CAR FILTERSChapter 1

General describtion of filters

1. Definition

Filtration is a process of separating dispersed particles from a dispersing fluid by means of porous media. The dispersing medium can be a gas (or gas mixture) or a liquid. Particles can be solid or liquid for gas medium and solid for liquid medium.

Upstream Downstream

Filter

Channel wall

Dispersed particles

Dispersing fluid

Particles deposited inside the filter

Filter thickness

Face of the filter with „filter cake“ of deposited particles

2. Types of filtration

Concerning to filtration surrouding:

Air filtration / Liquid filtration

Concerning to size of filtered particles:

Macrofiltration for particle size dp: 10-6 m < dp

Microfiltration 10-7 < dp < 10-6

Ultrafiltration 10-8 < dp < 10-7

Nanofiltration 10-9 < dp < 10-8

Reverse osmosis dp < 10-9

Concerning to filtration mechanism:

Flat filtration / Depth filtration

2.1 Air / liquid filtration

Examples of air filtration:

respirators, air ventilation systems (air condition, air cleaning etc…), vacuum cleaners, industrial filters for incineration, power plants, chemical processing, paint boxes, car filters (cabin filters, engine filters, exhaust filters)…

Examples of liquid filtration:

drink water treatment, waste water treatment, chemical processing, batteries, industrial filters (cutting operations, cooling liquids, spunlace…), car filters (oil filters, fuel (petrol) filters…)…

2.2 Relative size of common filtered particles

2.3 Surface filtration

All particles which are bigger than pores are captured on the flat filter surface. It is typical for example for fabric or spunbond filters. Thus for these filters the pores distribution and permeability are important properties. Surface filtration is common for liquid filtration. Surface filters are described in subject „High funcional textiles“

Direction of flow

Textile filter expressed as a set of cylinders placed in parallel

Captured particles

2.4 Depth filtration

Depth filter are able to capture particles that are too small to be sieved out as in flat filtration. Particles, which can be a lot of smaller than the distances between the fibers penetrate into the fiber structure. Filtered particles are captured in terms of the filtration mechanisms. This type of the filtration process is importatn for the most of filter applications. Next chapters about filtration variables, properties and mechanisms refer first of all to the deep filtration.

Direction of flow

Textile filter expressed as a set of cylinders placed in parallel

Captured particles

3. FILTRATION THEORY

Filtration variables

• Filter variables

• Flowing medium variables

• Captured particles variables

Filtration properties

• Efficiency

• Pressure drop

• Lifetime

• Resistivity against environment

• Others (permeability, porosity...)

Filtration mechanisms• Diffusion deposition• Direct interception• Inertial deposition• Electrostatic

deposition• Sieve effect

It´s simple to say “what is filtration” but difficult to describe relations between filter properties and filtration variables which influence the filtration process

This is what we can change

This is what we try know

This is what we need

Filter efficiency

It is the ratio of particles captured by a filter over the total number of particles found in the air upstream of the filter. Filter efficiency can either be based on specific particle size ranges or based on the total number of particles of all sizes.

3.1 Filtration properties I.

100.12

1

G

GE

Efficiency can be defined by formula 1, where G1 is an amount of penetrated particles (which haven´t been captured) and G2 is total amount of particles upstream formula 1.

Expression G1/G2 is named „Penetration“ of filter

Efficieny is changing during the filtration process (see chapter 6.3.4 Nonstationary filtration)

Pressure drop

Pressure drop indicates the restance to flow. It is defined as a difference between the pressure of flowing media upstream and downstream of the filter. For expression of pressure drop is necessary to assign air flow or air velocity (linear relation).

p = p1 - p2, where p1 is pressure drop upstream and p2 downstream

of the filter. Pressure drop is changed during the filtration proces (see chapter 6.3.4 Nonstationary filtration).

Filtration properties II.

Filter lifetime

Filter lifetime determines the time when the filter must be removed. It is defined as a time or as an amount of the filtered particles, which are loaded into the filter until the filter is full.

