A fluid mechanics model of inhaled air gases, nitrogen (N2) and oxygen (O2) gases, and exhaled gas components (CO2 and water vapor particles) through a facial mask (membrane) to shield the COVID-19 virus is established. The model was developed based on several gas flux contributions that normally take place through membranes. Semiempirical solutions of the mathematical model were predicted for the N95 facial mask accounting on several parameters, such as a range of porosity size (i.e., 1–30 nm), void fraction (i.e., 10−3%–0.3%), and thickness of the membrane (i.e., 10–40 µm) in comparison to the size of the COVID-19 virus. A unitless number (Nr) was introduced for the first time to describe semiempirical solutions of O2, N2, and CO2 gases through the porous membrane. An optimum Nr of expressing the flow of the inhaled air gases, O2 and N2, through the porous membrane was determined (NO2 = NN2 = −4.4) when an N95 facial mask of specifications of a = 20 nm, l = 30 µm, and ε = 30% was used as a personal protection equipment (PPE). The concept of the optimum number Nr can be standardized not only for testing commercially available facial masks as PPEs but also for designing new masks for protecting humans from the COVID-19 virus.

1.
A.
Habib
and
K.
Habib
, “
Modelling and quantification of gas flux through an artificial epidermis
,”
J. Biomimetics, Biomater., Tissue Eng.
1
,
49
56
(
2008
).
2.
J.
Akhtar
,
A. L.
Garcia
,
L.
Saenz
,
S.
Kuravi
,
F.
Shu
, and
K.
Kota
, “
Can face masks offer protection from airborne sneeze and cough droplets in close-up, face-to-face human interactions?—A quantitative study
,”
Phys. Fluids
32
,
127112
(
2020
).
3.
M. H.
Chua
,
W.
Cheng
,
S. S.
Goh
,
J.
Kong
,
B.
Li
,
J. Y. C.
Lim
,
L.
Mao
,
S.
Wang
,
K.
Xue
,
L.
Yang
,
E.
Ye
,
K.
Zhang
,
W. C. D.
Cheong
,
B. H.
Tan
,
Z.
Li
,
B. H.
Tan
,and
X. J.
Loh
, “
Face masks in the new COVID-19 normal: Materials, testing, and perspectives
,”
Research
2020
,
7286735
.
4.
T.
Dbouk
and
D.
Drikakis
, “
On coughing and airborne droplet transmission to humans
,”
Phys. Fluids
32
,
053310
(
2020
).
5.
T.
Dbouk
and
D.
Drikakis
, “
On respiratory droplets and face masks
,”
Phys. Fluids
32
,
063303
(
2020
).
6.
A.
Khosronejad
,
C.
Santoni
,
K.
Flora
,
Z.
Zhang
,
S.
Kang
,
S.
Payabvash
, and
F.
Sotiropoulos
, “
Fluid dynamics simulations show that facial masks can suppress the spread of COVID-19 in indoor environments
,”
AIP Adv.
10
,
125109
(
2020
).
7.
K. A.
Prather
,
C. C.
Wang
, and
R. T.
Schooley
, “
Reducing transmission of SARS-CoV-2
,”
Science
368
(
6498
),
1422
1424
(
2020
).
8.
S.
Kumar
and
H. P.
Lee
, “
The perspective of fluid flow behavior of respiratory droplets and aerosols through the facemasks in context of SARS-CoV-2
,”
Phys. Fluids
32
,
111301
(
2020
).
9.
R.
Mittal
,
R.
Ni
, and
J.
Seo
, “
The flow physics of COVID-19
,”
J. Fluid Mech.
894
,
F2
(
2020
).
10.
J. P.
Simpson
,
D. N.
Wong
,
L.
Verco
,
R.
Carter
,
M.
Dzidowski
, and
P. Y.
Chan
, “
Measurement of airborne particle exposure during simulated tracheal intubation using various proposed aerosol containment devices during the COVID-19 pandemic
,”
Anaesthesia
75
(
12
),
1587
1595
(
2020
).
11.
S.
Verma
,
M.
Dhanak
, and
J.
