Microstructural evaluation and recommendations for face masks in community use to reduce the transmission of respiratory infectious diseases

Background and Objective Recommendations for the use of face masks to prevent and protect against the aerosols (≤5µm) and respiratory droplet particles (≥5µm), which can carry and transmit respiratory infections including severe acute respiratory syndrome coronavirus (SARS-CoV-2), have been in effect since the early stages of the coronavirus disease 2019 (COVID-19). The particle filtration efficiency (PFE) and air permeability are the most crucial factors affecting the level of pathogen transmission and breathability, i.e. wearer comfort, which should be investigated in detail. Methods In this context, this article presents a novel assessment framework for face masks combining X-ray microtomography and computational fluid dynamics simulations. In consideration to their widespread public use, two types of face masks were assessed: (I) two layer non-woven face masks and (II) the surgical masks (made out of a melt-blown fabric layer covered with two non-woven fabric layers). Results The results demonstrate that the surgical masks provide PFEs over 75% for particles with diameter over 0.1µm while two layer face masks are found out to have insufficient PFEs, even for the particles with diameter over 2µm (corresponding PFE is computed as 47.2%). Thus, existence of both the non-woven fabric layers for mechanical filtration and insertion of melt-blown fabric layer(s) for electrostatic filtration in the face masks were found to be highly critical to prevent the airborne pathogen transmission. Conclusions The present framework would assist in computational assessment of commonly used face mask types based on their microstructural characteristics including fiber diameter, orientation distributions and fiber network density. Therefore, it would be also possible to provide new yet feasible design routes for face masks to ensure reliable personal protection and optimal breathability.


