A mathematical model for accurately predicting face mask wearer's inhalation exposure to self-exhaled and external pollutants

Face masks reduce the wearers’ inhalation exposure to external pollutants, but intensifying the exposure to their self-exhaled pollutants. To quantify the wearers’ inhalation exposure to the two sources of pollutants, a mathematical model for transient-state conditions was firstly established and scientifically validated, with an average relative deviation of only 3 % from the experimental data and only 6 % from the validated CFD simulated results. Proportion of leakage flow rate via gap (γ) was mainly affected by breathing flow rate (L_exh/inh) and gap's area (S_g), followed by face mask's surface area (S_m) and thickness (M_m). The 7 L/min of L_exh/inh led to the maximum inhalation fraction (IF) of self-exhaled pollutants at about 54 %, implying that wearing face masks poses a threat to the wearer's health. When face mask's volume increased from 50 mL to 150 mL, the relative intake dose (ID^∗) of external pollutants decreased by 0.12 but the IF of self-exhaled pollutants increased by 9 %. When face mask's filtration efficiency increased from 10 % to 90 %, the IF of self-exhaled pollutants and the ID^∗¯ of external pollutants decreased by 13 % and 0.23, respectively. The increase of 0.80 in γ decreased the IF of self-exhaled pollutants by 8 % but increased ID^∗¯ of external pollutants by 0.19, implying that protective performance always contradicts on the inhalation exposure to self-exhaled pollutants. The model established provides a new method to evaluate the performance of face masks rapidly and accurately, and further benefits the improvement of face masks and even other respiratory protective equipment.