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Determination of Pressure Drop and Filtration Efficiency
of Filled Nanofiber Based Filters by using 3D Filtration Model
WANNES SAMBAER1,2
, MARTIN ZATLOUKAL1,2
and DUSAN KIMMER3
1Centre of Polymer Systems, University Institute
Tomas Bata University in Zlin
Nad Ovcirnou 3685, 760 01 Zlin
CZECH REPUBLIC
2Polymer Centre, Faculty of Technology
Tomas Bata University in Zlin
TGM 275, 762 72 Zlin
CZECH REPUBLIC 3SPUR a.s.
T. Bati 299, 764 22 Zlin
CZECH REPUBLIC
Abstract: In this work, two different boundary conditions dealing with the filter cake formation due to particle-
particle interaction (fully sticking and slip conditions) has been tested in a theoretical study. Filtration efficien-
cy and pressure drop are evaluated utilizing realistic SEM image based 3D structure model, transition/free mo-
lecular flow regime, Brownian diffusion, particle-fiber interactions, aerodynamic slip and sieve. It has been
found that the filtration efficiency of the fully sticking condition is higher than when particle slip was allowed.
The pressure drop shows the opposite trends. Additionally, visualisations of the cake formation were created
and has revealed that the cake is double in size and less dense in case of full sticking conditions.
Key-Words: Cake formation, Nanofiber Based Filter, 3D Filtration Modeling
1 Introduction Nanofibers based nonwovens are widely applied in
different areas such as filter media, tissue
engineering, personal protective clothing, cosmetic
skin care, life science, nanosensors and other
medical and industrial applications [1-6]. Filter
media is one of the largest application group of nan-
ofiber nonwovens due to their small fibers (having
fiber diameter typically in order of tens and hun-
dreds of nanometers), high surface area (which sig-
nificantly increases their filtration efficiency), and
low filtration pressure drop (due to aerodynamic slip
occurrence at the nanofiber surfaces). Until now,
numerous studies were done to get a better under-
standing in the filtration mechanism. Therefore ex-
perimental studies [7-8] as well as theoretical stud-
ies [9-14] on clean and filled filters have been done.
This work will focus on cake formation due to parti-
cle-particle interactions during the filtration process.
In several studies dealing with cake formation the
fully sticking boundary condition has been used
which has been experimentally proved for certain
test conditions for particle sizes between 10 nm and
5 µm [15-16]. This assumption has been used in
other cake forming investigation studies. On the
other hand there are also more advanced theories
were particle chains are dynamic and are able to
bend or break [19]. Therefore, in this work a theo-
retical comparison between two different boundary
conditions for particle-particle interactions applied
on nanofiber based filters penetrated by ultra-fine
particles will be examined. To full fill this aim, a 3D
filter media model has been created and the filtra-
tion efficiency and pressure drop methodology has
been suggested and used to simulate air filtration
considering both suggested boundary conditions.
2 Filter Media Model Creation In this work the methodology proposed in our pre-
vious work [20] has been applied to create a 3D fil-
ter media model. This methodology utilizes a SEM
top view image of the nanofiber based filter to build
up the model. Here, the nanofiber based filter pre-
pared by electrospinning is used, see Fig. 1. This
grayscale SEM image has been transformed to a
black/white image by applying a proper threshold
level. In the following step the centerlines have been
calculated from this binary image and a single three
dimensional layer has been created by fitting
spheres in the fiber area with as centerpoint a point
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 144
of the centreline. In the final step these single layers
have been combined to reach the complete 3D mod-
el according the experimentally defined mass area
of the filter. A perspective view of the used filtration
media model in this work is depicted in Fig. 2.
Fig. 1: SEM image of a nanofibers nonwoven based
filter prepared by electrospinning process.
Fig. 2: Utilized 3D model of the filtration media.
3 Filtration Process Simulation 3.1 Flow Field Calculation In this work, the filtration efficiency is predicted by
tracing each individual particle inside the nanofiber
structure considering small fiber diameters/particles
and low pressure drops. In such case, the gas flow
field can be assumed to be uniform due to signifi-
cant slip flow occurrence at the fiber surface as sug-
gested by Maze et al. [13]. In the utilized filtration
model, the Brownian motion is the driven force of
the particle movement and has been calculated with
the equations defined by Maze et al. [13].
