Investigation of Filtration Efficiency of Nanofiber Based Filters in

Ultrafine Particles Range during Cake Formation

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: A filtration model taking particle-fiber as well as particle-particle interactions into account was

suggested and applied on a 3D simulation model of the nanofiber based filter, which was based on its SEM

image. A theoretical study was done to evaluate the filtration efficiency as a function of number of particles,

way of distributing the particles and the penetration profile through the filter. It was clearly shown that the cake

formation has a significant effect on the filtration efficiency. Additionally, a visual representation of the cake

formation was generated according the suggested model to get a better understanding of the cake morphology.

Key-Words: Nanofiber Based Filter, Cake Formation, 3D Filtration Modeling, Electrospinning

1 Introduction Fibrous based air filters are widely used to filter

particles out of air. Nowadays nanofiber nonwoven

based filters are of high interest due to their ability

to reach a high filtration efficiency for ultrafine

particles with a low pressure drop due to

aerodynamic slip around the nanofibers. Until now

numerals studies were done in order to predict the

filtration efficiency of such filters. These studies has

been done experimentally [1-2] and theoretically in

two-dimensions [3-4] as well as in three-dimensions

[5-8] but their predicting capabilities are reduced

because the utilized filtration models are not taking

clogging of particles in the filter into account. On

the other hand, several research workers have

developed models, based on experimental research,

which are taking clogging into account [9-12].

Experimental and theoretical analyses of deposition

morphology were already successfully established

for fiber structures [13-16] and tube geometries [17-

19]. From these studies it has been found that the

accumulation of particles can be defined in three

steps [19]. In the first step capillary deposition takes

place, which occurs when particles are touched to

the surface of the filter media. This is followed by

capillary clogging, which is accumulation of

particles due to sticking of the particles to the fiber

surface in combination with the interception of

already caught particles. In the final step, the

particles are only caught by interception of other

particles, which leads to a large increase in cake

growth. Until now this type of filtration simulations,

taking clogging into account, has mainly been done

for microfiber structures or for tube geometries but

has not often been applied for nanofiber nonwoven

structures. Therefore the aim in this work is to

evaluate the effect of clogging of the filter, during

the time by taking particle-particle as well as

particle-fiber interaction (including aerodynamic

slip and Brownian motion of the particles), on the

filtration efficiency into account within a transition-

free molecular flow regime.

2 Model Development 2.1 Filter Media Model

In order to create a 3D filter media model the

methodology introduced in our previous work [5]

has been used. This methodology to create a 3D

media model is based on a SEM image of the

nanofiber based filter which taken from. The top

fibers from this SEM image have been filtered by

applying a well-defined threshold level to make a

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

ISBN: 978-1-61804-065-7 138

black/white image from the greyscale image. In the

following step, the centerlines are calculated and

circles are fitted in the fiber area with as center point

a point of the centerline. In the last step, the circles

are rotated according the depth and a 3D model

layer is created. This model layers are used to create

the complete 3D model according the

experimentally defined mass area. The result of the

filtration media model obtained by this methodology

can be seen in Fig 1, where eight stacked layers

inside, at the top as well as in the perspective view

are depicted. The mass area was equal to the

experimentally defined mass area (0.877 g/m²) and

the thickness of the nonwoven model was calculated

to be 4.49 µm. Additionally, the morphological

properties were measure according our previous

work [20] and it has been found that the average

fiber diameter is approximately 120nm and the

average pore size 200 nm.

Fig 1: Used filtration media model shown in

perspective, top and side view.

2.2 Filtration Model

2.2.1 Flow Field Calculation Due to the small fibers in the structure aerodynamic

slip can occur. The amount of slip is defined by the

Knudsen number (fdKn /2λ= ), which shows that

in the range of fibers used in this work the flow is in

the transition-free molecular regime (Kn > 0.25).