Introduction
Since China reported a pneumonia outbreak in Wuhan, and the causative organism was identified as a new coronavirus namely, novel coronavirus: nCOV-severe acute respiratory syndrome coronavirus (SARS-CoV-2), there has been intense debate over the transmission modes of SARS-CoV-2 [1][2][3][4][5][6] . Although the World Health the other hand, aerosols tend to be smaller than 5μm. Similar to droplets, they are generated during activities like breathing, talking and coughing [10] . The important properties of aerosols in the spread of the disease are their ability to travel long distances (7-8m from a cough), to stay in the air for more than 1 h and to be inhaled to the bottom of the respiratory tract [11,12] . Natural respiratory activities such as breathing, talking, and coughing can generate a broad range of particle sizes, from submicron aerosols to large droplets [12,13] . After being declared as a public health emergency of international concern, recommendations for protection and prevention of COVID transmission were published [14] . Among all the personal protective equipments (PPEs), face masks and respirators have been widely used as first-protection equipment and are of critical importance to prevent the spread of the aerosols and respiratory droplets especially when the social distancing measures are difficult to maintain [15][16][17] . As illustrated in Fig. 1 , respiratory particles, which can remain in the air for some time as a result of coughing, sneezing, speaking or exhaled breath, can carry airborne pathogens and compounds and are one of the transmission routes for the infectious diseases [18][19][20][21][22][23][24][25][26] . Comprehensive reviews on face masks have been recently published to inform public, academia, and industry [27,28] . Karmacharya et al. [29] focused on filtration, self-sterilizing and self-cleaning capabilities of facemasks, type of facemasks, critical parameters for filtration efficiency, and existing decontamination methods. Possible use of novel antimicrobial material technologies for infection prevention clothing were discussed in depth and successfully implemented by Cano-Vicent et al. [30] and Takayama et al. [31] . Moreover, Tcharckhtchi et al. [32] presented a literature ranging from different kinds of facemasks, their application areas, advantages and drawbacks to the influence of external parameters (such as, particle size, air flow velocity), and filter characteristics (for instance, filter thickness and packing density). Tanisali et al. [33] compared the effectiveness of different face masks from cloth mask to N95 masks in aerosol dispersion in SARS-CoV-2 infection. The meta-analysis in [34] concluded that the use of face masks by public reduces the risk of transmitting respiratory infections, such as, influenza, SARS-CoV-2.
Although PPEs in occupational hygiene areas are subjected to strict testing standards and guidelines, including ISO 9237:1995 standard for determination of permeability of fabrics to air, EN 149 standard for testing and marking requirements for filtering half masks (FFP1-2-3), EN 14683:2019 (Type I-II-IIR) and ASTM F2100 (Level 1-2-3) standards describing the requirements and testing methods of medical masks, ordinary face masks and alternative options (scarfs, kerchiefs, etc.) in our daily lives do not necessarily follow these standards [35][36][37] . As being sold nowadays online and in the retail shops, these masks have wide-range of styles, fabrics and number of layers (also known as plies). However, their performance metrics, in terms of the particle filtration efficiencies (PFEs) and air permeability, often vary and are yet to be well rationalized and correlated with their intrinsic microstructural properties [38,39] . The first metric is important for reducing the disease transmission while the latter is essential for the breathability, i.e. wearer comfort. Therefore, in order to correlate the mask performance and microstructure, an assessment framework was developed combining the X-ray microtomographic 3D imaging and computational fluid dynamics (CFD) methods. The investigations were limited to the prevalent off-the-shelf two layer face masks (made out of two nonwoven fabric layers) and surgical masks (made out a of melt-blown fabric layer covered with two non-woven fabric layers). As shown in Fig. 2 , X-ray microtomography was used to extract the geometric details of these masks at micrometer length scale and used as the solution domain for the CFD simulations. In the PFE analyses, the smoothed particle hydrodynamics (SPH) method was used to examine the particle movements through layers and focused on a spectrum of {0.1, 0.3, 0.5, 1.0, 2.0} μm particle diameters representing the aerosols. Simultaneously, finite volume method (FVM) was implemented to investigate the air permeability of these masks. The results demonstrate that the surgical masks provide PFEs over 75% for particles with a diameter over 0.1μm while two layer face masks are found to have insufficient PFEs, even for particles with a diameter over 2μm (the corresponding PFE is computed as 47.2%).
Based on the research findings, a computational design framework was also proposed for the next generation off-the-shelf masks. With this design framework, the effects of fiber diameter, orientation distribution and network density of non-woven fabric layers on the breathability and PFE were examined. In this research, breathability can be described as a degree of a fabric permitting air to pass through. The degree of breathability is disproportional to pressure drop while air passes through the facemask. Hence, the optimum/optimal design in terms of breathability can be assumed to be the one with the lowest pressure drop. The numerical results indicated that face masks with at least one meltblown layer with randomly oriented fibers having diameter of app. 6.5μm, and higher stretching percentages in the thickness direction provided relatively high PFE with good air permeability.

Micro-computed tomography and mesh generation
For the microstructural analysis and volume reconstruction purposes, approximately 2mm wide strips were cut from each mask using a surgical knife. The strips were attached on to the top of carbon fibre sample holder rods using cyanoacrylate glue. Care was taken to avoid separation of the mask plies and imbibition of the glue into the imaged region of the strip.
The mounted strips were imaged with 1.15μm pixel size using an Xradia MicroXCT-400 tomograph. X-ray tube acceleration voltage and power were set to 30 kV and 4 W, respectively, for optimal contrast and resolution. A total of 1750 projection radiographs were taken with 10 × optical magnification and 5 s exposure time for each radiograph. The total imaging time was approximately 7.5h per sample, including an 1.5h stabilization period at the beginning of the imaging process.
The projection images were reconstructed into a volumetric 3D image using the filtered backprojection algorithm implemented in the pi2 software 1 (version 3). Both absorption and phase reconstructions using the Paganin method [40] were made. In the reconstructed images, the fibres forming the layers of the mask are shown as bright regions on a dark background corresponding to air. Relatively high contrast-to-noise ratio allowed segmentation of the fibres from the background by applying Otsu thresholding [41] to both reconstructions. The absorption contrast image was further refined by removing all isolated foreground regions whose volume was less than 500 voxels, as these regions were likely caused by imaging noise and/or imaging artefacts, and were not part of the mask structure showing as a large connected foreground region. An example of the output of each of the processing stages is shown in Fig. 3 .
In the absorption contrast image the smallest fibres are well defined, but the larger ones show significant phase-contrast artefacts. Consequently, the smallest fibres are well segmented in the absorption contrast segmentation, and the larger ones in the phasecontrast segmentation. In order to account for this while keeping the maximum resolution, the segmentations made from both reconstructions were combined using boolean OR operation to form the final binary image representing the fibre phase (see Fig. 3 ).
Finally, the binary images were converted to surface meshes using the iso2mesh toolbox 2 (version 1.9.0) [42,43] . The binary images were first downsampled to one half, followed by triangular isosurface extraction using the 'simplify' strategy of the vol2surf function. The keepratio parameter was set to 0.1. The final surface mesh was saved as an .stl file.