3.2 Fiber-Particle Interaction
When a fiber-particle interaction occurs during the
flow, the stick or slip at the fiber surface is defined
by the force balance developed in our previous work
[11] based on the force balance suggested by J.
Altmann and S. Ripperger [22]. This force balance
takes the drag force, lift force, van der Waals force
and friction force between fiber and particle into
account. It is assumed here that the flow through the
particular pore between the fibers can be viewed as
the Poiseuille flow in a 2D duct, which is character-
ized by its gap distance and height. Due to the aero-
dynamic slip created by the thin fibers the gas vis-
cosity has been corrected at high Knudsen numbers
(Kn>0.01). In order to calculate this corrected vis-
cosity the viscosity definition proposed by M.J.
McNenly et al. [23] has been used in our filtration
model.
3.3 Particle-Particle Interaction In order to investigate the possible differences in
cake formation due to particle-particle interaction in
static and dynamic conditions, two different bound-
ary conditions has been proposed and tested.
The first assumption, which is generally used [15-
18], takes no particle-particle slip into account. This
means that fully sticking conditions between parti-
cles will be applied as illustrated in Fig 3a. In this
case the buildup chains will be seen as static, which
means that they cannot bend or break down during
the filtration process.
In the second assumption, slip around the particle is
allowed to simulate the dynamic like character of
the particle-particle interaction. Therefore it is as-
sumed that a particle can slip over another particle
until two connection points (between particle-
particle or particle-fiber) has been reached. In Fig
3b, the situation is shown where a first particle is
touched to the fiber surface and a second particle
slips over it until an extra touching point with the
fiber is obtained. The next particle slips over the
previous until the condition of two touching points,
in this case a particle, is fulfilled. It has to be men-
tioned that the particles are slipping over each other
in a plane defined by the touching point and the ver-
tically aligned centerline though the particle.
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 145
Fig.3: Two boundary conditions descriptions;
a. Single touching point, b. Double touching points
4 Proposed Pressure Drop Calcula-
tion In order to evaluate the pressure drop during the
filtration process over a filled filter a novel tech-
nique has been proposed in this work. This method-
ology utilizing the generated 3D model for pressure
drop calculation, which is depicted in Fig. 2. To de-
fine the overall pressure drop through the structure
the model has been divided in numerous thin layers
with equal thickness as illustrated in Fig. 4a. From
all this thin layers the pressure drop has been calcu-
lated with the main assumption that the air flow is
based on the pore size normalization with respect to
the largest in this single layer. In order to evaluate
the biggest pore the Euclidian distance map of a
single binary layer (see Fig. 4b.) has been used. In a
distance map, all black pixels (representing a pore)
are labelled with a number (visualized by a gray-
scale value) which gives the shortest distance to a
white pixel (representing a fiber) as illustrated in
Fig. 4c. The maximum found value in the obtained
distance map has been used as maximum pore radi-
us used in the basic equation to calculate the pres-
sure drop over a circular capillary, expressed as:
∆� = �.�.�.
�.�.� .�� , Eq. 1
where Q is the volume flow rate of the air through
the filter, L is the height of a single slice, R is the
radius of the representative pore and η’ is the Knud-
sen number dependent gas viscosity defined by
McNenly et al. [23] as
( )[ ]3
210 arctana
pKaaa +=′ ηη
Eq. 2
where η is the gas viscosity at given pressure and
temperature, a0=1.066, a1=0.679, a2= -2.082, a3=
0.866. Kp is particle based Knudsen number defined
as 2λ/dp, where λ is the mean free path of molecules
and dp is particle diameter.
The sum of all pressure drops calculated according
the previous described calculation for every slice of
the model will result in the overall pressure drop
over the filter model.
This methodology has been verified for four differ-
ent nanofiber based filters produced from a polyure-
thane solution by electrospinning and it has been
found that the suggested methodology is able to cap-
ture the trends in a good way with a certain over-
prediction as shown in the bar plot in Fig. 5.
In this work this suggested technique will be used to
calculate the pressure drop over filled filter struc-
tures for one filter type during the filtration process.
Fig. 4: Pressure drop calculation based on slices of
the fiber media model and creation of the distance
map
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ISBN: 978-1-61804-065-7 146
0
100
200
300
Pre
ss
ure
Dro
p [
Pa
]
Simulation
Measured
A B C D Fig. 5: Bar plot of the measured and simulated
pressure drop for four different nanofiber based
filters.
