18], and the penetration distance of a pulsed jet has been shown to be greater than that of a steady jet [19]. The circulation motion of the generated vortex rings also serve to enhance the transport of the small airborne particles suspended within the flow field [17]. In the case of multi-pulsed events, the volume required for such expirations originates deeper in the lungs. As such, if the site of infection is also deep in the lungs (the site where very small droplets originate), then the pulsatile flow can also potentially expose more contagions to the environment [5].

To reduce the dispersion of infectious aerosol and transmission of airborne infectious diseases, the United States’ Centers for Disease Control and Prevention (CDC) and the World Health Organization (WHO) recommend the use of face masks [20, 21]. The effectiveness of wearing a face mask to reduce disease transmission has been well established in literature [17, 22, 23]. In particular, it has been shown that particle (also referred to as droplet) dispersion in the original expiratory direction (i.e., directly through the mask) is significantly reduced [24, 25]. A number of studies have also investigated the filtration efficiency of masks under different conditions (see for example [26,27,28]). Whilst flow is reduced through the mask wall, studies have identified significant flow leakage at the side and top edges of masks (including N95, surgical, cloth, homemade). This leakage has been studied experimentally using smoke flow visualization [29,30,31], Schlieren imaging [32] and CFD [23].

This work therefore has a two-fold objective: (1) To quantify leakage flow fields around a surgical mask for the first time, and (2) To assess the influence of pulsatility on the leakage volume expelled around a surgical mask (i.e., the effectiveness of the mask). Three different flow rate conditions are considered in this work to quantify the influence of multiple pulses on the dynamics of aerosol dispersion: a single-pulsed cough (S1), a double-pulsed cough (D1) wherein both pulses match S1, and a single-pulsed cough (S2) wherein the area under the flow rate curve matches that of D1. A custom-built pulsatile expiratory flow simulator is used to generate the expiratory events, and flow visualization and particle image velocimetry are used to study the flow fields. In this study, the pulsatile expiratory flow simulator with no mask is first validated against literature. Quantitative flow field measurements are then used to identify and classify the leakage flow velocity profiles at the top and sides of a surgical mask. Lastly, the effect of pulsatility on the effectiveness of the surgical mask is examined by determining the leakage flow penetration distance and the normalized leakage volume expelled for each S1, D1 and S2.

## Methods

### Experimental setup

A custom-built pulsatile expiratory flow simulator (shown in Fig. 1a) in the Applied Fluids Research Group at Auburn University generates multi-pulsed coughing events. A computer-controlled solenoid valve (ASCO General Service Solenoid Valve, 8263H002, St. Louis, Missouri, USA) is used to provide the desired flow rates by controlling a pressurized air source at the wall. Since solenoid valves produce square-wave like flow rate profiles [35], an in-line pressure relief chamber is used to produce a more realistic (smoother) expiratory flow rate profile. An in-line gas flowmeter (Kelly Pneumatics Gas Flow Sensor, KPI-DMFS-1, Newport Beach, California, USA) is used to measure the flow rate at a sampling rate of 500 Hz, providing accurate mass flow rate readings. The outlet of the simulator is a pipe with length, L = 121.9 cm, and diameter, D = 2.54 cm, resulting in a pipe with L/D ≈ 48. A mannequin face is placed at the end of the pipe with a corresponding 2.54 cm outlet to fit the pipe, allowing us to place the surgical mask on the mannequin’s face. The mask used in this study is a commonly available surgical mask (Bigox 3-Ply non-medical). The surgical mask is a 17 cm × 9.5 cm rectangle, as shown in Fig. 1b. This mask has a metal nose insert to fit the face, which is fit to the mannequin before each run. Elastic strings attach it around the mannequin’s ears. A marker on the mannequin’s nose is used as a guide to place the mask in the same location for each experiment. Furthermore, to test the sensitivity of the mask placement on the mannequin, the mask is placed at 1.27 cm (0.5D) and 2.54 cm (1D) below the base-line mask placement (see Fig. 1c). To prevent any ambient air currents from the room’s ventilation system from interfering with the measured flow, all experiments were conducted in an ~3 m × 3 m × 3 m enclosure.

