WARSAW UNIVERSITY OF TECHNOLOGY

WARSAW UNIVERSITY OF TECHNOLOGY FACULTY OF CHEMICAL AND PROCESS ENGINEERING

Ph.D. Thesis

Ewa Sikorska, M.Sc.

Deep water purification under fibrous filter loading condition.

Supervisor: Prof. Leon Gradoń

Warsaw 2017

ACKNOWLEDGEMENTS First and foremost I would like to express my deepest gratitude to my supervisor, Prof. Leon Gradoń for all the support and encouragement he gave me throughout my studies. His precious suggestions and inspiration initiated this research and developed it to a multidisciplinary level. Thanks to him I never was alone with my problems. He infected me with passion for science, which I will always have in my heart. My appreciation also extends to Amazon Filters Ltd., who co-founded this research. Especially I would like to thank Andrzej Kaczyński for introducing me into the industry of filtration and also for his technical knowledge and support. Thanks to Wouter Pronk I was given a chance to develop the biotic contamination removal in Swiss Federal Institute of Aquatic Science and Technology Eawag in Dübendorf, Switzerland. Frederik Hammes, Brian Sinnet and Jacqueline Traber were exceptionally helpful during the research there. I will never forget the people I have met, who cheered me up in bad times and shared the joy of glory days. Friends from my Faculty, colleagues I have met in Switzerland as well as my fellow Master’s students – they all gave me unforgettable memories and each one of them somehow affected the way of my life. Most of all, I am indebted to my family, whose value to me only grows with age. Without the support from my mom, dad, brother and husband I would never have been able to start, proceed and finish my studies. Thank you very much, Everyone!

STRESZCZENIE Woda jest materiałem strategicznym. Odzyskiwanie tego surowca jest szczególnie istotne w zrównoważonej gospodarce wodnej każdego kraju. Filtracja wgłębna należy do najbardziej wydajnych technik oczyszczania wody. Do dziś nie opracowano jednak metody kompleksowego opisu tego procesu. Niniejsza praca zgłębia temat nieustalonej filtracji wgłębnej wody i wskazuje konieczność zmiany dotychczasowych norm stosowanych do oceny jakości filtrów. Ze względu na charakter separacji cząstek stałych, praca filtrów powinna być oceniana na podstawie specyfiki procesu ich obładowywania. Rozkład czasowoprzestrzenny depozytów determinuje rzeczywistą efektywność filtracji. W niniejszej pracy przeanalizowano zachowanie różnych typów filtrów podczas obładowywania. Dla standardowych filtrów mono- i wielowarstwowych określono wpływ początkowej struktury filtra, czyli średnicy włókien i porowatości, na jego właściwości separacyjne, tj. skuteczność, pyłochłonność, spadek ciśnienia. Opracowano metodę opisu ilościowego zmian czasowo-przestrzennych materiału podczas procesu filtracji. Zjawiska lokalne zostały uogólnione do rozważań makroskopowych w zaproponowanym modelu procesu. Model ten jest użyteczny do wstępnego szacowania pracy filtra o zadanej strukturze. Zaproponowano również zastosowanie włókniny o bimodalnym rozkładzie średnic włókien, aby rozszerzyć zakres używania filtrów włókninowych. Dodatek nanowłókien do każdej warstwy filtracyjnej filtra zwiększył właściwości separacyjne standardowej włókniny w zakresie cząstek podlegającym ruchom dyfuzyjnym. Filtry te są dedykowane do separacji zanieczyszczeń nanometrycznych o jednorodnym rozkładzie rozmiarowym, usuwanych dotychczas głównie przy użyciu drogich technik membranowych. Dodatkowo, ze względu na możliwość obecności w wodzie obiektów biologicznych, opracowano technikę wytwarzania oraz testowania filtrów kompozytowych o właściwościach antybakteryjnych i bakteriostatycznych. Wprowadzenie nanocząstek ZnO i Ag na powierzchnię włókien zwiększyło żywotność włókniny poprzez redukcję efektu biofoulingu. Praca dowodzi, że poprzez zmianę struktury oraz materiału filtra można usprawnić jego wydajność. Odpowiednio zaprojektowany i wytworzony filtr włókninowy będzie pracował całą swoją objętością, utrzymywał właściwości separacyjne w całym czasie pracy. SŁOWA KLUCZOWE: filtracja wgłębna, filtry włókninowe, porowatość, technika rozdmuchu stopionego polimeru, woda. 5

ABSTRACT Water is a strategic material. Recycling it is an important component of balancing its use. Deep-bed filtration with the use of fibrous filters is an inexpensive purification method and seems to be very effective in spreading water recovery. So far no comprehensive work about particularly fibrous filters behavior during the nonsteady state water filtration process was made. This work deepens the knowledge about water depth filtration process in fibrous filters. It shows how necessary it is to evaluate filter performance during the entire time of its use. The knowledge about the filter’s momentary and local loading is crucial for process analysis. The influence of the initial structure, i.e. fiber diameter and porosity, of mono- and multilayer standard fabrics on their separation properties, flow resistance and lifetime was evaluated through porosity development. A method of its quantitative evaluation during the process was developed. Local phenomena were widely explained and generalized to global, macroscopic conclusions in a process model formulation. The proposed model is simple, reliable and helps in preliminary estimation of the filter structure. A fibrous structure characterized by a bimodal distribution of fiber diameters was proposed as an improvement of the standard melt-blown fabric. A method of its production was developed. The addition of nanofibers to every filtration layer increased separation efficiency in the removal of diffusional particles. The use of such mixed-fiber filters is suggested for the removal of nano-sized objects with a narrow contamination size distribution. As the feed stream is permanently organically loaded, the process analysis was also additionally performed for bacterial removal. A production technique of filters made of a composite of polypropylene with antibacterial nanoparticles on the fibrous surface was proposed. A method of verification of antibacterial/bacteriostatic properties was developed. The filters made of polypropylene with ZnO and Ag nanoparticles exhibited desired antibacterial and bacteriostatic properties. Their lifetime was increased without any significant increase of production costs. The structural and material modifications are the future of the improvement of fibrous filters. With a good filter structural design and the developed filter’s manufacturing process proposed in this work, nano-sized contamination removal is now possible. KEYWORDS: depth filtration, fibrous filters, melt-blown technology, porosity, water. 6