Particle simulations
The present computational assessment strategy mainly focuses on aerosol filtration, i.e., particles with a diameter less than 5μm, and air permeability simulations, which does not account for the variations of particle emissions [44] . The filtration was evaluated with use of SPH, a mesh-free Lagrangian particle method, i.e., particles having masses move together with the material while computing the value of physical parameters through the weighted contributions of the neighboring particles [45,46] . Because of being a mesh-free method, SPH does not suffer from large deformations and mesh distortions [47] . Therefore, it is a convenient method to treat dynamic problems such as fluid flows, spraying and ballistics in a relatively natural manner, which has been validated with the vast number of experiments and benchmark problems elaborated in the literature [48][49][50][51][52] . In the present study, the mass conservation was satisfied with the constant particle number and densities ρ while the conservation of momentum in terms of Navier-Stokes 2 Available at https://iso2mesh.sourceforge.net formulation is expressed as where D v Dt is the substantial derivative of the velocity, ∇ p is the pressure gradient, g is the gravitational acceleration, ∇ 2 v is the Laplacian of the velocity, μ is the dynamic viscosity. Eq. 1 was solved in the scheme of explicit central-difference time integration algorithm and time histories of the field variables for all the particles were obtained with the Abaqus/Explicit solver [53] . The relationship between the pressure p and density ρ for particles, which were assumed to possess the mechanical characteristics of water, was expressed with the linear Us-Up Hugoniot form of the Mie-Gruneisen equation of the state as [54] Here, E m is the internal energy per unit mass and η is the nominal volumetric strain. The speed of sound c s and reference density ρ 0 were taken as 1.425 ×10 6 mm/s and 1 ×10 −9 tonne/mm 3 , respectively. The material constants 0 and s were assumed to be 0.28 and 1.75, respectively [55] . In addition, the Abaqus built-in surface behavior formulation was also used to (I) prevent the particle penetration to each other and the mask layer surfaces and (II) characterize the particle movements within the layers. Based on the experimental studies on friction coefficient of fabrics, Coulomb friction of 0.25 was used for non-woven fabric layers while Abaqus built-in ROUGH keyword was used for the surface friction of meltblown fabric layers mimicking its electrostatic adsorption characteristics [56,57] . Therefore, with the provided layer surface conditions, particles colliding with fibers experience friction, which decreases their kinetic energy. If the friction cancels the momentum of the particle, the particle sticks on the fiber; thus, cannot penetrate into the other side of the mask layer.

