Transcript 9.1: Summary of selected methods for improving filtration properties

Chapter 9.
FILTRATION
Part III.
Selected methods for improving filtration
properties
9.1: Summary of selected methods for improving filtration
properties:
•Filter density growth
•Filter thickness growth
•Defined fiber orientation
•Pleated filters
•Electrically charged filters
•Fiber diameter, microfibers, nanofibers
•Fiber shape
9.2 Filter density growth
Filter density  (or packing fraction c) increases filter efficiency and pressure
drop too.
9.2.1 Relation between packing fraction and filter efficiency:
We can suppose relation between packing fraction c and these filtration
mechanisms (see chapter 8.3 and 8.4):
1.
Inertial impaction:
Eir  - 1/(ln c)2
2.
Diffusional deposition:
ED  -1/(ln c)1/3
3.
(9.1)
Sieve effect:
1 c
Es 
c
(9.2)
(9.3)
Relation between efficiency of particular filtration
mechanisms and packing fraction
direct
inerception
10,0000
inertial
impaction+dire
ct interception
0,1000
0,0100
diffusional
deposition
0,0010
0,0001
0
0,05
0,1
0,15
Relation between the packing fraction and
calculated pore size (cylindrical fibers, fiber
diameter 20 micrometers, hexagonal structure)
0,2
packing fraction (1)
pore size (micrometers)
efficiency (%)
1,0000
500
400
300
200
100
0
0
0,05
0,1
0,15
0,2
packing fraction (1)
0,25
0,3
9.2.2 Relation between packing fraction and pressure drop
According to cell theory of Kuwabara for cylindrical fibers oriented
perpendicularly to flow we define:
p 
16.c .h. .U
(9.4)
 1
c2 
d f .  . ln c   0,75  c  
4
 2
2
Relation between packing fraction and calculated
pressure drop for needlepunch filter with thickness 4 mm,
fiber diameter 20 micrometers and air velocity 0,6 m/sec
pressure drop (Pa)
Where c is packing fraction, h is
filter thickness,  is viscosity, U is
face velocity and df is fiber
diameter [Brown, R.C., 1993].
4000
3500
3000
2500
2000
1500
1000
500
0
0
0,05
0,1
0,15
0,2
packing fraction (1)
0,25
0,3
9.4 Filter thickness growth
9.4.1 Filter efficiency:
We can assume that depth filter is made from large number of layers [Brown R C, 1993].
1. For monodisperse aerosol we can assume that number of particles penetrated through
one lyer of thickness x is proportional to beginning number of particles N, to the
thickness x and to the constant -  describing efficiency of the filter:
N = -  . N . x
(9.5).
We can solve it as a simple differential equation
ln (N(x)) + C = - x, and for assumption that for x=0 is N(x) = N0 we obtain equation:
ln (N(x)/N0) = - x 
N(x)/N0 = e -x = P .... penetration
(9.6)
2. For polydisperse aerosol we can assort particle sizes in classes and each size class is
characterised by specific filtration constant . For two sizes of aerosol with fraction
number  we obtain equation:
P= (1- ). exp (-1x) +  exp (- 2x)
(9.7)

and generally we obtain:
P ( x )   A .e  . x d
0
(9.8)
Penetration of
polydisperse aerosol
through the depth filter
9.4.2 Pressure drop – linear relation (see (9.4)).
9.5 Defined fiber orientation
9.5.1 Theory
The velocity field defined in each point of space is important to predict most of filtration
mechanisms and the pressure drop too. For the description of the velocity field is usually
used the stream function defined:
vx 


, vy 
y
x
(9.9),
where  is stream function, vx and vy are velocity in direction and x, y are co-ordinate
folders.
The calculation of stream function depends on which simplification we use. The simplest
case is an “isolated fibre theory” [] which assume only one fibre oriented perpendicularly
to incoming stream. The latter workers showed that this theory is overly simplified. The
effect of other fibres and the fibre orientation is so significant that is impossible to neglect
it or to involve only as boundary conditions. A simple form of Navier-Stokes equations
gives the pressure drop:
p  . 2U
(9.10),
where p is a Nabla operator of pressure drop,  is viscosity and 2U is a Laplace
operator of velocity []. The pressure drop is possible correctly counted for the isolated
fibre or for an array of fibres.