TABLE OF CONTENTS ACKNOWLEDGEMENTS ....................................................................................................... 3 STRESZCZENIE ....................................................................................................................... 5 ABSTRACT ............................................................................................................................... 6 TABLE OF CONTENTS ........................................................................................................... 7 1. INTRODUCTION, AIMS AND SCOPE OF THE THESIS ................................................. 9 2. SEPARATION TECHNIQUES ........................................................................................... 12 3. DEPTH FILTRATION ........................................................................................................ 16 3.1. Filter types ......................................................................................................................... 17 3.2. Filtration mechanisms ....................................................................................................... 19 4. FILTER PRODUCTION...................................................................................................... 25 4.1. Melt-blown technology ..................................................................................................... 27 5. FILTER TYPES ................................................................................................................... 32 5.1. Monolayer fabrics ............................................................................................................. 32 5.2. Multilayer fabrics .............................................................................................................. 32 5.3. Mixed-fiber fabrics ............................................................................................................ 33 5.4. Examined filter structures ................................................................................................. 34 6. FILTER CHARACTERIZATION ....................................................................................... 35 6. 1. Material thickness ............................................................................................................ 35 6.2. Pore diameter..................................................................................................................... 37 6.3. Fiber diameter ................................................................................................................... 39 6.4. Porosity.............................................................................................................................. 47 7. EXPERIMENTAL VALIDATION ..................................................................................... 66 7.1. Test stand........................................................................................................................... 66 7.2. Separation efficiency ......................................................................................................... 69 7.2.1. Polydisperse contamination, mass efficiency................................................................. 70 7.2.2. Monodisperse contamination, fractional efficiency ....................................................... 74 7.3. Pressure drop ..................................................................................................................... 83 7.4. Retention capacity and filter lifetime ................................................................................ 86 8. FILTRATION MODEL ....................................................................................................... 89 8.1. Separation efficiency ......................................................................................................... 90 8.2. Pressure drop ................................................................................................................... 102 9. BIOFOULING ................................................................................................................... 107 9.1. Formation of a deep-bed filter structure modified with ZnO and Ag ............................. 108 7

9.2. Movement of bacteria near the fiber ............................................................................... 111 9.3. Antibacterial/bacteriostatic test ....................................................................................... 112 9.4. Composite filter behavior during loading ....................................................................... 114 10. CONCLUDING REMARKS ........................................................................................... 119 REFERENCES ....................................................................................................................... 122 APPENDIX 1 ......................................................................................................................... 132

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1. INTRODUCTION, AIMS AND SCOPE OF THE THESIS Water is a finite and irreplaceable natural resource. It is an integrated part of the world’s ecosystem without which no life would be possible. However, due to its inefficient use, water is becoming a limited value. Due to global climate change and population growth it is predicted that by 2030 half of the world’s population will be living in high water-stressed areas (UNESCO, 2014). This eminent threat has made the world to turn to water reclamation and reuse. Investment in treatment technologies requires developing new products or optimizing current techniques that are already known to meet high-quality freshwater demands. Deep-bed filtration is one of the most effective available water purification methods. At the same time, the technique enables the removal of submicron particles with absolute (99,98 %) efficiency (Sutherland, 2008). The use of an additional pumping system is not required, as filter materials are highly porous. The production of both types of depth filters, either granular or fibrous, is simple and inexpensive. Only membrane filters can concur with depth media in quality of the filtrate (Tien, 2012), although their use is relatively expensive and to obtain a reasonable flux a high-pressure pumping system is needed. Hence, challenges posed by the removal of constantly smaller contamination entailed studies deepening the knowledge about fibrous filters as an inexpensive method of water treatment. So far no comprehensive work about particularly fibrous filter behavior during the non-steady state filtration process was made. All models useful for filter structure design, i.e. for a quick approximation of the filter’s behavior, were based on equations formulated for granular filters. Although the physical laws governing the flow through either granular or fibrous media are similar, there are a few differences influencing the operating conditions, indicating a necessity of distinct description of these filters’ performance. Furthermore, a description of a fibrous filter structure during its loading was never before a subject of detailed consideration. This thesis presents experimental and theoretical results of an extensive research program concerning various aspects of water filtration in fibrous filters. The principal aim of this study was to analyze time- and space-dependent functions characterizing the filter structure and performance during the filter loading. Within the framework of the main purpose, there were a few other, more specific goals to achieve, namely: 1. To examine the penetration depth of particulate matter being removed. 9

2. To develop a method of quantitative description of structural changes within the filter during its loading. 3. To verify the influence of porosity and fiber diameter on the filter performance. 4. To evaluate the effect of resuspension phenomena. 5. To create a model of process simulation useful for filter design. 6. To investigate whether a mixed-fiber fabric structure improves the quality of the filtrate. 7. To determine the antibacterial and bacteriostatic properties of composite filters manufactured with the addition of Ag and ZnO nanoparticles. The above objectives were included in the following outline of my dissertation. Chapter 2 introduces a brief description of separation processes and filter types. Depth filtration was analyzed in detail in Chapter 3. The possibilities of melt-blown technology, thought to be the most promising method of fibrous filter production, were described in Chapters 4 and 5. Then, the performance of fibrous materials of different structures, i.e. monolayer, standard multilayer gradient and mixed-fiber multilayer gradient, was analyzed. Characterization of various filtering fibrous structures can be made through the thickness of filtration layer, pore size, diameter and packing density of fibers. The ways of measuring these parameters were listed in Chapter 6. Their structural description is easy and widelyknown for a clean fabric, thus all of the examined materials were fully characterized prior to filter loading. It enabled further investigation of the influence of the filter initial structure on the filter performance. The main feature of depth filtration is that at the moment when loading begins, particles start to deposit on filter elements, or later on top of one another, within the entire filter material. Therefore, the initial fibrous structure evolves. Depending on the location within the filter volume as well as depending on the progress in process time, the porosity and fiber diameter change their values. In Chapter 6 the best way of quantitative characterization of these changes was chosen and delivered for multilayer filters, as the representatives of the most complex structures. Resuspension phenomena were comprehensively analyzed as well. Experimental research was performed in a flow-through experiment under a constant flow condition. All tests were conducted in an industrial scale experiment developed in compliance 10

with EN 13443-2 (EN 13443-2:2005+A1:2007, 2007), described in Chapter 7. The separation efficiency, retention capacity, lifetime and pressure drop across mono- and multilayer filters were measured during the entire filtration cycle, thus until reaching a 2,5 bar value of pressure drop. The influence of fiber diameter distribution and packing density on filter performance was evaluated. Based on the results, in Chapter 8 a model of process simulation was proposed. It was dedicated to multilayer gradient filter design as they are the most commonly used materials. The foundations of estimation of the filter performance were particle mass balance and kinetics of deposit accumulation delivered for an infinitesimal volume of the filter material. For the pressure drop predictions a model was established upon the general form of Darcy’s law also made for macroscopic scale of the system. Chapter 9 additionally concerns some aspects of biotic contamination removal. As the feed stream is permanently organically loaded, the process of water treatment is often associated with operational problems, such as loss of flux and shortening of filter life (Williams and Edyvean, 1998). Thus, material modifications to obtain antibacterial or bacteriostatic properties in the fibers were performed to prevent the biofouling effect. A production technique of filters made of a composite of polypropylene with ZnO and Ag nanoparticles was proposed. A method of verification of antibacterial and bacteriostatic properties was developed. The performance of composite filters was compared with their equivalent structures made of pure polypropylene. In conclusion, all the results were summarized in Chapter 10.