5 Theoretical Study and Discussion In this part of the work, two above-described possi-
ble particle-particle boundary definitions will be
evaluated and tested with respect to the filtration
efficiency and pressure drop predictions during the
cake formation on top of the nanofiber based filter.
Therefore, a filter model has been build up based on
the SEM image depicted in Fig.1 as described be-
fore (see Fig. 2). In the next step an experimentally
determined particle distribution given in Table 1 of
50000 particles has been randomly penetrated
through the model considering both types of bound-
ary conditions. Hereby the filtration efficiency and
the pressure drop during the simulation for both
considered boundary conditions have been visual-
ized in Fig 6.
Table 1: Experimentally defined particle distribu-
tion.
Particle Size [nm] Fraction [%]
20 0.35%
35 10.08%
50 24.83%
70 31.25%
100 20.27%
140 9.69%
200 2.90%
280 0.59%
400 0.06%
From this graph it can be seen that the filtration effi-
ciency in the case of the full stick between the parti-
cles will increase faster than in case of the slip over
the particles is allowed. This can be explained by
the fact that the cake growing rate will be more pro-
nounced in the first case. Moreover it has been
found that the pressure drop is higher in the case of
two touching points has been required. Due to this
allowed slip the particle will penetrate deeper in the
structure and the pore size will decrease, which will
result in a higher pressure drop. The steeper increase
located at a higher mass area, shows that at this load
level the structure get satisfied with particles which
lead to a pressure increase. This is not the case when
single stick has been used. In this case a linear in-
crease in the pressure drop is obtained.
Fig. 6: Filtration efficiency and pressure drop as a
function of mass area for both boundary conditions.
In order to visualize the differences in the cake for-
mation, the simulated structures with the build up
cakes is shown in Fig.7. in perspective, side and cut
top view. In these visual represented simulation re-
sults, it can clearly be seen that the cake height is
approximately double in high for the single contact
point condition. Moreover it can be seen that less
particles can penetrate deep in the structure when
fully stick condition is applied which explains the
better filtration efficiency. From the cut view,
which has been made just above the upper fiber, can
be seen that the cake is much denser in the case of
two touching points which obviously leads to higher
pressure drops as shown before.
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 147
Fig. 7: Cake formation in perspective, side and cut
view for the two performed simulations.
6 Conclusion In this work a three dimensional nanofiber nonwo-
ven filter media model has been created based on a
SEM image. A theoretical study of the cake for-
mation due to particle-particle interactions has been
done for two different boundary conditions (no slip
and slip). In this study it has been found that in case
of full particle-particle interaction (no slip) the effi-
ciency is higher while the pressure drop is lower in
comparison with the case when particle slip is al-
lowed. Additionally, a visual representation of the
cake formations for both cases has revealed that the
cake height is double for no slip condition in com-
parison with the particle-particle slip condition.
Acknowledgements:
The authors wish to acknowledge the Grant Agency
of the Czech Republic (grant No. P108/10/1325)
and Operational Program Research and Develop-
ment for Innovations co-funded by the European
Regional Development Fund (ERDF) and national
budget of Czech Republic, within the framework of
project Centre of Polymer Systems (reg. number:
CZ.1.05/2.1.00/03.0111) for the financial support.
References:
[1] Brown R.C. Air Filtration: An integrated Ap-
prouch to the Theory and Applications of Fi-
brous Filters, Oxford: Pergamon Press, 1993.
[2] Brown, P.J., and Stevens, K. Nanofiber and
nanotechnology in textiles, Cambridge: Wood-
head publishing, 2007.
[3] Andrady, A.L., Science and technology of
polymers nanofibers, John Wiley & Sons, Inc.,
New Jersey, 2008.
[4] Hutten, I.M. Handbook of Nonwoven Filter
Media, Burlington: Elsevier, 2007.
[5] Huang, Z.M., Zhang, Y.Z., Kotika, M., et
al., A review on polymer nanofibers by electro-
spinning and their applications in nanocompo-
sites, Composite Science and Technology,
Vol.63, 2003, pp.2223-2253.
