CAR FILTERS Chapter 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. UpstreamDownstream 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: m < dp Microfiltration10 -7 < dp < Ultrafiltration < dp < Nanofiltration10 -9 < dp < Reverse osmosisdp < 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. Efficiency can be defined by formula 1, where G 1 is an amount of penetrated particles (which haven´t been captured) and G 2 is total amount of particles upstream formula 1. Expression G 1/ G 2 is named „Penetration“ of filter Efficieny is changing during the filtration process (see chapter 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 = p 1 - p 2, where p 1 is pressure drop upstream and p 2 downstream of the filter. Pressure drop is changed during the filtration proces (see chapter 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 = E s.m p where E s is mean filter efficiency and m p 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 standard it is defined by formula: where M s is permeability (l/dm 2 /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 k 1 is the permeability coefficient (m 2 ),  is the dynamic viskosity (Pa.sec), and h (m) is the thickness of the filter. Filtration properties III.

4. According Hagen-Dupuit-D´Arcy´s model is permeability defined as: where K 3 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  p i and K 1i are pressure drop and peremability coefficients of each layers 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 (F p = p.A pore ). D is pore diameter,  is liquid surface tension, p is gas pressure and A pore 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 F p = p. A pore 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:

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 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 Mechanismsdirect 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, E r is efficiency of direct interception mechanism represented by parameter N r, E i is efficiency of inertial impaction represented by Stokes number Stk, E d is efficiency of diffusional deposition mechanism represented by Peclet number Pe and E e is efficiency of electrostatic mechanism represented by the parameter Nq. 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: N r = dp/df (d p is particle diameter, d f is fiber diameter) dfdf fiber streamlines (air moving trajectory) dpdp Relation between parameter N r and efficiency of direct interceptiom mechanism: E R  N r 2 ; the simpliest relation is: E R =N R 2 / , more exactly: where  =-0,5.ln(c)-0,75 is hydrodynamic factor and m = 2/(3.(1-c))

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. . .d p.v (where F is the force, d p 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 d p is particle diameter,  is particle density, U is air face velocity,  is air viscosity and d f is fiber diameter. Efficiency of inertial impaction E i depends on the intensity of the point particle inertia. If inertia is negligible then E i will be zero, if the inertia is infinite then E i will be 100 %.

Relation between the Stokes number and efficiency of inertial impaction: For low Stokes number efficiency is lead by direct interception: E ir =E R +(2.  ) -2.J.St, where E R 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: E I =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 k B is Boltzmann constant, K is Kelvin temperature,  is air viscosity, d p 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

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 N D is defined: where d f is fiber diameter, U is air flow velocity and P e is named „Peclet number“. Diffusional capture efficiency: According to Fokker-Planck equation was aproximated relation between the N D (or 1/P e ) and diffusional capture efficiency E D = 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: E D = 2,7. Pe -2/3 When we calculate with the slip flow (see chapter 9) the resulting capture efficiency is bigger.

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 fiber where 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 particles where D 1 is the dielectric constant of the particle and d p is particle diameter. 3. Charged particles, neutral fiber where D 2 is dielectric constant of the fiber and d f is fiber diameter.

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, U 0 is the velocity far form the fiber, d f is fiber diameter, d p 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

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 -  - 

Efficiency of each filtration mechanisms Numeric relations between the filter variables and capture efficiency of each mechanisms filter density c fiber diameter d f particle diameter d p particle mass  face velocity U viscosity of air  relative charge q, Q direct interception - 1/d f 2 dp2dp inertial impaction 1/(ln c) 2 1/d f or 1 – k.d f d p 2 or 1-1/d p 2  or 1-k/  U or 1-k/U 1/  - diffusional deposition 1/(ln c) 1/3 1/d f 2/3 -1/U 2/3 1/  2/3 - electrostatic deposition -1/d f 1/d p or d p 2/3 or 1/d p 1/2 - 1/U or 1/U 1/3 or 1/U 1/2 1/  q.Q or Q 2/3 or q

3.3.3 Filtration mechanism of flat filtration – „Sieve effect“ E s = 1 for d p  d pore; ; E s = 0 for d p < d pore, where E s is efficiency of sieve effect and d pore 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.