According to EN 779 standard the filter lifetime is defined as a „Dust holding capacity“:

J = Es.mp where Es is mean filter efficiency and mp is the amount of the

particles loaded into the filter until the final pressure drop (250 or 400 Pa) was reached

Permeability

It is the ability of a material to allow the passage of a liquid or gas through porous material. It is possible to find more defininitions, whic depend on the level of simplification:

1) According to EDANA 140.1 standard it is defined by formula:

where Ms is permeability (l/dm2/min), Q is the flow (l/min)and A is the filter surface. Permeability is tested with

the pressure drop 196 Pa (98,1 Pa for some standards)

2) According to the Darcy´s law the permeability is defined by formula:

where K is permeability (m/Pa/sec) and p is the pressure drop (Pa).

3) According to the Darcy,s law is possible to define permeability as a „permeability coefficient“ defined by formula:

where k1 is the permeability coefficient (m2), is the dynamic viskosity (Pa.sec), and h (m) is the thickness of the filter.

Filtration properties III.

A

QM S

pA

QK

.

pA

hQk

.

..1

4. According Hagen-Dupuit-D´Arcy´s model is permeability defined as:

where K3 is permeability coefficient and C is form coefficient.

This model is suitable for higher flow of viscose liquid (such as water etc…). When we compare HDD model with D´Arcy´s law, the main difference is nonlinear relation between flow and pressure drop.

Permeabilityof laminated textiles

For simple D´Arcy´s law it is possible to deduce relation between the permeability of one layer and more layers. For most of the applications we can assume that the flow through the laminated textile is the some as flow through one layer. Than the total pressure drop and total permeability are defined:

and ,

where pi and K1i are pressure drop and peremability coefficients of each layers

2

3

...

..

.Q

A

hCQ

AK

hp

i

it pp i itotal KK 11

11

Filtration properties IV.

Porosity and pore size

Porosity of porous medium is defined as a percentage of the porous material volume not occupied by fibers.

Very important is size or size distribution of pores, which depends on the pore definition and on the used test method.

Testing methods:

1. Image analysis of 2D microscopic wiew – direct method

2. Sifting of defined particles through the textile

3. Penetration of liquid agent into the textile – relation between pore size and surface tension of liquid.

a) Wetting agent is pushed away from textile due to pressured gas – Bubble point method

b) Non-wetting agent is pushed into the textile – Mercury porosimetry

For more informations see subject „High functional textiles“.

Filtration properties V.

Description of simple Bubble point method:We assume circular pores. Wetting liquid (wetting angle = 0) try to go through the pores due to wetting force F= .D. . Against this force we can act by pressured gas (Fp = p.Apore). D is pore diameter, is liquid surface tension, p is gas pressure and Apore is pore cross section surface. When the first bubble of gas is going through the pore – both forces are in equilibrium. At first bubbles are going through the maximum pore. When we can measure flow rate of gas is possible to measure the distribution of pore sizes.

D

F = . . D

Fp = p . Apore

textile

Wetting agent

bubble

Filtration properties VI.

3.1.1 Change of filtration properties

Statinary and nonstacionary filtration

It is important that the filtration properties are changing during the filtration process. A captured particle, since it occupies a finite space, becomes part of the filter structure, able to contribute both to pressure drop and to filtration efficiency. When we neglect this assumption the filtration process is named „stationary“. It is possible in the beginning of the filtration process. When we assume that the deposited particle influences filter properties the filtration process is named „nonstationary“ [Pich, 1964]. Secondary proceses of nonstationary filtration are:

1. Filter clogging – particles fill the filter structure• increase of pressure drop• increase of filter efficiency

2. Particle disengagement• decrease of filter efficiency

3. Capillary phenomena• flushing of drops• formation of fluid layers in placed where the fibers are spiced• condensation of water

4. Loss of electric charge • decrease of filter efficiency

5. Filter destruction

3.1.2 Test method of filtration properties:

Tested properties are efficiency, fractional efficiency, pressure drop, pressure drop vs. air flow, filter lifetime etc... Properties are tested as initial or during filtration process. Methods are differ in the particle substance (electrical properties, adhesion etc...), particle size (coarse/fine), particle size range (monodisperse, polydisperse), particle concentration etc...

1) Synthetic dust

The dust is blend prepared from melted anorganic (and organic) particles. The most known is ASHRAE dust that has the some parameters as the dust around Arizona roads [ASHRAE 52,2, 1999]. It is used for coarse filters (particles are coarse and polydisperse). It is possible to test change of properties during the filtration process and filter lifetime. Dust is measured by weighting method. This method is very popular and easy to use. However, it is open to criticism because weight measurements give predominantly the weight of the largest particles in the sample. Used standards are: EN 779 [EN 779, 200], ASHRAE 52,2 etc...

