1. Chapter 9. FILTRATION Part III. Selected methods for improving filtration properties

2. 9.1: Summary of selected methods for improving filtration properties: Filter density growth Filter thickness growth Defined fiber orientation Pleated filters Electrically charged filters Fiber diameter, microfibers, nanofibers Fiber shape

3. 9.2 Filter density growth Filter density  (or packing fraction c) increases filter efficiency and pressure drop too. 9.2.1 Relation between packing fraction and filter efficiency: We can suppose relation between packing fraction c and these filtration mechanisms (see chapter 8.3 and 8.4): 1.Inertial impaction: E ir  - 1/(ln c) 2 (9.1) 2.Diffusional deposition: E D  -1/(ln c) 1/3 (9.2) 3.Sieve effect: (9.3)

5. 9.2.2 Relation between packing fraction and pressure drop According to cell theory of Kuwabara for cylindrical fibers oriented perpendicularly to flow we define: (9.4) Where c is packing fraction, h is filter thickness,  is viscosity, U is face velocity and d f is fiber diameter [Brown, R.C., 1993].

6. 9.4 Filter thickness growth 9.4.1 Filter efficiency: We can assume that depth filter is made from large number of layers [Brown R C, 1993]. 1. For monodisperse aerosol we can assume that number of particles penetrated through one lyer of thickness  x is proportional to beginning number of particles N, to the thickness  x and to the constant -  describing efficiency of the filter:  N = - . N.  x(9.5). We can solve it as a simple differential equation ln (N (x) ) + C = -  x, and for assumption that for x=0 is N (x) = N 0 we obtain equation: ln (N (x) /N 0 ) = -  x  N (x) /N 0 = e -  x = P.... penetration (9.6) 2. For polydisperse aerosol we can assort particle sizes in classes and each size class is characterised by specific filtration constant . For two sizes of aerosol with fraction number  we obtain equation: P= (1-  ). exp (-  1 x) +  exp (-  2 x)(9.7) and generally we obtain:(9.8)

7. 9.4.2 Pressure drop – linear relation (see (9.4)). Penetration of polydisperse aerosol through the depth filter

8. 9.5 Defined fiber orientation 9.5.1 Theory The velocity field defined in each point of space is important to predict most of filtration mechanisms and the pressure drop too. For the description of the velocity field is usually used the stream function defined: (9.9), where  is stream function, v x and v y are velocity in direction and x, y are co-ordinate folders. The calculation of stream function depends on which simplification we use. The simplest case is an “isolated fibre theory” [] which assume only one fibre oriented perpendicularly to incoming stream. The latter workers showed that this theory is overly simplified. The effect of other fibres and the fibre orientation is so significant that is impossible to neglect it or to involve only as boundary conditions. A simple form of Navier-Stokes equations gives the pressure drop: (9.10), where  p is a Nabla operator of pressure drop,  is viscosity and  2 U is a Laplace operator of velocity []. The pressure drop is possible correctly counted for the isolated fibre or for an array of fibres.

9. For isolate fibre oriented parallel with the stream in front of the filter is possible to simplify the expression (5) because in 2D sight the pressure drop is changing only along the axis y, which is perpendicular to the fibre axis x. The expression (9.10) is changing: (9.11) where dp/dy is the pressure derivation with respect to the axis y,  is viscosity and  2 U is a Laplace operator of velocity. For the Kuwabara model of filter the pressure drop is then expressed by formula: (9.12), where  p p is the pressure drop of fibres aligned parallel with the air stream,  is the viscosity, c is the packing fraction, h is the filter thickness, U is the velocity of the air in front of the filter and r is the fibre radius. For the filter with the fibres oriented perpendicular to the air stream the pressure drop  p k is two times bigger:  p k = 2  p p (9.13).