[6] Kimmer, D., Vincent, I., Petras, D., Fenyk,
J., Zatloukal, M., Sambaer, et al., Application of
Nanofibres in Filtration Processes, Nanocon
2010, 2nd International Conference, pp.415-422.
[7] Leung, W.W.F., Hung C.H. and Yuen P.T.
Effect of face velocity, nanofiber packing density
and thickness on filtration performance of filters
with nanofibers coated on a substrate , Sep. Purif.
Technol., Vol. 71, No.1, 2010, pp.30-37.
[8] Podgorski, A., Balazy A. and Gradon L. Ap-
plication of nanofibers to improve the filtration
efficiency of the most penetrating aerosol parti-
cles in fibrous filters, Chem. Eng. Sci,. Vol. 61,
2006, pp.6804-6815.
[9] Hosseini S.A. and Tafreshi H.V. Modeling
particle filtration in disordered 2-D domains: A
comparison with cell models, Sep. Purif. Tech-
nol., Vol. 74, 2010, pp.160-169.
[10] Zhou B., Tronville P. and Rivers R. Genera-
tion of 2-Dimensional Models for CFD Simula-
tion of Fibrous Filter Media with Binder, Fibers
and Polymers, Vol. 10, No. 4, 2009, pp.526-538.
[11] Sambaer W., Zatloukal M. and Kimmer D.
3D modeling of filtraion process via polyure-
thance nanofiber based nonwoven filters pre-
pared by electrospinning process, Chem. Eng.
Sci., Vol. 66, 2011, pp.613-623.
[12] Maze B., Tafreshi H.V., Wang Q.,
Pourdeyhimi B. A simulation of unsteady-state
filtration via nanofiber media at reduced operat-
ing pressures, J. Aerosol Sci., Vol. 38, No. 5,
2007, pp.550-571.
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 148
[13] Hosseini S.A. and Tafreshi H.V. Modeling
permeability of 3-D nanofiber media in slip flow
regime, Chem. Eng. Sci., Vol. 65, 2010, pp.2249-
2254.
[14] Hosseini S.A. and Tafreshi H.V. 3-D simu-
lation of particle filtration in electrospun nano-
fibrous filters, Power Technol., Vol. 201, 2010,
pp.153-160.
[15] Wang H.C. and Kasper G. Filtration effi-
ciency of nanometer-size aerosol-particles, J.
Aerosol Sci., Vol. 22 , No. 1, 1991, pp. 31–41.
[16] Pawu K.T. and Braaten D.A. New perspec-
tives on rebound and re-entrainment process-
es, Aerosol Sci. Tech., Vol. 23 , No. 1, 1995, pp.
72–79.
[17] Mädler L., Lall A.A. and Friedlander S.K.
One-step aerosol synthesis of nanoparticle ag-
glomerate films: Simulation of film porosity and
thickness, Nanotechnology Vol. 17, No. 19,
2006, pp. 4783–4795.
[18] Rodríguez-pérez D., Castillo J.L. and
Antoranz J.C. Relationship between particle de-
posit characteristics and the mechanism of par-
ticle arrival, Physical Review Letters, Vol. 72,
No. 2, 2005, pp. 021403-1–021403-9.
[19] Huang, B., Turton R., Park J., Famouri P,
and Boyle E.J. Dynamic model of the riser in cir-
culating fluidized bed, Powder Technol., Vol.
163, No. 1-2, 2006, pp. 23-31.
[20] Sambaer, W., Zatloukal, M. and Kimmer,
D., 3D modeling of filtration process via polyu-
rethane nanofiber based nonwoven filters pre-
pared by electrospinning process, Chemical En-
gineering and Science, Vol.66, 2011, pp.613-
623.
[21] Maze, B., Tafreshi, H.V., Wang, Q.,
Pourdeyhimi, B, A simulation of unsteady-state
filtration via nanofiber media at reduced operat-
ing pressures, Journal of Aerosol Science
Vol.38, 2007, pp.550-571.
[22] Altmann, J., Ripperger, S., Particle deposi-
tion and layer formation at the crossflow micro-
filtration, Journal of membrane Science,
Vol.124, 1997, pp.119-128.
[23] McNenly, M.J., Gallis, M.A., Boyd, I.D.,
Empirical slip and viscosity model performance
for microscale gas flow, International Journal
for Numerical Methods in Fluids, Vol.49, 2005,
pp.1169-1191.
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 149