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2. SEPARATION TECHNIQUES Separation process can be defined as an operation which transforms a mixture of substances into 2 or more distinctive products. The process is based on differences in physical or chemical properties of mixture’s components, i.e. size, shape, density or chemical affinity. According to mechanism forcing the division, 5 major groups of solid/liquid separators can be distinguished (Tarleton and Wakeman, 2007): 1. Gravitational a. Sedimentation: -

Thickeners, clarifiers, classifiers, flotation columns

b. Filtration: -

Batch: single leaf Nutsche

-

Semi-continuous: sand bed

-

Continuous: gravity belt, screen

2. Centrifugal a. Sedimentation: sedimenting centrifuges, hydrocyclones b. Filtration: filtering centrifuges 3. Vacuum filtration: -

Batch: multi-element leaf, single leaf Nutche, single leaf tilting pan

-

Continuous: horizontal belt, horizontal rotary table, horizontal tilting pan, rotary drum, rotary disc

4. Pressure filtration: -

Batch: multi-element candle, multi-element leaf, plate and frame press, precoat Nutsche and multi-element leaf, precoat plate and frame press, recessed plate filter press, sheet filter, single leaf Nutsche

-

Semi-continuous: bag, cartridge, dead-end membrane, low shear crossflow sand bed, fibre bed, simplex strainer

-

Continuous: belt press, duplex strainer, high shear crossflow, rotary disc, rotary drum, sand bed, tower press

-

Variable volume: diaphragm filter press, screw press, horizontal element tube press, vertical diaphragm filter press, vertical element tube press 12

5. Separation within a force field -

Magnetic field: high gradient magnetic, high intensity magnetic, low intensity magnetic

-

Low voltage electric field: low gradient electrical

-

Ultrasonic field: ultrasonic assistance

-

Combined field.

With the use of various separators different qualities of products can be achieved. Sedimentation process occurs naturally so the amount of removed matter results from the balance of forces acting on a particle within a fluid. Gravitational force is mainly dependent on particle mass, thus sedimentation rates can be artificially increased by the addition of coagulants or flocculants. In case of processes driven by centrifugal force, the quality of products is limited by the mass of suspended particles and angular velocities resulting from the apparatus construction. Filtration-type processes rely on a porous barrier, referred to as a “filter”, which captures particles at its surface layer or within its entire volume. The distinction is made upon a ratio between the particle size and the size of a barrier’s aperture. The first type of filtration is called surface/cake filtration. The filter acts like a sieve – the smaller the size of a pore the smaller collected particles. Solids deposited on the upstream side of the filter material are called “cake”. A liquid passing the filter element is termed “filtrate”. Depending on the flow direction at the filter’s intake, the cake can be continuously removed by the suspension flowing tangentially (cross-flow filtration) or it can be accumulated while the flow is perpendicular (conventional surface filtration). As soon as the first layer of the cake is formed, subsequent filtration takes place on the cake surface and then the filter medium starts to provide a supportive function. In the second type of filters, depth filters, solid removal is accomplished by particle deposition throughout the filter medium, as the suspended particles are supposed to be smaller than the pore sizes. Deposition results from local conditions within the porous material, particle pathway deviations and adhesion forces. As depth filters do not perform like sieves, some particles might pass through them. Therefore, their separation efficiency, especially for nano-sized contamination, cannot achieve 100 %. Depending on the pressure source all filtration techniques can be generally divided into vacuum, low and high pressure processes. The driving force might also come from gravitation or centrifugal forces.

13

The last group of separation techniques is dedicated to selective removal of materials which exhibit special features in an external force field. Removal is dependent on the strength of interactions between the collector and the removed matter. Although the above techniques have been developed by many researchers to improve the performance of chosen methods (Brandt et al., 2017; Tarleton, 2015), the classification of the above devices into subsequent treatment stages made by Tiller (Tien, 2012; Tiller, 1974) is still used: 1. Pretreatment: a. Chemical: flocculation, coagulation b. Physical: crystal growth, filter aid addition, freezing and other physical changes 2. Solids concentration: a. Thickening, hydrocycloning b. Clarification 3. Solids separation: a. Recovery of solid particles – cake formation: -

press, vacuum, gravity filters (bath or continuous)

-

centrifuges: sedimenting or filtering

b. Clarification – no cake formed: deep granular beds, cartridges 4. Post-treatment: a. Filtrate – polishing: membranes, ultrafiltration b. Cake: -

Washing: displacement, reslurry

-

Deliquoring: drainage, mechanical, hydraulic

Membrane techniques are still the best

in liquid polishing. With the use of a proper

membrane type it is possible to remove suspended as well as dissolved matter. However, the total cost of production of 1 m3 of pure water is considered to be the highest among all filtration methods (Ioannou-Ttofa et al., 2017). A proper pre-treatment can reduce membrane load and biofouling, and consequently decrease membrane operational costs. Depth filtration with fibrous filters enables the removal of suspended matter of the smallest size of submicron objects without having to use additional apparatus. Furthermore, depth filter materials do not generate high flow resistance so they can be added to a process without a significant 14

economic loss. Over 40 years ago they were considered to be the best clarifying filters (Tiller, 1974) and with the progress made in this field their use has become even more universal.

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3. DEPTH FILTRATION The application of depth filters can be highly beneficial if they are properly used. To enable penetration of particles into the structure of a porous material, removed particles have to be smaller than the material’s pore size. The empirical 1/3 law specifies the maximum contamination size, equal to 1/3 of the filter’s average pore size, which can be removed by deep-bed filtration mechanisms (Tien, 2012). Deposition of larger particles leads to quick surface clogging. The influent suspension cannot be highly concentrated either. The amount of particles in a fluid is typically below 1 % and is often as low as or lower than 100 ppm (Tien and Ramarao, 2007). It is considered that in highly concentrated slurries particles jostle with one another at the entrance to each pore, bridging together across the opening to the pore. Build-up particles create a cake and change the character of the process to surface filtration. Particle deposition either at the material’s surface or within its volume causes an increase in hydraulic resistance. However, due to higher initial porosities and distribution of particles within the entire filter element, the local decrease in the area free for the fluid flow and thus the increase of hydraulic resistance is lower for depth than for surface filters. The lower the flow resistance the less energy is necessary for fluid pumping and the process is cheaper. Generally, deep bed filtration can be applied to treat large quantities of suspensions at a relatively low cost. The size of removed contamination depends on the fluid velocity and structural properties of the depth filter. With time the filter performance changes, as presented in Fig. 3.1. With the deposition of particles on the collector surface, the local conditions within the filter change. Initially, the separation efficiency increases. The accumulated matter develops an area available for deposition of constantly up-flowing particles. Once agglomerates start to form, the character of the process changes. The second, “working” stage of the filtration process begins. Retained particles become additional collector elements increasing the separation effectiveness of the filter material. They also influence local conditions within the filtrating structure. As most industrial applications are related to filtration under constant flow conditions, the accumulated matter decreasing pore spaces increases local shear stress. When shear stress reaches its critical value, the built-up agglomerate within a pore breaks and relocates within the filter material or flows directly to the filtrate. Temporary drops in separation efficiency might be noticed, but due to constant filtrating surface development the average filter performance is constantly improved. As soon as the maximum retention capacity of the filter is reached, thus most filter pores clog, a breakthrough occurs and the 16

deposit is being washed out of the structure by rapidly increased intake suspension pressure. Monitoring of the pressure drop caused by the filter and the accumulated deposit helps to predict the breakthrough stage or filter damage, which also may occur in surface filtration. However, in surface filtration, due to the filter acting like a sieve, separation efficiency is constant during the entire process and a breakthrough is related to filter destruction. The maximum values of pressure drop are always provided by the filter’s manufacturer and to achieve a good quality of the filtrate a proper technological regime should be respected.

