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

wannessambaer@gmail.com

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

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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.

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