Simulation of flow behaviour
The finite volume method (FVM) in STAR CCM+ was utilised to compute flow field around the investigated fibrous mediums [58] . The microstructure of these mediums is the key parameter causing resistance to flow, which is the fundamental reason for the pressure drop P that maintains the pressure level at lungs and accommodates the required airflow for breathing. Together with this, Fig. 3. Cross-sectional slices through the CT image of the two-layer mask sample (top two rows) and surgical mask sample (bottom two rows) and in various processing phases. First row from left to right: Absorption reconstruction, the same location after Otsu thresholding, and after small foreground region removal. Second row: Phase reconstruction, the same location after Otsu thresholding, and the edges of the final segmentation overlaid on the original absorption reconstruction. The third and the fourth rows follow the same format. The same scale bar applies to all the panels. air permeability, the key performance parameter of breathability or an assessment metric the face-mask wearer comfort, is inversely proportional to P . Permeability of the fibrous networks is formulated with Darcy's Law as follows where t web and V f are the thickness of the fibrous network and face velocity of the fluid (air in our case), respectively [59] . The unknown parameter in the permeability equation is P , which is predominantly influenced by the microstructure of porous medium. Analytical or empirical models for estimating the P parameter are proposed in literature, such as [60,61] . Both the analytical and empirical flow models rely on the simplifications in the geometry of microstructure and flow behaviour. The actual microstructure of non-woven face masks include more complexities such as random alignments of fibres and fibre-to-fibre contacts controlling interconnected pore network. Some theoretical models in literature such as [62][63][64][65] were proposed to estimate permeability of simple fibre networks. These models express permeability in terms of only fibre volume fraction and they over-predict or under-predict actual values. They can be, however, used for verification of numerical simulations to some extent. The air flow domain in this case is a cuboid, where the front and back surfaces are defined as the velocity inlet and pressure outlet, respectively (see Fig. 4 ). P is the difference between inlet and outlet pressures. A no slip boundary condition was implemented to the surface of the fibre surfaces, whereas a slip boundary condition was used to model shear behaviour of air flow on side walls. The base criteria for no-slip BC on the fibres is the Knudsen number K n , defining which flow regime is valid around a fibre. When K n < 0 . 001 , a no-slip with continuum flow regime is valid around each fibre [66] .

Particle filtration efficiency and air permeability of the face masks for community use
For the particle filtration efficiency (PFE), the total volume of 100μl particle agglomerate was expelled over approximately 1mm × 1mm mask surface area and monitored for t = 50ms, which is based on the respiratory particle aggregate formation period investigated by Wang et al. [70] . The initial particle agglomerate was formed with a script that both generates uniformly distributed pseudorandom particles and simultaneously avoids the particle penetration. Three sets of simulations were designed for each case by using the script. Following the proposed velocity ranges for the particle filtration in the literature, an inlet flow velocity of 10 0 0mm/s (exhalation) was used [67,71] . Adapting the filtration efficiency definition in the literature [32,72] , PFE was evaluated as the ratio between the number of particles heaped over the fiber surfaces and the total number of particles expelled within the investigated duration.
Average diameter of fibres in two layer non-woven medium are measured from X-ray volume data as 35μm. For the three-layer porous medium, on the other hand, the mask is composed of two calendared fabric layers (front and rear ones) and one melt-blown fabric layer (middle one) with 35μm and 6.5μm diameter fibres, respectively.
Particle filtration and air permeability performances of the investigated face masks were successfully simulated. Streamlines in the flow domains were computed with respect to flow path and projected fluid pressure over the fibres were presented in Figure 5 (a-d).. The corresponding permeability and permeability values are reported in Table 1 . Comparing the tabulated air permeability values, two layer masks were deduced to be more comfortable to use rather than surgical masks. However, they have less PFEs than surgical masks, e.g., approximately 25% for submicron particles and 50% for particles over 2μm. This shows that masks comprising only

Table 1
Comparison of average values for air permeability and particle filtration efficiencies (PFEs) of the prevalent two-and three layer face masks for community use. * : The filtration efficiencies in [57] are the weighted averages for the particle size ranges less than or more than 0.3μm. * * : The filtration efficiencies in [73]  two non-woven layers provide significantly less protection against spreading the disease. The face velocity of air flow through the filter medium was between 100 mm/s and 10 0 0 mm/s, which is relatively high for particle trapping due to diffusion. We, therefore, assumed the leading particle deposition mechanisms are impaction and interception. This implies particles are mainly captured by the fibre surfaces encountering aerosols.