Fig. 3.1. Stages of depth filtration.

3.1. Filter types In theory every material of relatively large pore sizes and sufficient depth might act like a deep-bed filter. Commercially, 2 types of beds are of particular interest to clarifying processes - granular and fibrous. The physical laws governing the flow through either type of the media are similar, although there are few differences influencing the operating conditions. The obvious dissimilarity is in the shape of collector elements - granules or spheres in granular media and fibers or cylinders in fibrous media. Due to technical reasons, high porosities in fibrous materials are easy to obtain, in contrast to those of granular filter beds. A good example of a highly porous material is a polymer fabric made of nanofibers which can be extruded with the use of melt-blown technology. During the production, molten filaments solidify on top of each other, creating a densely packed rigid web. No additional bonding or 17

dense support is needed as fibers firmly stick together. Hence, particularly with the use of melt-blown technique either high or low porosity of the material can be obtained for a precise size of fibers. A granular filter needs a permeable barrier which will hold its entire bed. Therefore, there is a limit of granule size which will not clog the supportive material. This size also strictly determines the material’s maximum porosity, which results from the geometrical order of granules. Due to those structural limitations a comparison between granular and fibrous filter media should be performed for a common feature determining the total area available for deposition. It is a specific surface area, Sav, which defines the surface area of collector elements in a unit bulk volume of the filter material. For a system composed of N grains (Fig. 3.1.1a) of diameter dg, placed regularly on top and next to each other in a cubic volume of Ndg x Ndg x Ndg, and porosity εg, specific surface area, Sav,g, can be calculated as: 𝑆𝑎𝑣,𝑔 =

6(1−𝜀𝑔 )

(3.1.1)

𝑑𝑔

and for a system consisting of N straight fibers (Fig. 3.1.1b) of diameter df, length equal to Ndf, in a space of dimensions Ndf x Ndf x Ndf and porosity εf, specific surface area, Sav,f, can be obtained from: 𝑆𝑎𝑣,𝑓 =

4(1−𝜀𝑓 )

(3.1.2)

𝑑𝑓

Fig. 3.1.1. Schematic representation of granular (a) and fibrous (b) filters. Hence, to receive the same amount of collector area in a cross-section of the filter, different depths of granular, Lg, and fibrous, Lf, filters should be applied according to: 𝐿𝑔 𝐿𝑓

=

4(1−𝜀𝑓 )

𝑑𝑔

𝑑𝑓

6(1−𝜀𝑔 )

18

(3.1.3)

In a typical granular filter the granulate size is 0.5 mm in diameter and its porosity reaches 60 %. In a standard fibrous filter the average size of the collector element is 5 μm and its porosity reaches 90 % (Sutherland, 2008; Tien and Ramarao, 2007). Thus, it follows from Eq. 3.1.3 that to achieve a similar specific surface area of those 2 filter types, the length of the granular bed should be 17 times higher than the one of the fibrous filter. It is the effect of strong surface development in the fibrous material via the application of fibers with a relatively small diameter and high packing density, compared to granular media. Moreover, such a structure increases the probability of particle-collector contact, thus higher separation efficiency of nano-sized contamination, whose movement results mostly from stochastic Brownian motion, can be obtained. Considering these structural limitations, higher effectiveness of lower-sized contamination removal is possible while using fibrous filters. Granular beds usually are made of materials such as sand, minerals, ceramics or others which are highly resistant to corrosion and high temperature. Their loose structure is also easy to backwash. On the contrary, the firm net of fibrous filters is hard to clean. Furthermore, materials such as plastic, cellulose or cotton, out of which the most popular filtration fabrics are produced, are not neutral in severe conditions. In most cases it is not a problem as filters are cheap and easy to replace. However, for example in pharmaceutical industry, when the sterilization of a fibrous element is necessary, granular filters will be more suitable.

3.2. Filtration mechanisms A particle flowing through a depth filter can be efficiently retained by the material if it is transported towards the collector surface and if the particle-collector surface interactions favor the attachment. The particular mechanisms that can bring the suspended matter close to the fiber surface are (Vigneswaran, 2009): diffusion, hydrodynamic action, interception, inertial impaction, sedimentation and straining. The pathways of particles determined by each mechanism are presented in Fig. 3.2.1.

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Fig. 3.2.1. Schematic representation of deep-bed filtration transport mechanisms. Molecules of liquids are in a constant, thermal random motion. Solid particles suspended in a liquid which are small enough, usually in case of water treatment of submicron size, bombarded by those thermal vibrations of molecules might result a similar stochastic movement, termed as Brownian motion or diffusion. The speed at which they move can be expressed in terms of a diffusion coefficient Dmol, defined through the Nernst-Einstein equation: 𝑘 𝑇𝐶

𝐵 𝐶 𝐷𝑚𝑜𝑙 = 3𝜋𝜇𝑑

𝑝

(3.2.1)

where kB is the Boltzmann constant, T – absolute temperature, CC – the Cunningham slip correction factor, μ – dynamic viscosity and dp – particle diameter. The non-dimensional Peclet number, NPe, describes the strength of diffusive movement, determining the relationship between the convectional and diffusional transport as: 𝑑 𝑈

𝑁𝑃𝑒 = 𝐷 𝑓

𝑚𝑜𝑙

(3.2.2)

where U is the superficial velocity of the liquid and df – fiber diameter. Low values of the Peclet number characterize transport dominated by Brownian motion, and high values of the Peclet number describe domination of convective effects. Diffusion coefficient is dependent on particle size and thermodynamic properties of the fluid (Eq. 3.2.1). Diffusive motion can be also enhanced at low velocities as particles spent more time in the filter material and the probability to meet the collector increases. The presence of fibers in a fluid flow field results in a curvature of streamlines in a close neighborhood of the fibers. The flow is generally laminar with some velocity profile and a shear gradient. The rotation of particles moving in a liquid causes a random deviation of 20

particles pathways across flow streamlines, what may lead to contact with the filter element. This type of movement is known as hydrodynamic action. Due to its complexity it is still impossible to be measured through any characteristic number. The particle-collector contact can also result from direct interception. When a particle moves along fluid streamlines that pass the fiber in a distance not larger than the particle diameter, deposition may occur due to this effect. This mechanism defines the interception parameter NR, as the ratio: 𝑑𝑝

𝑁𝑅 = 𝑑

(3.2.3)

𝑓

Its importance increases with the growth of the relationship between the particle and fiber diameters. When the particle has high inertia, thus relatively large weight (high diameter or density, ρp) and high velocity, its pathway may not adjust as quickly as the fluid streamlines near the fiber and the trajectory may directly lead to collision with the fiber. It is dependent on the ratio of inertial to viscous forces determined in the Stokes number, NSt, which can be given by: 𝑁𝑆𝑡 =

𝜌𝑝 𝑑𝑝 2 𝑈 18𝜇𝑑𝑓

(3.2.4)

Inertial impaction is stronger for particles with high inertia. Fibers of lower diameters enhance this effect as well, while they change streamlines more rapidly and so the particle has less time to adjust. If the density of the particle is higher than the density of the fluid, ρ, the particle will settle down in the fluid due to gravitational force. The impact of gravitational force on convectional transport determines the gravitational parameter NG, given by: 𝑁𝐺 =

(𝜌𝑝 −𝜌)𝑑𝑝 2 𝑔 18𝜇𝑈

(3.2.5)

where g is gravitational acceleration. Sedimentation force increases with an increase in particle weight. Staining or sieving occurs when the particle diameter exceeds the size of the pore within the filter material. Although it is rather a mechanism of surface filtration, it also occurs in depth filters, especially during the separation of polydisperse contamination sieving.