2) Athmospheric dust spot efficiency

In the Atmospheric Dust Spot Efficiency ambient outdoor atmospheric air is passed through the unit being tested and samples are taken at the inlet and outlet of the unit to evaluate its collection efficiency on the dust particles suspended in the atmosphere. This test is replaced with DEHS aerosol method because athmosperic air composition is changing. Used standard was older version of EN 779 [Gustavsson, 1999] .

3) Oil aerosols (DEHS, DOP, paraffin oil)

As the test matter is used aerosol from liquid oily substances. The most known are: dioctylphtalate (DOP), diethylhexylsebacate (DEHS) and paraffin oil. Two types of oil aerosol are known: Cold and hot. If the oil is dispersed and dryed in cold ambient conditions (Laskin nozzle) then the size range of particles is wider (polydiperse aerosol). If the oil is dispersed and dryed in hot ambient conditions then is possible to obtain monodisperse particles (0,1-0,3 m). Particles are analyzed by laser particle counter or by spectrofotometric method. It is possible to detect efficiency of selected particle size (except paraffin oil). Particles are insenzitive to electrostatic field. Initial values of This method is used for fine and high efficient filters – HEPA (high efficiency particulate air filter) and ULPA (ultra low penetration air filter) filters.

4) NaCl aerosol

Sodium Chloride aquelous solution is dispersed and dryed. These polydisperse particles have mean size 0, 65 m and their penetration through the filter is analysed by spectrofotometer. This method is suitable for quick test of high efficient filters (respirators especially). Used standards are: BS 4400 [BS 4400, 1969], EN 143 [EN 143, 2000], etc...

5) Methylen blue test

The solution of methylen blue is dispersed and dryed. Particles are analysed by comparing of the blue colour intensity upstream and downstream the filter. It is suitable to high efficient filters. By reason of narow gauge usage is replaced by sodium chloride aerosol test.

Summary of test methods:method Test standard

name particle substance particle

diameter (m)

particle preparation

particle detection

ANSI/AHAM

Arizona roads dust 0,5 - 3 aerosol generator

aerodynamic sorter

ASHRAE EN

CAN

72% fine dust 23% molocco black

5% cotton linters

-

synthetic dust

ISO SAE

Testing dust 2 – 125 10 - 40

injector

weighting method

athmospheric dust

ASHRAE CAN

Athmospheric dust Cca. 0,3 straight from air

opacitometer (light opacity)

0,3 0,2 – 0,3

evaporation, condensation

ASTM ASME/ANSI

IES MIL-STD

UL

DOP test; di-octylphtalate

0,3 – 2 Laskin nozzle

0,1 – 0,3 evaporation, condensation

EN DEHS aerosol diethylhexylsebacate

0,2 – 3

Laskin nozzle

optical particle counter,

spectrofotometer

oil aerosol

EN BS

Paraffin oil; CP27 DAB7

0,40,26 evaporation, condensation

photometer of the light diffusion

aerosol NaCl BS EUROVENT

EN NF

NaCl particles 0,02-2 median

0,6

dispersion, drying

spectrofotometer

Methylene Blue test

BS

Methylen blue particles

- dispersion of water

solution

blue spot size

3.2 Filtration variables

Filtration variables are divided onto three groups:

1. Variables of filter material

2. Variables of filtered particles

3. Variables of filtration process

3.2.1 Variables of filter material:

•Filtration area

•Filter thickness

•Density and surface density of filter

•Uniformity of fibrous material

•Parameters of filter material•surface interactions between the filter material and filtered particles•electrical properties•mechanical characteristics (tenacity, elongation...)•resistance against surrounding factors (heat, solvents...)

•Parameters of fibers•fiber diameter, fiber fineness•shape of fiber cross-section•fiber surface preparations•Mechanical characteristics

•Filter structure•filter density gradient•fiber orientation

3.2.2 Variables of filtered particles

•Particle size

•Distribution of particle size

•Concentration of particles

•Shape and surface of particles

•Particle density

•Electrical properties

3.2.3 Variable of filtration process

•Face velocity (speed of filtered particles in front of filter)