Therefore absolute slip around the fibers can be

assumed as suggested by Maze et al. [6]. This leads

to the condition that the flow paths around the fibers

are not taken into account because the Brownian

motion is the driven flow for the particles in this

case. In this work the equations suggested by Maze

et al. [6] has been used for the calculation of the

Brownian diffusion paths.

2.2.2 Particle-Fiber Interaction

When a particle during its flow through the air gets

in contact with a fiber the particle can be caught due

to several types of attraction forces or it can slip

around the fiber due to aerodynamic slip. In order to

decide this, a force balance was used. The main

forces which are taken into account are the drag

force "FD", the lift force "FL", the adhesion force

"FA" and the friction force "FF" shown in a

simplified force balance in Fig 2. The equations

utilized for this force balance are summarized in the

following table (see Table 1). As a result of those

forces a decision can be made concerning the slip

around the fiber or attachment of the particle to the

fiber.

Table 1: Particle-Fiber interaction equations.

Equation Type Equation

Drag force 2

pwD d16.3F πτ=

Wall shear stress γητ &=w

Reduced gas

viscosity ( )[ ]3a

n210 Kaarctanaa +η′=η

Lift force

η

ρτ=

5.0

f

3

P

5.1

wL

d761.0F

Adhesion force

+=

21

21

2

_

6

25.1

RR

RR

aFA

ωπ h

Friction force totNF FF µ=

Friction coefficient f'µµ =

Parameter as

a function of Kn ( )3

210 arctana

dKnaaaf +=

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

ISBN: 978-1-61804-065-7 139

α

Fig 2: Suggested force balance for the particle-fiber

interaction.

2.2.3 Particle-Particle Interaction

In this work both, particle-fiber interaction

(described above) as well as particle-particle

interactions are taken into account. These

interactions are viewed as fully sticking boundary

conditions for particles between 10nm and 5µm.

This condition has been experimentally proved by

Wang and Kasper [21] and Pawu and Braaten [22].

This assumption has also been followed in several

other works in this area [19;23-24]. Therefore, the

dendrites formation during the filtration process will

build up due to this fully particle-particle stick

conditions. In this work, the dendrites will be

viewed in a static way, which means that the

dendrites will not deform or break down during the

filtration process as described in the work of Huang

et al. [18] due to the complexity of the model.

3 Experimental 3.1 Filtration Efficiency during Cake Formation In this study the simulated filtration media model

has been penetrated with 50000 particles, with an

experimentally defined distribution shown in Fig. 3.

The filtration efficiency was recorded during the

cake creation and plotted as a function of the mass

area (see Fig. 4). It has been found that the filtration

efficiency increases fast at the beginning and goes

slowly to the maximum filtration efficiency. This

can be explained by the strong particle-particle

interactions which are taking place during the

filtration process. As the amount of caught particles

is increasing, the particle-particle interactions are

increasing quickly due to a larger volume taken by

particles. This trend has also been shown in

experimental filtration tests by Thomas et al [13].

Additionally a visual representation is shown in Fig.

5 where the cake formation morphology can be seen

for this simulation.

10 100 1000

Particles Size [nm]

0

0.1

0.2

0.3

Nu

mb

er

of

Pa

rtic

les

pe

rA

rea

Fig 3: Particle distribution expressed as number of

particles per area as a function of particle size.

Fig 4: Filtration efficiency as a function of mass

area of the caught particles.

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

ISBN: 978-1-61804-065-7 140

Fig 5: Visualization of the penetration profile for

50000 randomly distributed particles.

3.2 The Effect of Distribution Type on the

Filtration Efficiency In the following simulation experiment the effect of

the distribution type on the filtration efficiency has

been investigated. In order to full fill this aim, three

independent simulations (with the previously given

distribution) have been performed and shown in Fig.

6. In the first simulation, the particles have been

injected from small to larger sizes. The filtration

efficiency curve results shows a large penetration of

small particles through the filter because in this

stage of the filter was relative clean. Larger particles

were caught by the interaction with the previously

caught smaller particles which results in a high

filtration efficiency for these particle sizes.