Design recommendations and future directions for next generation face masks
The simulated results over the prevalent face masks indicated that there is a room for development in consideration to both PFE and permeability. For this reason, a computational design framework for improving mask protection and wearer comfort was proposed. First, mock-up models of two layer face masks emulating actual microstructure extracted from CT images were generated with finite-element simulations, where 3D fibers were stacked on the top of each other in the through-thickness direction (TD). To have a realistic microstructure, constituent fibres were in contact and possible penetrations were minimised with contact algorithms [76][77][78][79] . Using in-house algorithms written in Python, the generated models in FE environment were converted into CAD models in Autodesk Fusion to be imported in Star CCM+ for CFD simulations.
The aforementioned particle simulations for both types of face masks demonstrated the significance of presence of melt-blown  layer on the PFE. The amount of material in each layer of two-and three layer face masks was measured to be the same (20 g/m 2 ). Two non-woven layers (40 g/m 2 in total) with 35μm fibres in the two layer face mask only filtered 20-25% of aerosols with a particle size of 0.3μm whereas a single melt-blown layer with 6.5μm fibres in a three layer face mask achieved to filter over 80% of them. In comparison with the prevalent off-the-shelf mask investigations, 15%-20% more PFE was achieved with the new design configurations.
Four unique geometries for each non-woven face mask were generated to investigate the effect of microstructure on filtration and permeability performances. Henceforth, orientation distribution of fibers, fibre diameter, and fiber network density were examined on the performance parameters. Fig. 8 (a)-(d) presents the input parameters for each design case. Design 1 forms the base model for two layer face masks and the constituent fibres are randomly distributed using an uniform distribution function ( f1 ) in the MD-CD plane. This random distribution was implemented into both layers of the two layer mask microstructure and the resultant fibrous network of the Design 1 is shown in Fig. 8 (b). Different than the distribution f1 , a normal distribution f2 (see Fig. 8 (c)) enabling preferentially aligned fibers in MD are also tested for both type of face masks.