Frankenfield
, “
Visualizing the effectiveness of face masks in obstructing respiratory jets
,”
Phys. Fluids
32
,
061708
(
2020
).
12.
Engineers design a reusable, silicone rubber face mask, https://news.mit.edu/2020/reusable-silicone-rubber-face-mask-0709,
MIT News Office
,
Cambridge, MA
,
2020
.
13.
T.
Jefferson
,
R.
Foxlee
,
C. D.
Mar
,
L.
Dooley
,
E.
Ferroni
,
B.
Hewak
,
A.
Prabhala
,
S.
Nair
, and
A.
Rivetti
, “
Physical interventions to interrupt or reduce the spread of respiratory viruses: Systematic review
,”
Br. Med. J.
336
,
77
(
2008
).
14.
M.
van der Sande
,
P.
Teunis
, and
R.
Sabel
, “
Professional and home-made face masks reduce exposure to respiratory infections among the general population
,”
PLoS One
3
,
e2618
(
2008
).
15.
C. R.
MacIntyre
,
S.
Cauchemez
,
D. E.
Dwyer
,
H.
Seale
,
P.
Cheung
,
G.
Browne
,
M.
Fasher
,
J.
Wood
,
Z.
Gao
,
R.
Booy
, and
N.
Ferguson
, “
Face mask use and control of respiratory virus transmission in households
,”
Emerging Infect. Dis.
15
,
233
(
2009
).
16.
T. M.
Cook
, “
Personal protective equipment during the coronavirus disease (COVID) 2019 pandemic—A narrative review
,”
Anaesthesia
75
,
920
(
2020
).
17.
T.
Greenhalgh
,
M. B.
Schmid
,
T.
Czypionka
,
D.
Bassler
, and
L.
Gruer
, “
Face masks for the public during the COVID-19 crisis
,”
Br. Med. J.
369
,
m1435
(
2020
).
18.
C.
Matuschek
,
F.
Moll
,
H.
Fangerau
,
J. C.
Fischer
,
K.
Zänker
,
M.
van Griensven
,
M.
Schneider
,
D.
Kindgen-Milles
,
W. T.
Knoefel
,
A.
Lichtenberg
,
B.
Tamaskovics
,
F. J.
Djiepmo-Njanang
,
W.
Budach
,
S.
Corradini
,
D.
Häussinger
,
T.
Feldt
,
B.
Jensen
,
R.
Pelka
,
K.
Orth
,
M.
Peiper
,
O.
Grebe
,
K.
Maas
,
P. A.
Gerber
,
A.
Pedoto
,
E.
Bölke
, and
J.
Haussmann
, “
Face masks: Benefits and risks during the COVID-19 crisis
,”
Eur. J. Med. Res.
25
,
32
(
2020
).
19.
A. K.
Habib
and
K. J.
Habib
, “
Barriers to COVID-19 containment: The role of vulnerable populations
,”
J Pulm. Respir. Sci.
5
(
S1
),
000S1
006
(
2020
).
20.
World Health Organization
, Advice on the Use of Masks in the Context of COVID-19: Interim Guidance,” WHO Reference Number: WHO/2019-nCov/IPC Masks/2020.4,
World Health Organization
,
2020
.
21.
R.
Jackson
,
Transport in Porous Catalysis
(
Elsevier Science Publishers
,
Amsterdam
,
1977
).
22.
K.
Habib
and
A.
Habib
, “
General model of hydrogen transport through nanoporous membranes
,”
Composites, Part B
35
,
191
195
(
2004
).
23.
S.
Hwang
and
K.
Kammenmeyer
,
Membranes in Separations, Techniques in Chemistry
(
John Wiley and Sons
,
New York
,
1975
), Chap. VII, pp.
68
70
24.
The Penguin Dictionary of Physics
, edited by
V.
Illingworth
(
Penguin Books
,
London
,
1991
).
25.
See http://www.lmnoeng.com/Flow/GasViscosity.htm for Gas Viscosity Calculator.
26.
W. L.
Robb
, “
Thin silicone membranes‐their permeation properties and some applications
,”
Ann. N. Y. Acad. Sci.
146
,
119
(
1968
).
You do not currently have access to this content.