### Flow conditions

To study the effects of pulsatility, three different flow conditions are tested in this study as illustrated in Fig. 1d: a single-pulsed cough (S1), a double-pulsed cough (D1) wherein both pulses match S1, and a single-pulsed cough (S2) wherein the area under the flow rate curve (Cough Expired Volume (CEV)) matches that of D1. By controlling the pressure of the air source and the pulse width of the solenoid valve, the desired Cough Peak Flow Rates (CPFR) and pulsed flow rate durations are obtained. For single-pulsed coughs (S1), this corresponds to a flow duration of T1 ≈ 0.225 s. The CPFR is ≈ 4.5 L/s; this is consistent with previously observed values in human coughing flow profiles [10]. It should be noted the CEV from the coughing simulator is expected to be higher than for a human cough. The single-pulse flow rate curve generated by the simulator is approximately symmetric, whereas the flow rate profile of a human cough has been previously approximated as a combination of gamma-probability-distribution functions, capturing the asymmetry of a human cough [10]. Similarly, the double-pulsed cough (D1) flow rate is obtained by adjusting the control inputs; it must be noted that this generates two pulses of equal amplitude and duration; future studies will examine the effects of multi-pulsed events with decreasing amplitude to represent a more realistic human cough [10]. The three flow rate profiles (S1, D1, S2) are repeated both with and without a mask, 3–5 times per experiment. The average standard deviation through the coughing event of these measured flow rate profiles is respectively: 0.12 LPS, 0.29 LPS and 0.15 LPS. For the mask placement sensitivity study (placement as shown in Fig. 1c), two additional experiments are conducted for the S1 case referred to as S1a and S1b (each of which were also repeated 3 times). The flow leakage around the mask is studied using two techniques, flow visualization and particle image velocimetry (PIV), which are discussed in the following sections.

### Flow field assessment

#### Flow visualization

Flow visualization is initially used to examine the effect of pulsatility on the surgical mask configuration, both qualitatively and by measuring the flow penetration distance. Smoke generated by an Antari Z-800II Fog Machine (Taoyuan City, Taiwan) is used to visualize the flow. A luer-lock placed at the beginning (inlet) of the outlet pipe allows us to pre-fill the pipe with smoke for each experiment such that it is expelled during the expiratory event. The luer-lock is closed after filling and remains closed for each coughing event. A Nikon Z50 mirrorless camera is used to image the flow at 11 fps. A variable focal length lens was used with an exposure time of 1/1250 seconds at an aperture of f/1.8. The exposure time was chosen to minimize any blurring in the images. Flow visualization images are taken in Plane A and Plane B as defined in Fig. 1e, f. Surgical mask images taken in Plane A are taken with a focal length of 18 mm and Plane B with a focal length of 24 mm. No mask images in Plane A are also taken with a focal length of 24 mm. These planes are illuminated using a Laserglow Technologies 532 nm continuous laser (Toronto, Canada); the laser beam is converted to a light sheet via two cylindrical lenses.

#### Particle image velocimetry

Planar PIV is used to obtain quantitative measurements of the flow in Plane A and Plane B, both with and without a mask. Prior to experiments, the tent is seeded with smoke particles (Antari Z-800II Fog Machine, mean diameter 2 µm) and the pipe is also pre-filled with smoke, ensuring uniform particle seeding in the field of view through the entire expiratory event. A high-speed Photonics dual-head Nd:YLF pulsed-laser DM30-527 (Ronkonkoma, New York, USA) operating at 18 mJ/pulse at 250 Hz combined with a laser arm and light sheet generating optics (Intelligent Laser Applications GmbH, Jülich, Germany) is used to illuminate our field of view.

A Vision Research Phantom VEO 4K 990L high-speed camera (Vision Research Inc., Wayne, New Jersey, USA) is used to record particle motions. A Nikon AF variable focal length lens was used at a focal length of 50 mm for Plane A experiments and 18 mm for Plane B experiments. Image pairs were recorded at 250 Hz and at a resolution of 4096 × 2304 pixels, with δT = 2000 µs between images for S1 and D1, and δT = 1250 µs for S2. The commercially available Davis10 software (LaVision GmbH, Göttingen, Germany) was used both to record the image pairs, and to process the images using cross-correlation based PIV. The interrogation window underwent 4 multi-passes with a final window size of 32 × 32 pixels and 75% window overlap to produce 2-dimensional, 2-component (2D-2C) vector fields; this resulted in a final vector spacing of 1.5 mm.