10. 9.5.2 Verification and example of use Relation (9.13) was verificated by model and real filters. 1. The model filter was designed as a cube contained the cluster of equally oriented straight fibres. The cluster was prepared by cutting from polypropylene monofilament. Then was the cluster uniformly packed into the paper cube and tested in two directions. It means that the some structure was tested with different orientation of fibres to main stream. The test result have validated relation 9.13. Test parameters: length of the cube edge: 70 mm, density of filter model: 120 kg/m 3, material: polypropylene monofilament, test device: Bench Rig CEN 1100, aerosol NaCl, size of filtered particles: 0,02 – 2  m, tested area: 49 cm 2, air velocity: 0,6 m/sec The flow oriented in parallel with the fibre direction The flow oriented perpendicularly to the fibre direction 7 cm

11. 2. Real filters Two types of filters were compared. Both of them can be used as air filters and prefilters. They were made with the same parameters as far as the material composition, area weight and thickness concerns. They differ in orientation of fibres. The first material has the fibres oriented mainly perpendicularly to the air stream. This filter was made of cross laid and thermo – bonded web. The second material has fibres oriented mainly parallel with the air stream. This filter was made of perpendicular laid and thermo – bonded web. The filters were tested during their life. A method based on loading the air stream with synthetic dust was used to measure filtration properties. The principle of the method consists in penetration of the dust particles with defined size into the tested filter. The dust used in this test was the ASHRAE Standard 52.2 test dust [4]. The dust particles are dispersed in the air stream in defined concentration. The air with the dust particles passes through tested filter at defined velocity. During the loading process, the development of the filtration efficiency and the pressure drop are measured. The testing is finished when the pressure drop reaches the value of 250 Pa. Perpendicularly laid web Cross laid web

12. Test results: The average efficiency changes when the weight of the filter increases. Initial pressure drop don´t fulfil the theoretical hypothesis. The difference is not significant because the difference between the fibrous structures is not entirely achieved. It is impossible in real filter to order all fibres along one defined direction. Perpendicularly laid filter of area weight around 500 gsm has two times longer lifetime and approximately the some efficiency than the cross laid filter. This effect is possible to explain due to the change of filter structure during the filtration process. For a cross-laid filter the particles, which are mostly captured by direct interception concentrate on the surface of filter. They create a non permeable „cake“. In a perpendicularly laid filter, the particles penetrate deeper into the filter and they are more uniformly dispersed in the fibre web.

13. 9.6 Pleated filters 9.6.1 Description: HEPA (high efficiency particulate air) filters show high filtration efficiency These are used in the clean rooms, hospitals, laboratories etc. As the pressure drop of HEPA filters is rather high, these are often used pleated to increase their effective surface. The trajectory of heat flow through pleated filters is not straight. Therefore the air permeability is not proportional to the total area of the filter when the number of pleats per area unit increases.

14. 9.6.2 Theory: When we assume that pleated filter is placed into the square pipeline it is possible to count the real filter surface by formula: (9.14), Where A is real filter surface, x and y is proportions of the square pipeline, h is the thickness of pleated filter and n is the density of pleates (1/m). Pleating process leads to bigger filter surface and linear relation between the pressure drop and filter surface express very simple D´Arcy´s law. It is necessary to say that the material constant is changing too. For the pleated filter is the trajectory of the air flow more complicated so this flow is more inhibited. Thus the permeability constant of material little decreased when number of pleates increased. Nevertheless when we increase number of pleates the change of parameter k is smaller than the change of the filter surface until the situation when pleats of filter are too close. The relation between the filter surface and the filter efficiency is more complicated. Generally is possible to assume that for small captured particles filter efficiency increase when the air velocity around the fibers decreases. When the air flow is constant the air velocity around the fibers in pleated filter is smaller than in flat filter. Hence the efficiency of pleated filter is usually bigger. hb a x Jeden sklad

15. . 9.6.3 Experiment and results: Two types of spunbond/meltblown filters were tested for NaCl aerosol particles and face velocity 1 m/sec. The fall of pressure drop is significant. For bigger area density little increase when number of pleates is over critical range (pleates are too close together). The efficiency little increase because the velocity of the air flowing around to fibers is smaller and more complicated. Limiting structure

