slip airflow regime is characterized by an
increase in the Knudsen number, resulting in an
increased filtration efficiency via the slip effect.
The free molecular flow regime is a dominant
regime in which the diameter of fibers is much
smaller than the mean free path of the gas molecules. In general, nanoparticle-capturing fibers,
including electrospun fibrous filters and carbon
Airborne Nanoparticles: Control and Detection, Table 2 The filtration mechanisms and their filtration efficiency
Filtration mechanism
Single-fiber filtration efficiency
Definition
Point
Interception
Fiber
E R ¼
1Àa
ð
Þ R
2
Ku 1þR
ð
Þ or,
E R ¼ 0:6
1Àa
ð
Þ R
2
Ku 1þR
ð
Þ
1 þ
kn
R
À
Á
R ¼
dp
df
K u ¼ À
Ln a
2 À
3
4 þ a À
a
2
4
E R : filtration
efficiency by
the
interception
d p : particle
diameter
d f : fiber
diameter
K u : Kuwabara
hydrodynamic
factor
a: packing
density
(solidity)
Only a deposition
mechanism does not
result from a particle
departing from its
original streamline
Inertial impaction
Fiber
E I ¼
STK
ð
Þ J
2Ku
2
STK ¼
r p d
2
p CcU0
18mdf
J ¼ (29.6 À 28a
0.62
)R
2 À 27.5R
2.8
E I : filtration
efficiency by
the impaction
STK: Stokes
number
J:
dimensionless
Cc:
Cunningham
coefficient
r p : particle
density
m: air dynamic
viscosity
The most important
deposition mechanism
for large particles
Diffusion (Brownian
motion)
Fiber
E D ¼ 1:6
1Àa
Ku
1=3 2Pe
À2 = 3
Pe ¼
df U0
D
D ¼
kbTCs
3pmDp
C s ¼ 1 þ K n 1:027 þ 0:44 exp À0:78 = Kn
À
Á
Â
E D : filtration
efficiency by
the diffusion
P e : Peclet
number
D: particle
diffusion
coefficient
k b : Boltzmann
constant
T: absolute
temperature
C s :
Cunningham
slip correction
Only the deposition
mechanism that
increases as the
particle diameter
increases
Electrostatic deposition
Fiber _
Difficult to quantify because it requires
knowing the charge on the particles and
on the fibers
–
This mechanism is
often neglected unless
the particles and/or
fibers have been
charged in some
quantifiable way
92
Airborne Nanoparticles: Control and Detection
increase in the Knudsen number, resulting in an
increased filtration efficiency via the slip effect.
The free molecular flow regime is a dominant
regime in which the diameter of fibers is much
smaller than the mean free path of the gas molecules. In general, nanoparticle-capturing fibers,
including electrospun fibrous filters and carbon
Airborne Nanoparticles: Control and Detection, Table 2 The filtration mechanisms and their filtration efficiency
Filtration mechanism
Single-fiber filtration efficiency
Definition
Point
Interception
Fiber
E R ¼
1Àa
ð
Þ R
2
Ku 1þR
ð
Þ or,
E R ¼ 0:6
1Àa
ð
Þ R
2
Ku 1þR
ð
Þ
1 þ
kn
R
À
Á
R ¼
dp
df
K u ¼ À
Ln a
2 À
3
4 þ a À
a
2
4
E R : filtration
efficiency by
the
interception
d p : particle
diameter
d f : fiber
diameter
K u : Kuwabara
hydrodynamic
factor
a: packing
density
(solidity)
Only a deposition
mechanism does not
result from a particle
departing from its
original streamline
Inertial impaction
Fiber
E I ¼
STK
ð
Þ J
2Ku
2
STK ¼
r p d
2
p CcU0
18mdf
J ¼ (29.6 À 28a
0.62
)R
2 À 27.5R
2.8
E I : filtration
efficiency by
the impaction
STK: Stokes
number
J:
dimensionless
Cc:
Cunningham
coefficient
r p : particle
density
m: air dynamic
viscosity
The most important
deposition mechanism
for large particles
Diffusion (Brownian
motion)
Fiber
E D ¼ 1:6
1Àa
Ku
1=3 2Pe
À2 = 3
Pe ¼
df U0
D
D ¼
kbTCs
3pmDp
C s ¼ 1 þ K n 1:027 þ 0:44 exp À0:78 = Kn
À
Á
Â
E D : filtration
efficiency by
the diffusion
P e : Peclet
number
D: particle
diffusion
coefficient
k b : Boltzmann
constant
T: absolute
temperature
C s :
Cunningham
slip correction
Only the deposition
mechanism that
increases as the
particle diameter
increases
Electrostatic deposition
Fiber _
Difficult to quantify because it requires
knowing the charge on the particles and
on the fibers
–
This mechanism is
often neglected unless
the particles and/or
fibers have been
charged in some
quantifiable way
92
Airborne Nanoparticles: Control and Detection