### Data analysis

To calculate the penetration distance of the flow (no mask, and leakage flows in Plane A and Plane B), flow visualization images (such as Fig. 2a, c) are initially converted to a binary image in MATLAB. The dimensionless penetration distance is measured along the jet axis and is taken as the farthest point along the jet axis within a moving search window. For no mask, the jet axis is horizontal (parallel to x, as shown in Fig. 2a) and the dimensionless penetration distance is defined as xD/D where xD is the penetration distance along the jet axis. For Plane A and B, the leakage flow jet axis will be at an angle to the xy or xz axis, and the dimensionless penetration distance is defined as xD,jet,i/D, where i indicates Plane ‘A’ or ‘B’. These rotated axes are xjet,Ayjet,A, and xjet,Bzjet,B respectively. The rotated axes for Plane A and Plane B can be found in the Results and Discussion. When calculating the penetration distance, 3–5 runs of each case are taken and averaged. In each case (no mask, Plane A top mask leakage, Plane B side mask leakage), the scaling laws were fit using Atn + c in both the starting jet stage and interrupted jet stage, where A and c are constants to fit the scaling laws, n is the known exponential for the starting jet and interrupted jet stages, and t is time.

Using the resultant velocity field from PIV, the finite-time Lyapunov Exponent (FTLE) is computed using the LCS MATLAB Kit Version 2.3 by the Biological Propulsion Laboratory at the California Institute of Technology [36,37,38]. The FTLE is useful in analyzing time-dependent velocity fields, as ridges in the FTLE field are used to define Lagrangian Coherent Structures (LCS) [36, 39]. The FTLE $$\sigma _t^{t + T}({{{{{{{\boldsymbol{x}}}}}}}})$$ is given by:

$$\sigma _t^T\left( {{{{{{{\boldsymbol{x}}}}}}}} \right) = \frac{1}{{|T|}}\ln \left\| {\frac{{d\phi _t^{t + T}\left( {{{{{{{\boldsymbol{x}}}}}}}} \right)}}{{d{{{{{{{\boldsymbol{x}}}}}}}}}}} \right\|$$
(1)

where $$\phi _t^{t + T}$$ denotes the flow map of particles from their location x at time t to t + T. For full details see Shadden et al. [36]. For T < 0, the LCS can be referred to as a ‘backward-time’ LCS (bLCS): this is an attracting LCS, wherein the trajectory of fluid particles converge towards the LCS [40]. Similarly, for T > 0, the LCS is a ‘forward-time’ or repelling LCS (fLCS). LCS material lines are also transport barriers. In this study, we use the bLCS to show attracting material lines in the flow field, as a means of demonstrating where particles in the flow are likely to accumulate. The integration length of an LCS |T| is somewhat arbitrary [36], and is generally taken as long as it takes to reveal the LCS. In this study, we use an integration length of 50 frames or |T| = 0.2 s.

To quantify the effectiveness of the surgical mask, the flow leakage velocity profile and normalized leakage volume are determined. To classify the leakage velocity profile, a line is taken perpendicular to the leakage flow axis. For no mask, the flow leakage axis is along the x axis. As aforementioned, for Plane A and Plane B a 2D transformation matrix is applied to the data such that the x axis aligns parallel with the leakage jet axis (xjet,i). The volume of leakage flow per unit span ($$V_{l,\;span}$$) is computed along a line perpendicular to the leakage flow axis in both planes and is given by:

$$V_{l,\;span}|_A = {\int}_{\!\!\!\!0}^{T} {{\int}_{\!\!\!\!{y}_{1}}^{y_2} {u_{jet,\;A}\left( {y_{jet,\;A}} \right)dy_{jet,\;A}dt} \quad } V_{l,\;span}|_B \\ = {\int}_{\!\!\!\!0}^T {{\int}_{\!\!\!\!{z}_1}^{z_2} {u_{jet,B}\left( {z_{jet,B}} \right)dz_{jet,B}dt} }$$
(2)

where ujet,i is first integrated over the distance over which the leakage velocity flow profile covers (i.e., y1 and y2 are the bounds of the leakage jet flow profile along the yjet,A axis and similar for zjet,B), and these values are then integrated over time for the duration of the pulse(s) (t = 0 to t = T).