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Particle transport mechanisms are important as they determine particle movement within the porous material towards collecting elements. In natural environment the above listed mechanisms do not act independently. They overlap each other. Which mechanism dominates depends on many parameters such as: fluid flow, particle and fabric properties. However, whether the particle will stay on filter elements or not, is decided by the interactions between the contacting particle and the fiber surface. The most important forces that govern the adhesion of particles are long-range: the London Van der Waals forces and the electrical double-layer interactions, and of short-range: the Born repulsion force and the hydration force (Vigneswaran, 2009). The long-range forces influence separation at distances up to approximately 100 nm from collector elements. The London Van der Waals forces’ origin comes from momentary pairwise oscillations in electron density, creating instantaneous dipole moments that draw two interacting surfaces together. Their value can be approximated by the empirical correlation of Tien (Tien, 2012): 2

2𝐻/𝑑𝑝

𝐹𝑣𝑑𝑤 = − 3 [ℎ2 (ℎ+2)2 ] 𝑛

(3.2.6)

where h is the separation distance between the particle and the fiber and n is the unit normal vector. The London-van der Waals interactions are mainly represented by a quantity referred to as the Hamaker constant, H. The Hamaker constant for a specific system depends on the Hamaker constants of its elements, thus in our case of a particle, Hp, fiber, Hf, and water, Hw, according to the following equation: 𝐻 = (√𝐻𝑝 − √𝐻𝑤 )(√𝐻𝑓 − √𝐻𝑤 )

(3.2.7)

The constants are dependent on the electronic structure of materials as well as their dielectric properties. The electrical double-layer interactions result from the formation of a double-layer of charge around solid materials placed in aqueous environments. Generally they depend on zeta potential value, which is defined as the electric potential difference between the dispersion medium and the stationary layer of the fluid attached to the suspended particle or the collector element. For the filtration process it may be calculated as follows (Hogg et al., 1966): 𝐹𝐸𝐷𝐿 =

𝜀𝑒 𝑑𝑝 (𝜁𝑝2 +𝜁𝑓2 )𝜅 exp(−𝜅ℎ) 4(1−exp(−2𝜅ℎ))

22

𝜁𝑝 𝜁

(2 𝜁 2 +𝜁𝑓2 − exp(−𝜅ℎ)) 𝑛 𝑝

𝑓

(3.2.8)

where ɛe is the dielectric constant of the liquid, ζp, ζf are the zeta potentials of the particle and the fiber respectively, κ is the inverse Debye length. When the particle reaches a distance of 5 nm or less, the short-range interactions start to become significant. They determine how close to each other two atoms can ultimately get. The Born repulsive force arises at some point in the particle approach, when the electron clouds of a particle and fiber surfaces begin to overlap. The strength of this force can be described as (Raveendran and Amirtharajah, 1995): 𝐹𝐵 = −

𝐻𝑑𝑝 𝜎𝑐𝑜𝑙 6

(3.2.9)

360ℎ8

where σcol is the collision diameter. The hydration force results from changes in ordering of liquid molecules during the particle approach. It can be defined through (Raveendran and Amirtharajah, 1995): ℎ

𝐹ℎ = −𝜋𝑑𝑝 𝐾ℎ′ (exp (− ℎ′))

(3.2.10)

where K and h’ are empirical constants. A sum of long- and short-range forces decides about a particle attachment or detachment, as presented in Fig. 3.2.2. The profile is directly related to interaction energy between the particle and the filter element. An energy barrier resulting from the repulsive forces prevents the approaching particle from adhering. If the particle collides with sufficient energy to overcome the barrier, the attractive forces will attract it strongly and cause irreversible adhesion. In this situation the energy reaches the minimum value. The contact is termed “primary minimum” and is characterized by the highest value of the total interaction force at low separation distances (Fig. 3.2.2). However, as the energy barrier may be too high to overcome repulsion, the suspended particle may deposit in the “secondary minimum” represented by the second positive peak value of surface forces at longer separation distances (Fig. 3.2.2). The adhesion is weaker than in the primary minimum, thus under detachmentfavorable conditions the particle may be re-suspended during further filter loading.

23

Fig. 3.2.2. A sum of the London-van der Waals, electrical double-layer, Born and hydration forces as a function of distance between the particle and the fiber. Depth filtration mechanisms concern both interactions within the suspension and interactions between the particle and the fiber. A proper knowledge about the mechanisms of particle transport provides guidelines how to design filter structures to achieve the best initial performance. Depending on the properties of solids, such as size or density, different mechanisms can be enhanced by changes in fiber diameter or fluid velocity. Through changes of the chemical properties of the suspension or the filter material, selective separation may be provided or resuspension of the accumulated matter may be reduced. Hence, the depth filtration process depends on fiber diameter and packing density of fibers as well as the type of filter material. With a proper choice of the filter production method and a good knowledge about the manufacturing process, a desired filter can be easily made.

24

4. FILTER PRODUCTION Fibrous filters are generally classified as nonwoven media. Nonwovens are defined as “structures of textile materials, such as fibers, continuous filaments, or chopped yarns of any nature or origin, that have been formed into webs by any means, and bonded together by any means, excluding the interlacing of yarns as in woven fabric, knitted fabric, laces, braided fabric or tufted fabric” (PN-EN ISO 9092:2011, 2011). For various purposes of liquid filtration, they are mainly produced out of polymers, glass and cellulose (Tab. 4.1). Table 4.1. Typical applications for filter fabrics (Sutherland, 2008). Material

Polypropylene

Application

Acids, alkalis,

Max service

Principal

Principal

temperature [°C]

advantages

disadvantages

130

Low moisture

-

solvents (except

absorption.

aromatics and chlorinated hydrocarbons). Polyethylene

Acids and

70

alkalis.

Easy cake

Soften at

discharge

moderate temperatures.

Polyester

Acids, common

100

Good strength

Not suitable for

organic

and flexibility.

alkalis.

solvents,

Initial

oxidizing

shrinkage.

agents. Nylon

Acids,

150

petrochemicals, organic

High strength

Absorbs water.

and flexibility.