For isolate fibre oriented parallel with the stream in front of the filter is possible to
simplify the expression (5) because in 2D sight the pressure drop is changing only
along the axis y, which is perpendicular to the fibre axis x. The expression (9.10) is
changing:
dp
 . 2U y
dy
(9.11)
where dp/dy is the pressure derivation with respect to the axis y,  is viscosity and
2U is a Laplace operator of velocity. For the Kuwabara model of filter the pressure
drop is then expressed by formula:
2..c.h.U
p p 
c2 
2 
r . 0,5 ln( c)  0,75  c  
(9.12),
4

where pp is the pressure drop of fibres aligned parallel with the air stream,  is the
viscosity, c is the packing fraction, h is the filter thickness, U is the velocity of the air
in front of the filter and r is the fibre radius. For the filter with the fibres oriented
perpendicular to the air stream the pressure drop pk is two times bigger:
pk = 2pp
(9.13).
9.5.2 Verification and example of use
Relation (9.13) was verificated by model and real filters.
1. The model filter was designed as a cube contained the cluster of equally oriented straight
fibres. The cluster was prepared by cutting from polypropylene monofilament. Then was
the cluster uniformly packed into the paper cube and tested in two directions. It means that
the some structure was tested with different orientation of fibres to main stream. The test
result have validated relation 9.13.
Test parameters:
length of the cube edge: 70 mm, density of filter model: 120 kg/m3, material: polypropylene
monofilament, test device: Bench Rig CEN 1100, aerosol NaCl, size of filtered particles:
0,02 – 2 m, tested area: 49 cm2, air velocity: 0,6 m/sec
The flow oriented
perpendicularly to
the fibre direction
7 cm
The flow oriented
in parallel with
the fibre direction
Pressure drop (Pa)
Initial pressure drop of model filters
400
350
300
250
200
150
100
50
0
372
186
parallel direction of
perpendicular
fibres
direction of fibres
2. Real filters
Two types of filters were compared. Both of them can be used as air filters and prefilters.
They were made with the same parameters as far as the material composition, area weight
and thickness concerns. They differ in orientation of fibres. The first material has the fibres
oriented mainly perpendicularly to the air stream. This filter was made of cross laid and
thermo – bonded web. The second material has fibres oriented mainly parallel with the air
stream. This filter was made of perpendicular laid and thermo – bonded web. The filters
were tested during their life.
Cross laid
web
Perpendicularly
laid web
A method based on loading the air stream with synthetic dust was used to measure filtration
properties. The principle of the method consists in penetration of the dust particles with
defined size into the tested filter. The dust used in this test was the ASHRAE Standard 52.2
test dust [4]. The dust particles are dispersed in the air stream in defined concentration. The
air with the dust particles passes through tested filter at defined velocity. During the loading
process, the development of the filtration efficiency and the pressure drop are measured.
The testing is finished when the pressure drop reaches the value of 250 Pa.
Filter efficiency vs. weight of the filter
cross laid filter
perpendicularly laid filter
90
88
efficiency [% ]
86
84
82
80
300
350
400
450
500
550
weight [gsm]
Lifetime of the filters with weight 510 gsm
perpendicular laid sample- 507 gsm - efficiency 89,4%
cross laid sample - 511 - efficiency 89,7%
250
pressure drop [Pa]
Test results:
•The average efficiency changes when
the weight of the filter increases.
•Initial pressure drop don´t fulfil the
theoretical hypothesis. The difference is
not significant because the difference
between the fibrous structures is not
entirely achieved. It is impossible in real
filter to order all fibres along one defined
direction.
•Perpendicularly laid filter of area
weight around 500 gsm has two times
longer lifetime and approximately the
some efficiency than the cross laid filter.
This effect is possible to explain due to
the change of filter structure during the
filtration process. For a cross-laid filter
the particles, which are mostly captured
by direct interception concentrate on the
surface of filter. They create a non
permeable „cake“. In a perpendicularly
laid filter, the particles penetrate deeper
into the filter and they are more
uniformly dispersed in the fibre web.
200
150
100
50
0
0
10
20
30
time [min]
40
50
9.6 Pleated filters
9.6.1 Description:
HEPA (high efficiency particulate air) filters show high filtration efficiency
These are used in the clean rooms, hospitals, laboratories etc. As the
pressure drop of HEPA filters is rather high, these are often used pleated to
increase their effective surface. The trajectory of heat flow through pleated
filters is not straight. Therefore the air permeability is not proportional to the
total area of the filter when the number of pleats per area unit increases.
9.6.2 Theory:
When we assume that pleated filter is placed into the square pipeline it is possible to count
the real filter surface by formula:
Jeden sklad
b
h
2
x
A  y.n. 4.h 2  2
n
(9.14),
a
x
Where A is real filter surface, x and y is proportions of the square pipeline, h is the thickness
of pleated filter and n is the density of pleates (1/m).