To enable a comparison across different cases, we normalize the leakage volume per unit span by the CEV per unit span (CEV/D), where CEV is determined from the mass flow rate curves shown in Fig. 1d, and is given by:

$$V_{leakage}|_A = \frac{{{\int}_0^T {{\int}_{y_1}^{y_2} {u_{jet,A}\left( {y_{jet,A}} \right)dy_{jet,A}dt} } }}{{\frac{{CEV}}{D}}}\quad V_{leakage}|_B = \frac{{{\int}_0^T {{\int}_{z_1}^{z_2} {u_{jet,B}\left( {z_{jet,B}} \right)dz_{jet,B}dt} } }}{{\frac{{CEV}}{D}}}$$
(3)

It is noted that care should be taken when interpreting this data not to extrapolate this volume leakage per unit span to a volumetric leakage flow, as the definition of Vleakage is based on planar measurements.

## Results and discussion

First, the pulsatile expiratory flow simulator without a mask is validated against existing literature. Second, the leakage flow that occurs at the top and sides of the surgical mask is quantified and classified. Last, the influence of coughing pulsatility on the effectiveness of the surgical mask is assessed both by quantifying the penetration distance and by estimating normalized leakage volume of the leakage flows.

### Validation of pulsatile expiratory flow simulator

The simulator was validated using three benchmarks: the CPFR of S1, the spread angle of D1, and the streamwise penetration distance of each S1, D1 and S2. As shown in Fig. 1d, the flow rate profile of the S1 cough reaches a peak of ~4.5 L/s which is within the reported CPFR range of measured female and male coughs [10]. Figure 2 shows the flow visualization and PIV results of an S1 ((a) and (b)) and a D1 ((c) and (d)) cough at T = 2T1. At this time, the difference in flow features between the two events is apparent. The vortex ring that is generated via the second pulse in D1 is seen both in the smoke flow visualization (Fig. 2c) and in the u velocity contour plot via the bLCS field (Fig. 2d). High values of a bLCS contour indicate regions of high particle attraction; as such, small airborne particles will be expected to follow these boundaries. As LCS structures are barriers to material transport, Fig. 2d indicates that a boundary between the first and second vortex rings exist in the D1 flow field at this time point. This is consistent with previous computational results of multi-pulsed particle-laden coughs, wherein the distribution of particles originating from separate pulses initially remain separate, prior to mixing at late times [5]. Figure 2c also shows the spread angle of the double-pulsed cough at T = 2T1, measured to be ≈20º from flow visualization. This is consistent with past studies, wherein the spread angle has been reported as 20.8º [12] and 23.9º [32].

The non-dimensional streamwise penetration distances xD/D for S1, D1 and S2 were measured via flow visualization. Past studies have characterized coughing flows as a two-stage jet, wherein the starting-jet stage (SJS) and interrupted-jet stage (IJS) are two distinct phases of flow. In the SJS, the temporal growth scales with t1/2; this phase is dominated by jet-like dynamics. In the IJS, the temporal growth scales with t1/4 and is dominated by puff-like dynamics, as the source is no longer delivering momentum to the flow [8, 12, 41]. The temporal growth in the IJS is therefore slower than in the SJS. These scaling laws are found to fit well with the no mask data, as shown in Fig. 2e.

### Identification and classification of leakage flow around a surgical mask

#### Top leakage (Plane A)

The first area of flow leakage that was examined was the top of the surgical mask. As is shown in Fig. 1e, the top leakage is measured in the plane down the middle of the mannequin’s face (Plane A). The flow leakage is shown via flow visualization and PIV for both an S1 (Fig. 3a−c) and D1 (Fig. 3d–f) cough. The time period is defined after the flow begins leaking from the top of the mask. It is interesting to note in the flow visualization (Fig. 3a, b, d, e) that the top flow leakage does not travel directly vertically upward. Rather, the flow stays by the mannequin head (even beyond the images presented in Fig. 3). As will be discussed below, this results in a wall jet along the mannequin’s forehead. Figure 3c, f show the total velocity contour plot, utotal = (u2 + v2)1/2, overlaid with bLCS contours for cough S1 and D1 respectively. The bLCS contours indicate that particles are expected to concentrate towards the plume front of both the S1 and D1; a bLCS contour beginning to form around the second pulse of D1 is also observed, indicating a second plume front of particle accumulation.