Fiber diameter, orientation distribution and network density
Based on the numerical findings, need for the structural development was deduced to be inevitable for the commonly used face masks. Such developments can be carried out through testing different microstructural parameters, such as, the fiber diameter, orientation distribution, and network density, for which a good balance should be determined. For this reason, various design cases were developed and simulated for non-woven layers as represented in Figs. 8 and 9 . Designs 1 and 2 was used to quantify the contribution of the orientation distribution of fibers to the permeability and filtration capacity of two layer face masks. For nonwoven face masks, the permeability measurements through thickness direction (TD) and transverse planes (TD-CD and TD-MD) are of main interests. The previous works such as [80,81] focused on transverse (i.e. through-thickness direction (TD)) air permeability of fibrous networks. They demonstrated that the transverse per- meability is independent of in-plane fiber orientations, whereas the variations in fiber orientations in transverse planes increases the transverse permeability by opening voids allowing the fluid passing through. In addition this, Zobel et al. [82] simulated the permeability of thermally-calendered non-wovens and, afterwards, claimed that the TD permeability is independent of orientation of fibers. A 2D computational model capturing statistical randomness of fibres of the N95 facemask was suggested to predict the fil-tration efficiency of individual layers [83] . Our parametric models mimicking the microstructures of off-the-shelf two layer face masks and three layer surgical masks have highly aligned fibers in transverse planes, meaning fibers are parallel to MD-CD plane and perpendicular to incoming air flow. Thus, the orientations of fibers in Designs 1 and 2 were only varied in the MD-CD plane as seen in Fig. 8 (a)-(b). As depicted in Fig. 9 (a) for two layer face mask designs, preferentially oriented fibers decreased the PFE as well as the air permeability, by 10% and 18percent, respectively. For our two layer face mask, variations in orientation distributions of fibers in MD-CD plane, which is orthogonal to flow direction, is one of the key parameters to be strictly retained.
The common theoretical models mentioned previously, such as the ones in [62,63,65] , express the permeability in terms of fibre volume fraction and diameter. The permeability is directly proportional to the square of fiber diameter. To test this argument, the diameter of fibers in Design 3 was reduced from 35μm to 25μm. Simultaneously, the PFE of the design was also assessed. The investigations resulted in a microstructure of face mask with 48% less permeability in comparison to our base model (Design 1), which is 5% away from the theoretical predictions. While reducing the fiber diameters, fibre volume fraction was retained along with the size of fibrous network model. This change, approximately, doubled the number of fibers in the model. For the tested fiber diameters, PFE was not significantly changed. This behaviour is attributed to that the pore size of the new geometry is not sufficiently small to filter the particles. In Design 4, however, the aim was to shrink the pores in both face mask layers for potential improvement in filtration. A minor positive change in the PFE was recorded, though a significant decrease in the air permeability was obtained as a trade-off. Fig. 9 (c) demonstrates particle simulations and stream-line representations of Designs 1-4.
As for the three layer face masks, the core layer is manufactured with a melt-blown process. Despite having a similar basis weight as the front and back layers, it facilitates a fibrous network with comparatively a higher filtration efficiency. Our numerical simulations demonstrated that the major proportion of aerosol particle entrapment occurs in this layer. In the parametric studies of three layer face mask, therefore, only the core layer was modelled for permeability and filtration simulations. The design parameters of parametric designs are demonstrated in Figure 8 (d). In Designs 5-7, the thickness of the core layer in TD was varied by 50% such that filtration and permeability performances are manipulated. The resultant CAD models of these fibrous networks at original, compression, and stretch states are demonstrated in Fig. 8 (e)-(g). Fig. 9 (b) show the plot of aerosol filtration and air permeability predictions for Designs 5-7. Meanwhile, Fig. 9 (d) demonstrates particle simulations and their stream-line representations. Apparently, from the Table 1 , three layer face mask reached up to 80% filtration efficiency against the particles with 1.0μm size and, however, relatively lower air permeability in comparison with the one for two layer face mask. 6.5μm fibres were distributed by using a fully-random orientation distribution in the finite-element (FE) model and the microstructural geometry of Design 5 was produced. The same FE model was compressed by 50% to produce Design 6 and stretched by 50% to generate Design 7. The facemask layers were stretched in the thickness direction (TD), and the base model was assumed to have 0% stretch or compression. The deformed FE geometries were converted into CAD models using inhouse Python scripts for flow simulations. Numerical simulations of these models suggest that the filtration efficiency of a fibrous network is independent of fiber network density (as a result of network compaction or stretching). The air permeability, however, can be fine tuned via compaction or stretching processes. In a recent work, Ando et al. [84] simulated flow-induced deformation of a fibrous media and its effect on filtration performance with a 3D fluid-structure interaction algorithm. The geometry of nonwoven media with high fiber densities (above 17%) is affected less by air flow mimicking coughing and the change in air permeability is ignorable. The implementation of 50% stretch into the melt-blown layer improved the air permeability with no significant trade-off in aerosol particle filtration. Oppositely, the two non-woven layer face mask does not need such stretch due to high existing permeability. The results obtained from Design 8 demonstrates that a fibrous medium with smaller fiber diameter, which is 6.5μm in our current case, is insensitive to orientation distribution of fibers. For instance, air permeability decreased by 25%, which is not desirable for face mask users. A face mask made from at least one meltblown layer with small fiber diameter (as studied in current case), uniform orientation distribution f1 of fibers, and lower fiber volume fraction can be recommended for face mask manufacturers.