Pleating process leads to bigger filter surface and linear relation between the pressure drop
and filter surface express very simple D´Arcy´s law. It is necessary to say that the material
constant is changing too. For the pleated filter is the trajectory of the air flow more
complicated so this flow is more inhibited. Thus the permeability constant of material little
decreased when number of pleates increased. Nevertheless when we increase number of
pleates the change of parameter k is smaller than the change of the filter surface until the
situation when pleats of filter are too close. The relation between the filter surface and the
filter efficiency is more complicated. Generally is possible to assume that for small captured
particles filter efficiency increase when the air velocity around the fibers decreases. When the
air flow is constant the air velocity around the fibers in pleated filter is smaller than in flat
filter. Hence the efficiency of pleated filter is usually bigger.
9.6.3 Experiment and results:
The fall of pressure drop is
significant. For bigger area
density little increase when
number of pleates is over critical
range (pleates are too close
together) .
SM 35 g/m2
100
Pressure drop (Pa)
Two. types of
spunbond/meltblown filters were
tested for NaCl aerosol particles
and face velocity 1 m/sec.
SM 117 g/m2
80
60
40
20
0
0
50
100
150
200
250
300
350
Density of pleates (number of pleates per meter)
SM 117 g/m2
SM 35 g/m2
Limiting structure
The efficiency little increase
because the velocity of the air
flowing around to fibers is
smaller and more complicated.
Pressure drop (Pa)
300
250
200
150
100
50
0
0
50
100
150
200
250
300
Density of pleates (number of pleates per meter)
350
9.8 Electricaly charged filter
The electrostatic charge inside the filter that is an added power to capture and hold
the particles loaded to filter (see chapter 8.3) without growth of pressure drop. Fibrous material
is not possible to consider as a solid material with homogenous electrostatic field. We assume
that individual fiber is an electric dipole and the total electrostatic field is very irregular,
because the fibers are not oriented regularly. Thus the principles which are used in physics are
more complicated.
The electrictrostatic charge arises in electret material. This is usually polymer, which
could be permanently polarized due to:
-Polar molecules dipoles inside polymer which are oriented by reason of external electric
field.
-Elementary electric dipoles, which arise by movement of electron/proton position due to
external electric field.
The polar material could be polarized more than non-polar but this electric field is unstable in
time due to fact that they are more hydrophilic. That is reason why the most common material,
which is commercially used for electrostatic charged filters, is polypropylene (or
polyethylene).
The fibrous material can be charged by means of the three methods:
1. Triboelectric process
Electrostatic charge arises due to the mechanical forces especially the friction. This
polarization usually makes unwanted property of polymers during it's processing .
2.
Corona charging
Within this method is a high voltage external electric field used to polarize the fibers before it's
processing or to polarize the finished filter. This charge is placed on the surface of the fibre.
3.
Electrostatic spinning
During the process of spinning when polymer is melted the external electrostatic field is
applied and then polar molecules are permanently oriented so the polarization of fibers is more
fixed in time.
Stability of charge in time:
Polarization of polymers is unstable in time (except electrostatic spinning) and the
electric field around the fiber dissipates. Consequently the filtration efficiency rapidly
decreases. Generally we know 3 main factors which increase the conductivity:
•Water or humidity, because the water is a medium with high inductive capacity and it act as a
"highway" for ions. The significance of humidity is bigger for the hydrophilic material.
•Temperature. The impact of temperature consists in fact that electric charge needs some
energy to move from it´s placement. When the temperature increases the charge kept in
shallow level of energy is lost [1].
•Radiation. The some reason as temperature. For example  radiation, X- ray, UV radiation...
•Captured particles that occupy charged surface of fiber and reduce electric charge.
How
filter efficiency increases after charging process
.
(corona charging, 30 kV)
Efficiency change of electrized needle
punch and spunbond/meltblown filter for
NaCl aerosol particles.
100
80
60
40
20
0
S/M
67,4
82,13
33
8,1
without charge
charged
needlepunch
Efficiency (%)
Efficiency (%)
needlepunch
Efficiency change of electrized needle
punch and spunbond/meltblown filter for
synthetic dust particles.
100
80
60
40
20
0
89,9
98
without charge
S/M
93,1 100
charged
Examples, how filter efficiency decreases during various test conditions.
.
Temperature (NaCl aerosol test):
Change of efficiency during heat exposition
90
Filtration efficiency (%)
80
70
N, 55 °C
SM, 55 °C
N, 100 °C
SM, 100 °C
N, no charge
SM, no charge
60
50
40
30
20
10
0
0
0,5
1
1,5
2
Exposition time (hours)
2,5
3
Relative humidity (NaCl aerosol test)
Long time test for change of efficiency during the
moisture exposing (highloft filter).