The top flow leakage velocity profile acquired in Plane A is taken perpendicular to the leakage flow axis (‘line A’), set at an angle θ to the x-y plane as shown in Fig. 4a, where the xjet,A axis aligns with the jet flow axis. At the top of the surgical mask the flow leakage velocity profile takes the form of a wall jet, which forms along the mannequin’s forehead. This was observed in each of the S1, D1 and S2 cases. The leakage velocity profile ujet,A is shown for S2 in Fig. 4b, wherein the time evolution of the wall jet at line A progresses from cool to warm colors. The wall jet that forms is self-similar and scales with the maximum velocity umax and the full width at half maximum yFWHM of the jet. This is shown in Fig. 4c. The normalized S2 data is shown in gray: the y-axis is normalized as ujet,A/umax and the x-axis is normalized by yjet,A/yFWHM. The maximum velocity (ujet,A/umax = 1) is centered over yjet,A/yFWHM = 0. The average normalized velocity profiles (shown in Fig. 4c) agree well with each other for all cases, only deviating as they move further away from the wall jet center-line (yjet,A/yFWHM > 3) when the velocity is low and the magnitude of vjet,A was observed to approach ujet,A.

In addition to the base-line S1 case, two additional S1 cases were run to test the sensitivity of different mask placements (S1a and S1b). These are defined in Experimental Setup and shown in Fig. 1c. The average normalized leakage flow velocity profiles for S1a (purple) and S1b (cyan) match reasonably well with the base-line cases taken at the topmost location on the mannequin’s nose. This indicates that even when the mask placement is placed 0.5D and 1D further down the nose, a self-similar wall jet is still formed along line A. The flow leakage velocity profile is therefore relatively robust to mask placement (assuming it is placed along the nose, as recommended by the WHO and CDC), and can be modeled as a wall jet. This also indicates the robustness of our chosen line A: the flow leakage velocity profile can be taken at different locations above the top of the surgical mask and will still return the same normalized wall jet. Figure 4d shows the time progression of the maximum velocity along line A, taken from when the flow begins leaking from the top of the mask. Two main features are observed. The first pulse of D1 and S1 closely follow each other, as is expected. However, the maximum velocity of S2 compared to S1 and D1 does not proportionally scale with the CPFR of S2 compared to S1 and D1. This suggests that the surgical mask has better attenuated the cough with higher CPFR.

#### Side leakage (Plane B)

The second area of flow leakage identified is at the sides of the surgical mask in Plane B. As is shown in Fig. 1f, this plane is taken at ~13° to the horizontal. This plane was chosen as it was observed to follow the flow leakage axis at the side. The leakage flow is shown in Fig. 5 via flow visualization and PIV; the image is viewing up at the inclined plane as indicated in Fig. 1f. Figure 5a, b show an S1 cough; Fig. 5c, d show a D1 cough. Each frame is shown at a time period of 2T1 after the flow begins leaking from the side of the mask. At this time, the second pulse of the D1 cough is clearly visible in the smoke flow visualization when compared to S1. To quantitatively examine this difference, the total velocity contour plot is shown, utotal, with bLCS contours overlaid on top. The bLCS contours indicate that particles are expected to concentrate towards the plume front of the first pulse in both S1 and D1, and also at the plume front of the second pulse for D1. This is consistent with previous observations [16], wherein rakes of particles implemented at an expiratory source were seen to accumulate at the plume front. This indicates that the plume front will contain a higher concentration of particles than the tail, as small aerosols that stay suspended in the respiratory cloud will conglomerate near the front. In the case of a double-pulsed cough, the tail may contain particles for longer than a single-pulsed cough, as the particle-containing second plume front propagates forward.