Discussion
To the best of the authors' knowledge, the present study is one of the first microscale assessment frameworks for commonly used face masks in public, which combines both X-ray microtomographic 3D imaging and CFD simulations. Despite the invaluable macroscale face mask investigations on the transmission of respiratory infectious diseases in the literature [32,57,85] , the nu-merical frameworks focusing on their microscale characterization and performance are almost non-existing with very few exceptions in the literature [84] . This is mainly due to the labourintensive volume reconstruction process and ever-increasing computational costs with the solution domain. Based on these facts, the framework focused on reconstructed and generated domains within micron-to-millimeter scale range. The investigations were then conducted to understand the effects of microstructural characteristics of face mask layers, which were taken as fibre diameter, fibre orientation distribution and network density, on the filtration efficiency and permeability of two layer face masks and three layer surgical masks. Such microstructural analyses play a critical role not only to understand the performance of the prevalent off-theshelf face masks but also to improve the face mask layer designs.
In line with the recent studies on transmitted particle sizes [83,86,87] , the particle diameter range of {0.1, 0.3, 0.5, 1.0, 2.0} μm was investigated. The present numerical model with the reconstructed face mask layers did not take the particle emission and flow speed variations into account because of the scale and duration of interest, following the previous studies in the literature [44] . In addition, the airflow direction was assumed to be orthogonal to the thickness direction (TD), through which the particles properly meet the face mask layers. Under these assumptions and limitations, the model provides a microscopic insight with time intervals of t = 50 ms that agrees well with the recent particle image velocimetry experiments [70] . The results were also observed to be in line with the recent experimental results [87,88] , showing the trade-off between the PFE and breathability in terms of air permeability. Especially, for the intermediate sizes of 0.1μm-0.3μm, the particles were obtained to be hardly captured by face masks with two non-woven layers as seen in Fig. 6 , which demonstrates their insufficiency. On the other hand, surgical masks composed of two non-woven and one melt-blown layers as reconstructed in Fig. 7 were deduced to produce sufficient PFE for the particle sizes under investigations. This outcome also revealed the significance of presence of melt-blown layer, around which the most droplets are to be trapped as the droplet sizes are larger than the fibre spacing. It is also likely that the melt-blown layer work as a barrier preventing droplets to evaporate and transform into smaller particles [38] .
The results obtained from the prevalent mask types were used as foundation for prospective face mask designs, through which different fiber diameter, orientation distribution, and network density configurations were examined. Based on the simulation results for these configurations, the fibre diameter was deduced to be the major factor in designing and controlling the fineness and filtration capacity of the face mask layers while the number of nonwoven layers were found out to be a less decisive parameter. These findings were found out to be inline with the investigations in the literature [89][90][91][92] . Having fibres with small diameters has a tradeoff in the breathability performance of face masks, meaning lower permeability, which can be overcome by reducing the compaction ratio (fiber network density) in TD. The investigated design configurations for new generation face masks were based on circular cross-sectional fibres mimicking the ones reconstructed from the X-ray microtomography of the readily available face masks. However, several investigations, such as in [93][94][95] , claimed that the fibres with triangular, quatrefoil, trilobal and elliptical crosssections have higher filtration efficiency than those with circular cross-sections. Although this behaviour could be attributed to the larger specific surface area and can facilitate prospective numerical studies, production and economical feasibility of such fibers should be thoroughly investigated. Nevertheless, in order to have a face mask with high filtration efficiency and comfort in terms of breathability, the results demonstrated that a face mask should have at least one nonwoven layer with fine (small) fibres and low compaction. Developments in non-circular fiber manufacturing processes and surface treatments would definitely be affirmative in the filtration efficiency and breathability.

Conclusions
The present study provides a novel and thorough assessment of the commonly used face masks in consideration to their microstructures, PFEs and air permeabilities by using X-ray microtomography and CFD simulations. A design space with the parameters defining the quality of the mask, i.e. fiber diameter, fiber network density and orientation distribution, was suggested, which aims at better protection and breathability. Hence, the introduced study and framework can be applied to design new face masks with computerized methods, which aims at minimizing the research and development effort s and cost s. Although the simulations were idealized and limited based on various assumptions, the presented results can simply contribute to reducing the transmission of respiratory infectious diseases for the prospective waves of pandemic and provide better comfort for the wearer with prolonged face mask use.

Statement of ethical approval
There was no participation of human or animal subjects during the investigations; therefore, the present study did not require any statement of ethical approval.

Declaration of Competing Interest
The authors declare they have no known competing financial interests of personal relationships that could have appeared to influence the work reported in this paper.