On the other hand, when in the second experiment

the order is reversed, the filtration efficiency is very

high due to the fact that large particles will take a lot

of volume to create particle-particle interactions.

Additionally the pores between the fibers are closed

which prevents infiltration of other particles.

In the third experiment, when the particles are

randomly distributed the filtration efficiency curve

shows a situation in between the previous two

simulations.

Fig 6: Filtration efficiency as a function of particle

size for three different ways of particle injection.

3.3 Penetration Profile inside the Filter In the following graph (see Fig. 7) the penetration

profile through the filter for different particle sizes

is provided. In this Figure, the volume ratio of the

caught particles (defined as the ratio of the caught

particle volume at given position to overall volume

of all caught particles in the filter). Note that, an

overall particle volume has been the same for all

considered particle sizes. It can be clearly seen that

particles with a smaller diameter are penetrating

deeper then particles with a larger diameter due to

sieve effect between the fibers. This can also be

clearly seen in the illustration depicted in Fig. 8.

Fig 7: Penetration profile inside the filter for three

different particles sizes.

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

ISBN: 978-1-61804-065-7 141

Fig 8: Visualization of the penetration profile for

particles with sizes 100, 200 and 300nm.

4 Conclusion It has been showed that the filtration efficiency can

be considerably increased due to cake formation on

the filter. It has also been shown that the order in

which the different particle sizes are injected into

nanofiber based filter has a significant influence on

the final filtration efficiency. Moreover, the

penetration of different particles sizes through the

filter has been investigated and visually represented.

5 List of Symbols µ [ - ] Friction coefficient

γ& [s-1

] Shear rate at the fiber wall

η [Pa s] Liquid viscosity

η' [Pa s] Normal gas viscosity

η'' [Pa s] Reduced gas viscosity

ρf [kg/m³] Fluid density

τw [N/m²] Local fiber wall shear stress

a [m] Adhesive distance

(0.4×10-9

m)

a0 [ - ] Constant 0=1.066,

a1 [ - ] Constant 1=0.679

a2 [ - ] Constant 2= -2.082

a3 [ - ] Constant 3= 0.866

dp [m] Particle diameter

FD [N] Drag force

FF [N] Friction force

FL [N] Lift force

FN [N] Normal force

Kn [ - ] Knudsen number

Knd [ - ] Particle diameter based

Knudsen number _

ωh [J] Lifschitz-van der Waals

constant (10-20

J)

Acknowledgements:

The authors wish to acknowledge the Grant Agency

of the Czech Republic (grant No. P108/10/1325)

and Operational Program Research and

Development 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] 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.

[2] Podgorski, A., Balazy A. and Gradon L.

Application of nanofibers to improve the

filtration efficiency of the most penetrating

aerosol particles in fibrous filters, Chem. Eng.

Sci. Vol. 61, 2006, pp.6804-6815.

[3] Hosseini S.A. and Tafreshi H.V. Modeling

particle filtration in disordered 2-D domains:

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

ISBN: 978-1-61804-065-7 142

A comparison with cell models, Sep. Purif.

Technol. Vol. 74, 2010, pp.160-169.

[4] Zhou B., Tronville P. and Rivers R.

Generation of 2-Dimensional Models for CFD

Simulation of Fibrous Filter Midea with

Binder, Fibers and Polymers, Vol. 10, No. 4,

2009, pp.526-538.

[5] Sambaer W., Zatloukal M. and Kimmer D. 3D

modeling of filtration process via

polyurethance nanofiber based nonwoven

filters prepared by electrospinning process,

Chem. Eng. Sci. Vol. 66, 2011, pp.613-623.

[6] Maze B., Tafreshi H.V., Wang Q.,

Pourdeyhimi B. A simulation of unsteady-

state filtration via nanofiber media at reduced

operating pressures, J. Aerosol Sci. Vol. 38,

No. 5, 2007, pp.550-571.

