On respiratory droplets and face masks

Abstract

Face mask filters-textile, surgical, or respiratory-are widely used in an effort to limit the spread of airborne viral infections. Our understanding of the droplet dynamics around a face mask filter, including the droplet containment and leakage from and passing through the cover, is incomplete. We present a fluid dynamics study of the transmission of respiratory droplets through and around a face mask filter. By employing multiphase computational fluid dynamics in a fully coupled Eulerian-Lagrangian framework, we investigate the droplet dynamics induced by a mild coughing incident and examine the fluid dynamics phenomena affecting the mask efficiency. The model takes into account turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet-droplet and droplet-air interactions. The model mimics real events by using data, which closely resemble cough experiments. The study shows that the criteria employed for assessing the face mask performance must be modified to take into account the penetration dynamics of airborne droplet transmission, the fluid dynamics leakage around the filter, and reduction of efficiency during cough cycles. A new criterion for calculating more accurately the mask efficiency by taking into account the penetration dynamics is proposed. We show that the use of masks will reduce the airborne droplet transmission and will also protect the wearer from the droplets expelled from other subjects. However, many droplets still spread around and away from the cover, cumulatively, during cough cycles. Therefore, the use of a mask does not provide complete protection, and social distancing remains important during a pandemic. The implications of the reduced mask efficiency and respiratory droplet transmission away from the mask are even more critical for healthcare workers. The results of this study provide evidence of droplet transmission prevention by face masks, which can guide their use and further improvement.

FIG. 1.

Initial saliva droplets size distribution. Reproduced with permission from T. Dbouk and D. Drikakis, “On coughing and airborne droplet transmission to humans,” Phys. Fluids 32, 053310 (2020). Copyright 2020 AIP Publishing LLC.

FIG. 2.

A 2D slice of the 3D computational domain using an advanced technique employing a hexahedral non-uniform structured mesh (≈0.52 × 10⁶ cells). The mesh is refined at the mouth-print, nose-print, and the face and then coarsened gradually in the streamwise cough flow direction with a multilevel refinement procedure. The overall computational domain dimensions are L = 1.6 m, W = 0.5 m, and H = 0.45 m.

FIG. 3.

Face mask fitting.

FIG. 4.

Cyclic conditions for the mouth inlet velocity U_f mimicking human coughing as observed experimentally by Hsu et al. λ_i = 0.38 s with i ∈ [1, 10].

FIG. 5.

Droplet filter surface interaction modes.

FIG. 6.

A subject coughing in a cyclic incident. A qualitative examination of airborne droplet transmission with and without wearing a surgical mask. The top and bottom figures show the results at 2 s and 3 s, respectively. Wearing a surgical mask that exhibits an initial efficiency of ∼91%. This cannot prevent the transport of the saliva droplets away from the subject. Many droplets penetrate the mask shield and some saliva droplet disease-carrier particles can travel more than 1.2 m. For visualization, the droplets were scaled by a factor of 600 compared to their actual size. The environmental conditions are zero wind speed, ambient temperature 20 °C, pressure 1 atm, and relative humidity 50%. The mouth temperature is 34 °C and the face skin temperature is 32 °C.

FIG. 7.

A subject coughing in a cyclic incident. A qualitative examination of airborne droplet transmission with and without wearing a surgical mask. The top and bottom figures show the results at 4 s and 5 s, respectively. Wearing a surgical mask that exhibits initial efficiency of ∼91%. This cannot prevent the transport of the saliva droplets away from the subject. Many droplets penetrate the mask shield and some saliva droplet disease-carrier particles can travel more than 1.2 m. For visualization, the droplets were scaled by a factor of 600 compared to their actual size. The environmental conditions are zero wind speed, ambient temperature 20 °C, pressure 1 atm, and relative humidity 50%. The mouth temperature is 34 °C, and the face skin temperature is 32 ° C.

FIG. 8.

A subject coughing in a cyclic incident. Top view of a qualitative examination of airborne droplet transmission with and without wearing a surgical mask. The top and bottom figures show the results at 2 s and 3 s, respectively. We consider a surgical mask that exhibits initial efficiency of ∼91%. The cover does not prevent the transport of the saliva droplets entirely away from the subject. Many droplets penetrate the mask shield, and some saliva droplet disease-carrier particles can travel more than 1.2 m. For visualization, the droplets were scaled by a factor of 600 compared to their actual size. The environmental conditions are zero wind speed, ambient temperature 20 °C, pressure 1 atm, and relative humidity 50%. The mouth temperature is 34 °C, and the face skin temperature is 32 °C.

FIG. 9.

A subject coughing in a cyclic incident. Top view of airborne droplet transmission with and without wearing a surgical mask. The top and bottom figures show the results at 4 s and 5 s, respectively. We consider a surgical mask that exhibits an initial efficiency of ∼91%. The cover does not prevent the transport of the saliva droplets entirely away from the subject. Many droplets penetrate the mask shield and some saliva droplet disease-carrier particles can travel more than 1.2 m. For visualization, the droplets were scaled by a factor of 600 compared to their actual size. The environmental conditions are zero wind speed, ambient temperature 20 °C, pressure 1 atm, and relative humidity 50%. The mouth temperature is 34 °C, and the face skin temperature is 32 °C.

FIG. 10.

A subject coughing while wearing a surgical mask. The top figures show the velocity magnitude contours at t = 3.06 s. The bottom figures show a schematic of the flow dynamics.

FIG. 11.

Mask wearer: subjects wearing a mask will reduce the respiratory droplet transmission while (partially) shielding themselves from other subjects experiencing a coughing incident. We show the results at 5 s simulation time for a surgical mask exhibiting an initial efficiency of ∼91%. The environmental conditions are zero wind speed, ambient temperature 20 °C, pressure 1 atm, and relative humidity 50%. The mouth temperature is 34 °C and the face skin temperature is 32 °C.

FIG. 12.

A subject coughing while wearing a surgical mask. The figures show the temperature contours at different times and side and perspective views.

FIG. 13.

Evolution of respiratory droplet Sauter Mean diameter (SMD), known as D32, over ten cough cycles. Linear fit: with mask (a = −0.725, b ≈ 56.14) and without mask (a = −0.215, b ≈ 73.27). The environmental conditions are zero wind speed, ambient temperature 20 °C, pressure 1 atm, and relative humidity 50%. The mouth temperature is 34 °C and the temperature of the face skin is 32 °C.

FIG. 14.

Accumulated mass of respiratory droplets over ten cough cycles. Linear fit: with mask (a = 0.063, b ≈ 1.01) and without mask (a = 0.24, b ≈ 9.19).

FIG. 15.

Mass transfer due to phase change (evaporation) of respiratory droplets over ten cough cycles. Linear fit: with mask (a = 0.248, b ≈ 0.22) and without mask (a = 0.832, b ≈ 0.33).

FIG. 16.

Analysis of different droplet types over cough cycles. N_s and N_e appear in Eqs. (6) and (7).

FIG. 17.

Uncertainty quantification: percentage of droplets leaving the computational domain during cough cycles regarding the total droplets expelled from both the mouth and nose.

FIG. 18.

Liquid Penetration Distance (LPD) evolution over ten cough cycles. Linear fit: with mask (a = −0.05, b ≈ 22.38) and without mask (a = 0.47, b ≈ 37). The environment is at ambient temperature, pressure, and relative humidity of 20 °C, 1 atm, and 50%, respectively. The mouth temperature is 34 °C and the face skin is 32 °C. The results are plotted from the end of the first cycle.

FIG. 19.

Filter efficiency over ten cough cycles. η₁ = η(n = 1) = 90.4% (R² = 0.97).