Not suitable for alkalis.

solvents, alkaline suspensions.

25

Glass

Concentrated

250

Suitable for a

Lacks fatigue

hot acids,

wide range of

strength for

chemical

chemical

flexing.

solutions.

solutions, hot

Abrasive

or cold (except

resistance poor.

alkalis).

In general, fibrous materials can be produced in water (wet laid) or air (dry laid) medium, depending on the fiber formation method (Hutten, 2016): I. Wet laid processes: 1. Wet end: involve a preparation of a dispersion of fibers in water and then filtering it through a moving screen to form a wet nonwoven sheet. 2. Dry end: involve various forms of mechanical and thermal devices to remove water from the formed sheet to achieve a dry sheet at the end of the process. II. Dry laid processes: 1. Fiber sourced: fibers are deposited onto a collector with the use of air stream, card or garnett and then formed into final web. Bonding of fibers is needed to achieve a firm structure. 2. Meltspun: fibers are formed from granulated polymers which are melted to desired temperature and extruded on a collector through a die containing a number of holes. The process of fiber formation in the extrusion chamber is accompanied by air. a. Spunbond: air stream is intended to cool the fibers, flowing perpendicularly to the fibrous surface. b. Melt-blown: air stream is for the filament attenuation and stretching, thus its flow is directed in parallel to the fiber path. 3. Flashspun: fabrics are formed from a solvent solution of polymer. The aim is to cause the filaments to form a highly fibrillated form during extrusion on a collector, through sudden evaporation of a solvent at lower pressure. After some physical treatment, such as washing and forming the final web, the material becomes useful. 26

4. Nanofiber spun webs: a. Electrospun: involve applying a strong electric potential to a polymer solution or melt flowing through a capillary to draw the polymer threads to a grounded collector. b. Centrifugal spinning: spinning is based on a centrifugal spinnerette which during rotation ejects a polymer solution or melt jet from the nozzle. The filament undergoes stretching and eventually deposits on a collector, as a solidified fiber. Fibrous fabrics for various liquid filtration purposes can be obtained in all of the above processes. The difference is in the complexity and cost of their manufacture as well as in the properties of formed materials. As the highest advantage of fibrous filters is in a greatly developed specific surface area, the most important values in produced materials are low diameters of fibers and their high packing densities. Nanofibers can be fabricated with different productivities in melt-blown, flashspinning, electrospinning and centrifugal spinning processes. Most of them can only produce loose fibers, which afterwards have to be formed in a proper filtrating structure and then bonded to create a stable material. The bonding process can be performed in: needle punch, hydroentanglement, stich, thermal or chemical bonding. The melt-blown technique is the only one that can efficiently produce multilayer fabrics with the desired distribution of fiber diameter and porosity, from polymer granulate to the readyto-buy product in a one-step process. The process is simple and inexpensive. Thus, this technique is widely used in industrial scale production of fibrous filters. According to Tab. 4.1 polypropylene is the most universal filtrating medium, thus filters produced out of this material in a melt-blown technology process were analyzed in this work.

4.1. Melt-blown technology One of the most promising methods of fibrous filter production is the melt-blown technique (Hutten, 2016). In a single production cycle filters of different structures can be easily produced (Bodasinski et al., 2015). A schematic of the stand for producing fibers by blowing a melted polymer is shown in Fig. 4.1.1.

27

Fig. 4.1.1. A scheme of production of fibrous material in the melt-blown technique (a), single nozzle (b) and nozzle’s aperture (c). A granulated polymer is poured into a container (1). The extrusion screw (2), driven by an electric motor with the gear system (4), transports the polymer into the die (5) with a desired flow rate. The polymer is melted and heated to the required value of its temperature using an electric heater (3). The die construction enables formation of melted polymer jets in the nozzle system (Fig. 4.1.1b). A single cylindrical jet formed in the nozzle hole is exposed to the stream of the hot air (6) flowing tangentially to the surface of the polymer jet. The shearstress at the interface polymer-air causes the stretching of melted filaments. In the zone of cooling, T0, the polymer filament is solidified and then collected on the pivot connected with the perforated filter core on it (7). The pivot rotates and moves to-and-from under the die. The filter structure is formed. For a better understanding of the process principles, a short introduction to modeling of a single-fiber formation has to be made. Analysis is made for a system representing a single aperture in the die (Fig. 4.1.2).

28

Fig. 4.1.2. Schematic of a single fiber formation. The basic model equations describing formation of a thin fiber in the melt-blown technology are derived under the following assumptions: the fiber has a cylindrical shape, the polymer has the same density for melted and solid phases, axial velocity within the melted fiber is uniform in the fiber cross-section, the polymer is a Newtonian liquid with the Arrhenius type of dependence of viscosity on temperature, the heat capacity of the polymer is constant, the temperature distribution is uniform in the fiber cross-section, the heat conduction in the axial direction is negligible. It is very difficult to solve a set of equations describing the process of fiber formation, i.e. continuity equation, momentum balance equation, constitutive equation and energy balance equation at the real condition of the melt-blown process. For practical purposes of designing the process and estimating its operational conditions, the modeling of the process is simplified assuming that the most important effect defining fiber diameter is the gradient of the axial stretching force,

𝑑𝐹 𝑑𝑥

, along the direction of stretching, x (Gradon et al., 2005). The gradient

results from interaction of the air stream flowing along the melted fiber: 𝑑𝐹 𝑑𝑥

𝑑𝑈

= 𝑄 𝑑𝑥 + 𝜋𝑑𝑓 𝜏𝑥

(4.1.1)

where Q is the mass flow rate of the polymer in the single hole at the die nozzle, U – linear velocity of the polymer at the exit of the hole, τx – shear stress at the polymer-air boundary.

29

Such theoretical analysis of single-fiber formation gives quantitative information about the diameter of the solidified polymer fiber, df, at the distance x from the nozzle hole of diameter D for precisely fixed model parameters, i.e., polymer constitutive properties, flow rates and temperatures of the polymer and air, and polymer pressure in the die. Packing density of fibers results from the variation of distance between the spinning nozzle and the pivot. Depending on the shape, diameter and length of the core/pivot, fabrics of various geometries and dimensions can be produced. Based on the above analysis of fiber formation process, production parameters of the meltblown technique were quantified. The process of manufacturing fibrous filters of a defined structure, i.e. spatial distribution of fiber diameter and porosity, was implemented in an installation (Fig. 4.1.3) designed and constructed by research groups from the Faculty of Chemical and Process Engineering of Warsaw University of Technology and Amazon Filters Ltd. A set of parameters, dedicated for specific filter types, was adjusted in the control panel (Fig. 4.1.4). Filters were manufactured until all process operations ended. Photographs of the used machinery are presented in Figs. 4.1.3 and 4.1.4 below.

30

Fig. 4.1.3. Pictures of the melt-blown installation: front view (a), housing (b), die and fiber collector (c).

Fig. 4.1.4. Control panel of the melt-blown installation. 31

5. FILTER TYPES Particle transport and deposition within fibrous filters mostly depends on local conditions resulting from the fibrous structure. As the contamination slurry can be of various properties, i.e. size or chemical composition, different structures for mechanical separation have been developed.