16. 9.8 Electricaly charged filter The electrostatic charge inside the filter that is an added power to capture and hold the particles loaded to filter (see chapter 8.3) without growth of pressure drop. Fibrous material is not possible to consider as a solid material with homogenous electrostatic field. We assume that individual fiber is an electric dipole and the total electrostatic field is very irregular, because the fibers are not oriented regularly. Thus the principles which are used in physics are more complicated. The electrictrostatic charge arises in electret material. This is usually polymer, which could be permanently polarized due to: -Polar molecules dipoles inside polymer which are oriented by reason of external electric field. -Elementary electric dipoles, which arise by movement of electron/proton position due to external electric field. The polar material could be polarized more than non-polar but this electric field is unstable in time due to fact that they are more hydrophilic. That is reason why the most common material, which is commercially used for electrostatic charged filters, is polypropylene (or polyethylene).

17. The fibrous material can be charged by means of the three methods: 1. Triboelectric process Electrostatic charge arises due to the mechanical forces especially the friction. This polarization usually makes unwanted property of polymers during it's processing. 2. Corona charging Within this method is a high voltage external electric field used to polarize the fibers before it's processing or to polarize the finished filter. This charge is placed on the surface of the fibre. 3. Electrostatic spinning During the process of spinning when polymer is melted the external electrostatic field is applied and then polar molecules are permanently oriented so the polarization of fibers is more fixed in time. Stability of charge in time: Polarization of polymers is unstable in time (except electrostatic spinning) and the electric field around the fiber dissipates. Consequently the filtration efficiency rapidly decreases. Generally we know 3 main factors which increase the conductivity: Water or humidity, because the water is a medium with high inductive capacity and it act as a "highway" for ions. The significance of humidity is bigger for the hydrophilic material. Temperature. The impact of temperature consists in fact that electric charge needs some energy to move from it´s placement. When the temperature increases the charge kept in shallow level of energy is lost [1]. Radiation. The some reason as temperature. For example  radiation, X- ray, UV radiation... Captured particles that occupy charged surface of fiber and reduce electric charge.

18. . How filter efficiency increases after charging process (corona charging, 30 kV)

19. . Examples, how filter efficiency decreases during various test conditions. Temperature (NaCl aerosol test):

20. Relative humidity (NaCl aerosol test)

21. Combination moisture/temperature/captured particles (synthetic dust test)

22. 9.9 Fiber diameter, nanofibers 9.1 Benefit of small fiber diameter The main benefit of smaller fiber diameter is the rapid increase of the filtration efficiency with the less significant decrease of the air permeability and related less significant increase of the pressure drop. In terms of the deep filtration the particle capture is given by interaction between particles and fiber surface. All filtration mechanisms are determined by fiber diameter. Figure shows the relation between the fiber diameter and relative fiber surface (fiber surface per 1 gram of circular fibers). It is possible to see that for fiber diameter less than 1 micrometer the relative surface increase very intensively. Nevertheless the pressure drop increases too because the air flow around the fibers is decelerated due to friction on fiber surface.

23. 9.2 Benefit of submicron fibers Boundary conditions of the flow around the submicron fibers, which are different compared to other fibers. These conditions are called “slip flow” [Pich J, 1964]. Due to slip flow the drag force decrease and the captured particles are carried more close to the fiber surface. For the calculation of stream function we can start from simple idea of the second Newton’s law expressed by simplified formula [Feynmann, 2000]: . (acceleration) = -  p -  + .  2 v(2) In the formula left side  is density (mass to unit volume), acceleration is velocity change along all co-ordinates and the time. In the right side are acting forces: pressure force to unit volume, outer force to unit volume (gravity force for example) and inner force to unit volume given by viscosity of fluid. Operators  (Nabla) and  2 (Laplace) change vector to number and again number to vector. The most complicated member is the viscosity (or drag) force, which is given by inner friction of fluid and friction between the fluid and fibre surface. The definition of viscosity is expressed by Newton´s law:  = .  v x /  y,(3) where  is drag force to area in parallel with flow,  v x /  y is the velocity in parallel with flow changed in direction perpendicular to flow and  is dynamic viscosity.