•Viscosity of the flow

•Temperature, pressure, humidity

3.3 Filtration mechanisms

Air (gas filtration) Liquid filtration

Type of filtration •Surface•Depth – more common

•Surface – more common•Depth

Mechanisms • direct interception

• inertial impaction

• diffusional deposition

• capture by electrostatic forces

• sieve effect

• direct interception

• inertial impaction

• sieve effect

3.3.1 Filtration mechanisms of depth filtration

R

fiber

charge on the fiber surface

diffusional deposition

inertial impaction

direct interception

capture by electrostatic forces

streamlines (air moving trajectory)

Total filtration efficiency

Ec is total efficiency, Er is efficiency of direct interception mechanism represented by parameter Nr, Ei is efficiency of inertial impaction represented by Stokes number Stk, Ed is efficiency of diffusional deposition mechanism represented by Peclet number Pe and Ee is efficiency of electrostatic mechanism represented by the parameter Nq.

NqEPeEStkENEEE edirrcc ,,,

Mechanisms:

• direct interception

• inertial impaction

• diffusional deposition

• capture by electrostatic forces .

Direct interception

Direct interception occurs when airborne particles behave in an entirely passive way with respect to the airflow. Airborne particles follow the streamline, which in steady state are independent of the air velocity. Particle will be captured when it is close to the fiber. This mechanism is independent of air velocity, air viscosity and density. Particle must be small, because inertial effects and external forces are neglected. This type of mechanism is common for simple respirators made from fibers of about 20 m, which operate in filration velocity about 0,04 m/sec. Furthermore interception acts along with other filtration processes.

Parameter of direct interception:

Nr= dp/df

(dp is particle diameter, df is fiber diameter)

df

fiber

streamlines (air moving trajectory)

dp

Relation between parameter Nr and efficiency of direct interceptiom mechanism:

ER Nr2;

the simpliest relation is: ER=NR2/, more exactly:

where =-0,5.ln(c)-0,75 is hydrodynamic factor and m = 2/(3.(1-c)) mR

RR

N

NE

1.

2

Inertial impaction

Any convergence, divergence or curvature of streamlines involves acceleration of the air, and under such conditions a particle may not be able to follow the airflow. What particle does depends upon its mass (inertia) and upon the Stokes drag exerted by the air. Stokes drag is defined as a force which acts on the moving sferical object inside of viscous liquid: F = 3...dp.v (where F is the force, dp is the particle diameter, is the dynamic viscosity and v is the face velocity of the airflow).

fiber

inertial impaction

streamlines (air moving trajectory)

Intensity of the point particle inertia is determined by Stokes number:

where dp is particle diameter, is particle density, U is air face velocity, is air viscosity and df is fiber diameter.

f

p

d

UdSt

..18

..2

Efficiency of inertial impaction Ei depends on the intensity of the point particle inertia. If inertia is negligible then Ei will be zero, if the inertia is infinite then Ei will be 100 %.

Relation between the Stokes number and efficiency of inertial impaction:

For low Stokes number efficiency is lead by direct interception:

Eir=ER+(2.)-2.J.St,

where ER is efficiency of direct interception, is hydrodynamic factor dependent on packing fraction c and J is constant dependent on c and parameter of direct interception Nr.

For high Stokes number efficiency of inertial impaction is defined:

EI=1-(/St),

where is constant dependent on flow field.

Diffussional deposition

The trajektories of individual small particles do not coincide with the streamlines of the fluid because of Brownian motion. With decreasing particle size the intensity of Brownian motion increases and, as a consequence, so does the intensity of diffusion deposition [Pich J,1964]. However the air flow effects on the particles motion too. Thus the real motion of small particles depends on Brownian motion and air flow.

Brownian motion is determined by diffusion coefficient D defined by the Einstein equation:

where kB is Boltzmann constant, K is Kelvin temperature, is air viscosity, dp is particle diameter and Cn is the Cunningham correction, which involve aerodynamic slip flow of particles:

where is mean free path of molecules (at NTP it is 0,065 m) and A, B, Q are constants (A=1,246; B=0,87; Q=0,42) [Brown RC, 1993].

diffusional deposition

streamlines (air moving trajectory)

fiber

p

B

d

TkCnD

...3

..

.2

.

...2

1pdB

p

eQAd

Cn

Coefficient of diffusional deposition:

Capture of particles by a diffusional deposition will depend on the relation between the diffusional motion and the convective motion of the air past the fiber. Dimensionless coefficient of diffusional deposition ND is defined:

where df is fiber diameter, U is air flow velocity and Pe is named „Peclet number“.