5.1. Monolayer fabrics Monolayer fabrics are uniform in porosity and fiber diameter within the entire structure. They are produced under constant production process parameters during the entire fabric extrusion. Such filters can be applied for separation of contamination of a particular size, fitting filter design and purpose. In case of polydispersed suspensions, due to low retention capacity in such systems, they can be also used as thin membranes for surface filtration.

5.2. Multilayer fabrics Multilayer structures are the most popular ones. By setting variable flows and temperatures of a polymer and air in the melt-blown technology process, a filter can be produced out of layers of fibrous fabrics differing in fiber diameter. By automatic regulation of the collector height in the melt-blown technology set-up, packing densities of fibers can be continuously changed. Most separation processes concern filtration of suspensions characterized by a broad size distribution, hence a typical depth filter is supposed to remove suspended particles of more than one size. One possibility is to design a structure for removal of the smallest contamination size. In such a case the filter will separate particles from a liquid efficiently. Unfortunately, its lifetime will be much shorter due to quick clogging of the filter at its surface. Therefore, to extend the filter lifetime, deposition of solids can be designed to reach the entire filter volume. It is possible by layering fabrics differing in fiber diameter and/or porosity, designed to remove particular fractions of suspension, on top of each other. The gradient multilayer structure is the most common one on the market. It enables separation of constantly smaller contaminations while the fluid flows through the material. It is made of fabric with a decreasing size of either fiber diameter or porosity in the flow direction. Large particles accumulate in front layers. As each layer is designed for removal of particular particle fractions, the smaller ones can still pass through the filter and be efficiently captured 32

in deeper parts of the material. Such hierarchic deposition increases the retention capacity of the filter, filter lifetime and minimizes pressure drop increase during the filter loading.

Fig. 5.2.1. Fibrous filter characterized by a gradient structure with decreasing fiber diameter.

5.3. Mixed-fiber fabrics Fabrics made in a standard melt-blown technology process are characterized by a particular distribution of fiber diameters (Tan et al., 2010). By throttling the flow of the polymer in one of the parts of the die (Bodasinski et al., 2015) structures with the bimodal distribution of fiber diameters, thus characterized by two different mean values, can be produced. It was proved for aerosol filtration, that a combination of nano- and micro sized fibers in a single filtration layer highly increases the filtration efficiency of the fabric especially for particles of the most-penetrating size (Przekop and Gradon, 2008). In case of liquids through research was conducted.

Fig. 5.3.1. Image of a standard (a) and mixed-fiber fabric

33

5.4. Examined filter structures In this work the performance of various fibrous filter structures was analyzed for different purposes. All experiments were performed on fabrics of cartridge structures (Fig. 5.4.1) of approx. 25,4 cm (10”) in length and 6,4 cm (2,5”) in external diameter with the thickness of filtration layer of 2,5 cm (1”). Such geometries are typical in domestic and industrial use. Loading of the filters was performed under the typical constant flow condition in the direction from outside to inside of the cartridge.

Fig. 5.4.1. Cartridge filter. The influence of fiber diameter and packing density/porosity on depth penetration of solids was verified on “MONO’ monolayer filters of fiber diameters: 2, 5, 10 μm and porosities: 0,84, 0,80, 0,74. The values of structural parameters were chosen as typical for fabrics designed for water filtration. The multilayer gradient structures STANDARD 1, 2 and 3 represent commercially available filters of Amazon Filters Ltd. with the absolute micron rating of 0,5, 1 and 3 μm, respectively. Their performance was examined and then generalized in a formulized model dedicated for quick estimation of process parameters in multilayer filter designing. Filters enhanced by addition of nanofibers in every filtration layer were produced based on the macrostructure of STANDARD 1, 2, 3 filters. The filters were denoted MIXED-FIBER 1, 2 and 3, respectively. The influence of bimodal fiber distribution on material porosity, separation efficiency, pressure drop, retention capacity and lifetime was investigated on time dependent functions. The performance of various types of fibrous structures was verified in a flow-through experiment. The experiment was used as the basis for a filtration model.

34

6. FILTER CHARACTERIZATION The structure of a depth filter which defines the filter performance can be characterized through the thickness of filtration layer, size of pores, diameter and packing density of fibers. The specific surface area of the fabric is also important. In the examined filters it results directly from the previously mentioned parameters so it was not considered in this work.

6. 1. Material thickness Thickness of the filtration layer determines the filter use. Some particles flowing through a fabric which is too thin may not have the possibility to deviate their pathways from the streamline enough to deposit on fibers. On the other hand, a layer which is too thick may separate particles efficiently, although, according to Darcy’s law, creating unnecessary flow resistance, which increases costs spent on liquid pumping (Sec. 9). Such reasons point out why optimization of this parameter is so important. The measurement of material thickness is simple. The best method is to use a micrometer, without squeezing the sample. However, due to the accessibility of measuring instruments, in this work material thickness was defined based on data from the production cycle (the number of layers of similar properties) and final overall thickness of the filtration layer, measured using a digital caliper. Results are presented in Tab. 6.1.1 below. Table 6.1.1. Thickness of filtration layer of tested filters. Filter type

Thickness of filtration layer [mm]

MONO 2 μm 1, 2, 3

15

MONO 5 μm 1, 2, 3

15

MONO 10 μm 1, 2, 3

15

STANDARD 1, MIXED-FIBER 1

1st layer (inlet)

0,3

2nd layer

1,8

3rd layer

1,8

35

4th layer

1,8

5th layer

2,1

6th layer

2,6

7th layer (outlet)

3,9

1st layer (inlet)

0,3

2nd layer

1,8

3rd layer

1,8

4th layer

2,1

5th layer

2,1

6th layer

2,4

7th layer (outlet)

3,7

1st layer (inlet)

0,3

2nd layer

1,7

3rd layer

2,0

4th layer

2,0

5th layer

2,0

6th layer

2,0

7th layer (outlet)

4,0




36

All filters were characterized by a similar external diameter of the fabric, of ca. 64 mm. The outer diameter of the core was equal to 34 mm. Thus, the total thickness of the filtration fabric was the same, equal to 15 mm. The gradient filters were composed of 7 layers differing in thickness, fiber diameter and packing density. The first layer of 0,3 mm in thickness was the most porous and was created only for suspension distribution. Therefore, in further work 1st and 2nd layers were considered together, as one layer. The construction of the filter structure was performed with the increasing thickness of deeper layers. The purpose of such a design is to improve separation efficiency in deeper parts of the filter for consistently smaller contaminations. Due to the mechanism of deposition of nano-objects, which is Brownian diffusion, smaller particles need a longer retention time in filter material to increase the probability of contacting the collector.