Change of efficiency during moisture exposition
N, 47 % RH
SM, 47 RH
90
N, 76 % RH
SM, 76 % RH
N, no charge
SM, no charge
70
charged, 670 gsm
without charge, 350 gsm
without charge, 670 gsm
90
60
80
50
70
40
60
Efficiency (%)
Filtration efficiency (%)
80
charged, 350 gsm
30
20
10
50
40
30
20
10
0
0
50
100
Exposition time (days)
150
0
0
50
100
150
200
250
Exposing time (days)
300
350
400
Combination moisture/temperature/captured particles (synthetic dust test)
Filter efficiency (%)
Change of efficiency during loaded dust, temperature and
moisture exposing.
without charge
charged
charged after moisture+temperature exposing
95
94
93
92
91
90
89
88
87
86
85
0
0,2
0,4
0,6
0,8
Loaded dust amount (g)
1
1,2
9.9 Fiber diameter, nanofibers
9.1 Benefit of small fiber diameter
Surface of 1 gram of PA6 fibers (m2)
The main benefit of smaller fiber diameter is the rapid increase of the filtration efficiency
with the less significant decrease of the air permeability and related less significant
increase of the pressure drop. In terms of the deep filtration the particle capture is given by
interaction between particles and fiber surface. All filtration mechanisms are determined
by fiber diameter. Figure shows the relation between the fiber diameter and relative fiber
surface (fiber surface per 1 gram of circular fibers).
It is possible to see that
Specific surface vs fiber diameter
for fiber diameter less
40
than 1 micrometer the
35
relative surface increase
30
very intensively.
25
Nevertheless the
20
pressure drop increases
15
too because the air flow
10
around the fibers is
5
decelerated due to
friction on fiber surface.
0
0.1
1
Fiber diameter (micrometer)
10
9.2 Benefit of submicron fibers
Boundary conditions of the flow around the submicron fibers, which are different compared
to other fibers. These conditions are called “slip flow” [Pich J, 1964]. Due to slip flow the
drag force decrease and the captured particles are carried more close to the fiber surface.
For the calculation of stream function we can start from simple idea of the second Newton’s
law expressed by simplified formula [Feynmann, 2000]:
. (acceleration) = -p -  + . 2v
(2)
In the formula left side  is density (mass to unit volume), acceleration is velocity change
along all co-ordinates and the time. In the right side are acting forces: pressure force to unit
volume, outer force to unit volume (gravity force for example) and inner force to unit
volume given by viscosity of fluid. Operators  (Nabla) and 2 (Laplace) change vector to
number and again number to vector. The most complicated member is the viscosity (or
drag) force, which is given by inner friction of fluid and friction between the fluid and fibre
surface. The definition of viscosity is expressed by Newton´s law:
 =  . vx/y,
(3)
where  is drag force to area in parallel with flow, vx/y is the velocity in parallel with
flow changed in direction perpendicular to flow and  is dynamic viscosity.
The main assumption of viscose fluid is that in the surface of static object the velocity is
zero. Nevertheless this assumption is valid only for very low values of Knudsen number. The
Knudsen number can be written as
(4),

Kn 
rf
where Kn is Knudsen number,  is the gas molecule mean free path and rf is specific
dimension – for fibres it is fibre diameter. For the air at standard conditions (atmospheric
pressure especially) is mean free path 0,067 m so for the fibre diameter smaller than 0,5 m
is the flow nature different. The velocity in the fibre surface is non-zero and this phenomenon
is called “slip flow”. It means that in this case the movements of air molecules are significant
and the flow is not continuous. The effect of slip flow needs to be considered when Kn is
around 0,25. Figure 4 shows the velocity profile of viscose flow around the fibre with
diameter bigger and smaller than 0,5 m.
velocity
Due to slip at the fibre surface is drag
profile
force of flow around fibre smaller for
submicron fibre than for bigger fibre so
the pressure drop is smaller too.
Furthermore the streamlines are placed
closer to fibre surface and this effect
10 m
0,1 m
lead to the bigger filter efficiency
[Graham K, 2002].