Diffusional capture efficiency:

According to Fokker-Planck equation was aproximated relation between the ND (or 1/Pe) and diffusional capture efficiency

ED = 2,9 . -1/3 . Pe-2/3

where is hydrodynamic factor ( = -0,5. ln(c)-0,75 by Kuwabara) [Brown RC, 1993].

Previous equation was verified by experiments with model filters with the some and observed functional dependance was the some with little different numerical coefficient:

ED = 2,7 . Pe-2/3

When we calculate with the slip flow (see chapter 9) the resulting capture efficiency is bigger.

Ud

D

PeN

fD .

1

Electrostatic forces:

Both the particles and the fibers in the filter may carry electric charges. Deposition of particles on the fibers may take place because of the forces acting between charges or induced forces. [Pich J, 1964]. The capture of oppositely charged particles is given by coulomb forces. The capture of neutral particles comes about by the action of polarisation forces. We can define three cases of interaction between particle and fiber. Used equations were derived from Coulomb´s law.

fiber

charge on the fiber surface

capture by electrostatic forces

streamlines (air moving trajectory)

1. Charged particle, charged fiberwhere q is the particle charge, Q is fiber charge per unit lenght of fiber and x is the distance between fiber and particle.

2. Charged fiber, neutral particleswhere D1 is the dielectric constant of the particle and dp is particle diameter.

3. Charged particles, neutral fiberwhere D2 is dielectric constant of the fiber and df is fiber diameter.

x

qQF

..21

3

3

1

122 .

2

1..4

x

d

D

DQF p

1

1.

.4 2

22

2

3

D

D

dx

qF

f

Coefficient of electrostatic mechanism, efficiency of electrostatic mechanism

We can interpret this parameter as a ratio of electrostatic forces to drag forces. From this parameter were derived equations for efficiency [Pich J, 1964].

B is mechanical mobility of the particle, U0 is the velocity far form the fiber, df is fiber diameter, dp is particle diameter and is viscosity

Coefficient of electrostatic mechanism

Efficiency of electrostatic mechanism

Charged fiber and charged particle

Charged fiber and neutral particle

Carged paricle and neutral fiber

00 .....3

..4

.

...4

Udd

qQ

Ud

BqQN

fpfQq

..

..

2

1.

.3

4

03

22

1

10 Ud

Qd

D

DN

f

pQ

1

1.

....3 2

2

02

2

0

D

D

Udd

qN

fpq

0....3

..4.

Udd

qQNE

fpQqQq

2

1

02

1.

Reln2

2qQq NE

31

0

31

0 .2

3QQ NE

3.3.2 Filtration variables vs.capture efficiency of filtration mechanisms

Efficiency of each filtration mechanisms

Relations how some filtration variables increase or decrease or not affect the efficiency of each filtration mechanisms

filter density

fiber diameter

particle diameter

particle mass

face velocity

viscosity of air

relative charge

direct interception

- - - - -

inertial impaction

? -

diffusional deposition

- -

electrostatic deposition

- -

32

1

dp

d

e

p

d p

Efficiency of each filtration mechanisms

Numeric relations between the filter variables and capture efficiency of each mechanisms

filter density

c

fiber diameter

df

particle diameter

dp

particle mass

face velocity

U

viscosity of air

relative chargeq, Q

direct interception

- 

1/df2 dp

2 - - - -

inertial impaction

1/(ln c)21/df or

1 – k.df

dp2 or

1-1/dp2

or 1-k/

U or1-k/U

1/ -

diffusional deposition

1/(ln c)1/3

1/df2/3 - 1/U2/3 1/2/3 -

electrostatic deposition

- 1/df

1/dp or

dp2/3 or

1/dp1/2

-1/U or1/U1/3 or1/U1/2

1/q.Q or Q2/3 orq

3.3.3 Filtration mechanism of flat filtration – „Sieve effect“

Es = 1 for dp dpore; ; Es= 0 for dp < dpore,

where Es is efficiency of sieve effect and dpore is pore diameter.

Relation between fiber and pore diameter according to Neckar [Neckar B., 2003]:

()

where q is fiber shape factor (zero for cylindrical fibers), c is packing factor, a and k are constats related to filter structure (usually a is ½).

For cylindrical fibers with hexagonal structure is k = 2-1/2.

.dpore fd

a

fpore c

c

q

kdd

1.

1.