[7] 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.

[8] Hosseini S.A. and Tafreshi H.V. 3-D

simulation of particle filtration in electrospun

nanofibrous filters, Power Technol. Vol. 201,

2010, pp.153-160.

[9] Billings, C.E. Effects of particle accumulation

in aerosol filtration, PhD Thesis, California

Institute of Technology, Pasadena, USA,

1966.

[10] Kanaoka, C., and Hiragi S. Pressure drop of

air filter with dust load, J. Aerosol Sci. Vol.

21, 1990, pp.127-137.

[11] Witten, T., Sander L. Diffusion-limited

aggregation, Physical Review Letters, Vol. 27,

1983, pp.5686.

[12] Payatakes, A.C. and Gradon L. Dendritic

deposition of aerosol by convective brownian

diffusion for small, intermediate and high

particle Knudsen numbers, American Int.

Chem. Eng. J. Vol. 26, 1980, pp.443-454.

[13] Thomas, D., Penicot P., Contal P., Leclerc D.

and Vendel J. Clogging of fibrous filters by

solid aerosol particles: Experimental and

modelling study, Chem. Eng. Sci. Vol. 56,

2001, pp.3549-3561.

[14] Cheung, C.S., Cao Y.H. and Yan Z.D.

Numerical Model for particle deposition and

loading in electret filter with rectangular split-

type fibers, Computation Mechanics Vol. 35,

No. 6, 2005, pp.449-458.

[15] Kanaoka, C., Hiragi S. and

Tanthapanichakoon T. Stochastic simulation

of the agglomerative deposition process of

aerosol particles on an electret fiber, Powder

Technol., Vol. 118, No. 1-2, 2001, pp.97–106.

[16] Karadimos, A. and Ocono R. The effect of the

flow field recalculation on fibrous filter

loading: a numerical simulation, Powder

Technol. Vol. 137, 2003, pp.109-119.

[17] Chang, Y., Huang, Y., Luo Z. and Zhang G. A

study on particle deposition morphology

within a constricted tube in the presence and

absence of the detachment mechanism, Sep.

Purif. Technol. , Vol. 63, 2008, pp.566-576.

[18] Huang, B., Turton R., Park J., Famouri p, and

Boyle E.J. Dynamic model of the riser in

circulating fluidized bed, Powder Technol.

Vol. 163, No. 1-2, 2006, pp. 23-31.

[19] Elmoe, T.D., Tricoli A., Grunwaldt J,

Pratsinis S. Filtration of nanoparticles:

Evolution of cake structure and pressure-drop,

J. Aerosol Sci. Vol. 40, 2009, pp.965-981.

[20] Sambaer, W., M. Zatloukal M. and Kimmer

D. The use of novel digital image analysis

technique and rheological tools to characterize

nanofiber nonwovens, Polym. Test. Vol. 29,

2010, pp.82–94.

[21] Wang H.C. and Kasper G. Filtration

efficiency of nanometer-size aerosol-particles,

J. Aerosol Sci. Vol. 22 , No. 1, 1991, pp. 31–

41.

[22] Pawu K.T. and Braaten D.A. New

perspectives on rebound and re-entrainment

processes, Aerosol Sci. Tech. Vol. 23 , No. 1,

1995, pp. 72–79.

[23] Mädler L., Lall A.A. and Friedlander S.K.

One-step aerosol synthesis of nanoparticle

agglomerate films: Simulation of film

porosity and thickness, Nanotechnology

Vol. 17, No. 19, 2006, pp. 4783–4795.

[24] Rodríguez-pérez D., Castillo J.L. and

Antoranz J.C. Relationship between particle

deposit characteristics and the mechanism of

particle arrival, Physical Review Letters,

Vol. 72, No. 2, 2005, pp. 021403-1–021403-9.

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

ISBN: 978-1-61804-065-7 143