To classify the flow leakage velocity profile at the side of the mask, a line was taken ~5 cm from the edge of the mask, perpendicular to the leakage jet axis (‘line B’) at an angle θ to the xz plane. The rotated axis is shown in Fig. 6a. In contrast to Plane A, the flow leakage profile at the side of the surgical mask takes the form of a free-shear jet. This was observed in each S1, D1 and S2. The leakage velocity profile ujet,B is shown for S2 in Fig. 6b, where the time evolution of the free-shear jet at line B progresses from cool to warm colors. As illustrated in Fig. 6c, the jet that forms is self-similar and scales with the maximum velocity umax and the width of the jet when ujet,B = 0.1 umax (referred to as z90). The normalized S2 data is shown in gray: the y-axis is normalized as ujet,B/umax and the x-axis is normalized by zjet,B/z90 and adjusted to align the peaks. All three cases take the form of a free-shear jet, and are self-similar when scaled by umax and z90.

Figure 6d shows the time progression of the maximum velocity along line B, taken from when the flow begins leaking from the side of the mask. Similarly to the top flow leakage in Plane A, the first pulse of D1 and S1 closely follow each other. Once again, the maximum velocity of S2 compared to S1 and D1 does not proportionally scale with the CPFR of S2 compared to S1 and D1. An additional observation is that the second pulse of D1 reaches a higher maximum velocity and persists for a longer duration than the first pulse (≈0.4 s compared to ≈0.3 s). It is possible that the first pulse dislodges or reduces the ‘quality of fit’ of the mask such that more expiratory flow escapes during subsequent pulses.

### Effect of pulsatility on leakage around a surgical mask

To assess the effect of pulsatility on the effectiveness of a surgical mask, the penetration distance and normalized leakage volume of the leakage flow expelled at the top of the mask in Plane A and at the side of the mask in Plane B are quantified. The penetration distance along the leakage jet axis, xD,jet,i/D, is shown in Fig. 7 for (a) the top leakage in Plane A and (c) for the side leakage in Plane B, taken from when the flow begins leaking from the side of the mask. Three key features are observed. Firstly, in both Plane A and Plane B the penetration distance scale with the same trends as for the no mask case. In the SJS jet-like dynamics dominate, and the temporal growth scales with t1/2. In the IJS puff-like dynamics dominate, and the temporal growth scales with t1/4. Secondly, it is also observed that for the top leakage in Plane A, the double-pulsed cough has a larger penetration distance than either of the single-pulsed coughs: D1 is ≈ 20% further than S1 after 2.5 s. In contrast, all three cases are comparable in the Plane B side leakage; the D1 cough only appears to be overtaking S2 at later times. Lastly, it is interesting to compare the non-dimensional penetration distances to the no-mask case. In the no mask case, the penetration distance of D1 was xD/D ≈ 33 at 2.5 s (for S1, xD/D ≈ 26). At the same time after beginning leakage from the mask (2.5 s), the D1 cough has reached 54% of its no mask penetration distance in the Plane A top leakage and 56% in the Plane B side leakage; similarly, the S1 cough has reached 56% of its no mask penetration distance in the Plane A top leakage and 72% in the Plane B side leakage.

The normalized volume of leakage flow (per unit input CEV, computed from Eq. (2)) along line A and line B (top and side of the surgical mask, respectively) is shown in Fig. 7b d, respectively. Two main features are observed. Firstly, at both the top and side leakage locations the double-pulsed cough contains more leakage volume expelled than either of the single-pulsed coughs (at least 40% greater than either single-pulsed cough’s top flow leakage in Plane A, and at least 30% greater than either single-pulsed cough’s side flow leakage in Plane B). This indicates that the pulsatile nature of the cough leads to a decrease in the effectiveness of the surgical mask. Previous studies have shown that perimeter leakage is primarily observed when a mask is loose and does not make a seal with the face [34, 42]. It is therefore possible that the first pulse of a multi-pulsed cough pre-loosens or reduces the ‘quality of fit’ of the mask (due to the increase in pressure inside the mask during a coughing event [23, 34]) before the second pulse, such that the effectiveness of the mask is reduced during subsequent pulses.