9.3 Comparation of various filtration materials
(with different parameters such as area density, thickness, material etc…)
100
90
80
Efficiency (%)
70
meltblown
charged meltblown
60
glass microfibers
needlepunch
50
40
air bonded bulk textile
PVAL nanospider
PA nanospider
30
20
PA/PUR nanospider
10
0
50
100
150
200
250
300
Pressure drop (Pa)
350
400
450
500
9.4 Examples how nanofiber layer improve filter properties:
Change of efficiency and pressure drop for spunbond (S) and spunbond /
meltblown (S/M) layer. S/M layer was electrized during the nanofiber spinning
proces (combination of electric charge and nanofiber affects).
100
95
90
85
80
75
70
65
60
55
50
Pressure drop
98,1
96,8
156
180
160
140
120
83
100
80
64
60
60,2
1
40
20
1,5
S
0
S/nano
S/M
S/M/nano
Pressure drop [Pa]
Efficiency [%]
Efficiency
Pressure drop for pleated polyamide nanofibers on the
paper sublayer
9.5 Pleated nanofiber layer
The way to reach HEPA
filters
pressure drop (Pa)
250
210
200
150
100
59
50
30
0
0
50
24
100
15
150
density of pleates (1/m)
Efficiency for pleated polyamide nanofibers on the paper
sublayer
Paper
sublayer
Nanofiber layer
efficiency (%)
100
95
89,1
90
91
92,49
93,87
93,25
100
150
85
80
0
50
density of pleates (1/m)
9.4 - Respirators – Example of the micron and submicron fibers application
Respirator filters are placed on the
human face and protect people against
the dust, viruses, bacteria, aerosols
etc. This type of filters must fit two
opposite requirements:
At first it is very low resistance against the flow, which is expressed as a pressure drop for
the engaged air flow rate. It is necessary to calculate on the potential of the human breath.
According to European standard EN 143 we had to follow maximum pressure drop 120 Pa
for the flow rate 30 l/min and 420 Pa for the flow rate 95 l/min respectively [EN 143, 2000].
At second it is high efficiency of capturing the filtered particles. The typical size of filtered
particles is shown in table 1. According the EN 143 standard the efficiency is tested for two
types of the particles. It is an aerosol NaCl with mean size 0,65 and paraffin oil with mean
size 0,4 m. Furthermore respirator must be antitoxic, resistant against the filtered particles
and water (from the human breath) and finally not very expensive.
Two melt-blown materials, electrostatic charged, which are used in respirators, were covered
by electrospun nanofibres. The filtration efficiency and pressure drop of the melt-blown –
nanofibre composite was measured as a function of area weight of nanofibre layers. Both
NaCl and paraffine methods were used to measure filtration efficiency. The pressure drop
was measured at two different air velocities.
efficiency (%)
Efficiency of capturing two types of particles vs.
nanofiber area density
100
99
98
97
96
95
94
93
Efficiency of
paraffin oil
particles
Efficiency of
NaCl aerosol
0
1
2
3
4
area density of
nanofiber layer (g/m2)
Efficiency of capturing NaCl and paraffin oil particles vs. nanofiber area density.
The test parameters (according EN 143 standard): Filtered particles were
polydisperse NaCl with mean size 0,65 m and polydisperse paraffin oil with mean
size 0,4 m, test air flow 95 l/min and filtration area 100 cm2.
pressure drop (%)
Meltblown only (95 l/min)
Meltblown only (30 l/min)
M+flat nanofibers (95 l/min)
M+flat nanofibers (30 l/min)
M+bulky nanofibers (95 l/min)
M+bulky nanofibers (30 l/min)
800
600
400
200
0
0
1
2
3
area density of nanofiber layer (g/m2)
Pressure drop of the respirator filter for the different area density of the PVA nanofiber
layer and for two different air flow rates. The test parameters (according EN 143
standard): Used particles NaCl, air flow 30 and 95 l/min, filtration area 100 cm2.
4
[Brown R C, 1993] BROWN, R. C.: Air filtration. 1st edition. Sheffield, 1993. ISBN 0
08 041274 2
[EN 143, 2000]
EN 143:2000: Respiratory protective devices-Particle filtersRequirements, testing, marking. European Comitee for Standardization,
Bruxelles 2000, Belgium.
[Feynman RP, 200] FEYNMAN, R. P., LEIGHTON, R.B., SANDS, M.: Feynmanovy
přednášky z fyziky s řešenými příklady. Sv.2/3. Praha 2000. ISBN
80-7200-420-4.
[Graham K, 2002] GRAHAM, K. et al.: Polymeric Nanofibers in Air Filtration Applications.
Fifteenth Annual Technical Conference  Expo of the American
Filtration  Separations Society, Texas, 2002
[Pich J, 1964]
PICH, J. Teorie filtrace aerosolů vláknitými a membránovými
filtry. Praha, 1964.