24. The main assumption of viscose fluid is that in the surface of static object the velocity is zero. Nevertheless this assumption is valid only for very low values of Knudsen number. The Knudsen number can be written as (4), where Kn is Knudsen number, is the gas molecule mean free path and r f is specific dimension – for fibres it is fibre diameter. For the air at standard conditions (atmospheric pressure especially) is mean free path 0,067  m so for the fibre diameter smaller than 0,5  m is the flow nature different. The velocity in the fibre surface is non-zero and this phenomenon is called “slip flow”. It means that in this case the movements of air molecules are significant and the flow is not continuous. The effect of slip flow needs to be considered when Kn is around 0,25. Figure 4 shows the velocity profile of viscose flow around the fibre with diameter bigger and smaller than 0,5  m. Due to slip at the fibre surface is drag force of flow around fibre smaller for submicron fibre than for bigger fibre so the pressure drop is smaller too. Furthermore the streamlines are placed closer to fibre surface and this effect lead to the bigger filter efficiency [Graham K, 2002]. velocity profile 0,1  m 10  m

25. 9.3 Comparation of various filtration materials (with different parameters such as area density, thickness, material etc…)

26. 9.4 Examples how nanofiber layer improve filter properties:

27. 9.5 Pleated nanofiber layer The way to reach HEPA filters Paper sublayer Nanofiber layer

28. 9.4 - Respirators – Example of the micron and submicron fibers application At first it is very low resistance against the flow, which is expressed as a pressure drop for the engaged air flow rate. It is necessary to calculate on the potential of the human breath. According to European standard EN 143 we had to follow maximum pressure drop 120 Pa for the flow rate 30 l/min and 420 Pa for the flow rate 95 l/min respectively [EN 143, 2000]. At second it is high efficiency of capturing the filtered particles. The typical size of filtered particles is shown in table 1. According the EN 143 standard the efficiency is tested for two types of the particles. It is an aerosol NaCl with mean size 0,65 and paraffin oil with mean size 0,4  m. Furthermore respirator must be antitoxic, resistant against the filtered particles and water (from the human breath) and finally not very expensive. Two melt-blown materials, electrostatic charged, which are used in respirators, were covered by electrospun nanofibres. The filtration efficiency and pressure drop of the melt-blown – nanofibre composite was measured as a function of area weight of nanofibre layers. Both NaCl and paraffine methods were used to measure filtration efficiency. The pressure drop was measured at two different air velocities. Respirator filters are placed on the human face and protect people against the dust, viruses, bacteria, aerosols etc. This type of filters must fit two opposite requirements:

29. Efficiency of capturing NaCl and paraffin oil particles vs. nanofiber area density. The test parameters (according EN 143 standard): Filtered particles were polydisperse NaCl with mean size 0,65  m and polydisperse paraffin oil with mean size 0,4  m, test air flow 95 l/min and filtration area 100 cm 2.

30. Pressure drop of the respirator filter for the different area density of the PVA nanofiber layer and for two different air flow rates. The test parameters (according EN 143 standard): Used particles NaCl, air flow 30 and 95 l/min, filtration area 100 cm 2.

31. [Brown R C, 1993]BROWN, R. C.: Air filtration. 1 st edition. Sheffield, 1993. ISBN 0 08 041274 2 [EN 143, 2000]EN 143:2000: Respiratory protective devices-Particle filters- Requirements, testing, marking. European Comitee for Standardization, Bruxelles 2000, Belgium. [Feynman RP, 200]FEYNMAN, R. P., LEIGHTON, R.B., SANDS, M.: Feynmanovy přednášky z fyziky s řešenými příklady. Sv.2/3. Praha 2000. ISBN 80-7200-420-4. [Graham K, 2002]GRAHAM, K. et al.: Polymeric Nanofibers in Air Filtration Applications. Fifteenth Annual Technical Conference  Expo of the American Filtration  Separations Society, Texas, 2002 [Pich J, 1964]PICH, J. Teorie filtrace aerosolů vláknitými a membránovými filtry. Praha, 1964.