6.2. Pore diameter Some models describing the separation process within the filter structure, for instance the most common microscopic model of Tien and Payatakes (Tien and Payatakes, 1979) or the network model of Yang and Balhoff (Yang and Balhoff, 2017), are based on tracking pathways of particular particles inside pore spaces of the filter media. For a correct description of this process, the dimensions of filter pore channels must be known. Pores of a fibrous filter are irregular in shape. The cross-section of a pore in the direction perpendicular to the fluid flow can be of a shape of miscellaneous polygons (Fig. 6.2.1). Therefore, it is hard to define their dimensions in a simple way. Several techniques were developed to determine pore size distribution in various materials, i.e. mercury intrusion porosimetry,

gas

adsorption

method,

mean-flow

pore

size

test,

computer

tomography/microscopy and the most common, bubble pressure test (Dullien, 2012; Wang et al., 2012). Determination of pore size distribution with the techniques requires a description of a pore shape in terms of a pore model. Most methods are based on the assumption of a cylindrical pore-shape with precise tortuosity. All deviations from this figure cause difficulties or make the method useless.

37

Fig. 6.2.1. Image of the clean filter layer. As can be seen in Fig. 6.2.1 depicting a clean fabric, the cross-section of pores is mostly in a trapeze or triangle shape. From our observations of the filter structure loaded with contamination after various time intervals it was concluded that contamination accumulates compactly on fiber intersections. As can be seen in Fig. 6.2.2, loading of the structure with particles causes a conversion of the pore cross-section shape to elliptical and circular. The deposit distributes unevenly within the material. Some pores clog more rapidly (Fig. 6.2.2b). The experimental measurement of the pore size in a clean or a partially loaded fabric, with the present measurement techniques could either destroy the deposit or due to the adopted model of a universal pore shape give faulty results. With all the above, pore size distribution is difficult to be reliably determined in fibrous filters and was not analyzed in this work.

38

Fig. 6.2.2. Picture of the filter layer during (a) ripening and (b) operable stage of the filtration process.

6.3. Fiber diameter Fiber diameter and packing density/porosity directly determine the initial particle capture efficiency (Sec. 3), thus further spatial loading of the filter structure, as well as the initial value of flow resistance and its development (Sec. 8). Fibrous filters produced in a well-designed melt-blown technology process are cylindrical in shape, so fiber size can be characterized by the fiber diameter of the cross-section plane. Fiber diameter distribution of a clean filter can be easily determined with microscope images. The diameter of randomly selected fibers in a picture is measured and usually presented in a form of size distribution. In this work the diameter of fibers of examined filter materials was measured using a TM - 1000 scanning electron microscope manufactured by Hitachi Ltd. Due to the character of the results, fiber diameter distribution was presented as a normal distribution function (Figs. 6.3.1-3) with the arithmetic average fiber diameter df,av, and standard deviation df, Ϭ., as the probability density function: 𝑓(𝑑𝑓 ) =

1 √2𝜋𝑑𝑓,𝜎

exp⁡(−

39

(𝑑𝑓 −𝑑𝑓,𝑎𝑣 ) 2𝑑𝑓,𝜎

2

2

)

(6.3.1)

Deformed or entangled fibers were not counted. Below, Fig. 6.3.1 presents results of fiber diameter distribution of the examined monolayer filters. As can be noticed, using the meltblown technique, the width of fibrous size distribution is broader for fibers with higher average diameter. However, the contribution of standard deviation in the results was similar, around 25 % of the average diameter.

probability density function [-]

1,0 0,8 0,6 MONO 2 µm MONO 5 µm

0,4

MONO 10 µm 0,2

0,0 0

5 10 fiber diameter [μm]

15

Fig. 6.3.1. Fiber diameter distribution of MONO 2, 5, 10 µm filters. Fig. 6.3.2 shows measurement results of STANDARD 1, 2, 3 multilayer gradient filters. The results cover the fiber diameter distribution of 90 %mass equivalent filters with bimodal fiber size distribution, as they were produced with a similar macro-skeleton. The size distribution of nano-fibers determining the remaining 10 % of filter mass in every filter layer of MIXEDFIBER 1, 2, 3 filters was included in Fig. 6.3.3.

40


1st layer 0,5 0,4 0,3 STANDARD 1 0,2

STANDARD 2 STANDARD 3

0,1 0,0 0


30


2nd layer 1,0 0,8 0,6 STANDARD 1 0,4


0,2 0,0 0

5


41

20


3rd layer 1,5

1,0 STANDARD 1

STANDARD 2

0,5

STANDARD 3

0,0 0

2


8

10


4th layer 2,0 1,6 1,2 STANDARD 1 0,8


0,4 0,0 0

2


42

8

10




0,5 0,0 0

1


4




0,5 0,0 0


3

Fig. 6.3.2. Fiber diameter distribution of STANDARD 1, 2, 3 standard gradient.

43


1st layer 0,5 0,4

MIXED-FIBER 1 MIXED-FIBER 2 MIXED-FIBER 3

0,3 0,2 0,1 0,0 0


30


2nd layer 1,0 0,8


0,6 0,4 0,2 0,0 0

5 10 15 fiber diameter [μm]

44

20


3rd layer 1,6 MIXED-FIBER 1 MIXED-FIBER 2 MIXED-FIBER 3

1,2 0,8 0,4 0,0 0

2


10


4th layer 2,0 1,6


1,2 0,8 0,4 0,0 0

2


45

10


5th layer 2,5 2,0


1,5 1,0 0,5 0,0 0

1


5


6th layer 2,5 2,0


1,5 1,0 0,5 0,0 0


3

Fig. 6.3.3. Fiber diameter distribution of MIXED-FIBER 1, 2, 3. mixed-fiber filters. Multilayer filters are designed for the removal of contamination characterized by a broad size distribution. According to the equations governing the mechanisms of particle transport (Sec. 3) the smaller fiber diameter the more effective separation efficiency of contamination. Thus for the final clearance of the filtrate, i.e. the least particles removed, the layer with the smallest collector sizes should be the decisive one if similar porosity values of the fabrics are assumed. The last, 6th layer of STANDARD 1, 2, 3 filters is characterized by the average fiber

46

diameter of 1,3, 2,0, 1,8 μm respectively. In previous layers (Fig. 6.3.2) the dependence of fiber size with the filter type is not maintained. The bimodal fiber distribution of MIXED-FIBER 1, 2, 3 filters is presented in Fig. 6.3.3. Micro- and macro-fibers were produced in the die simultaneously. 10 % of the fabric mass was composed of fibers 2-7 times smaller than the macro-structure. The diameter of these micro-fibers is also decreasing with the layer number. In this work, due to the size of the least fiber diameter, in mixed-fiber structures the micro- and macro-fibers were named ‘nano-’ and ‘macro-‘ respectively. As will be evidenced later, the filter behavior cannot be foreseen only based on the fiber diameter size. In fact the porosity of the fabric is the key factor.

6.4. Porosity Porosity, ε, is a measure of void spaces in a material. Thus, a packing density of the filter bed, α, is equal . It can be measured with porosimeters, optical methods, geometric or mass considerations (Dullien, 2012). For years, these methods have been developed by many researchers (Siddiqui et al., 2017; Robin et al., 2016; Zou and Malzbender, 2016; Anovitz and Cole, 2015), although they still have some limitations. The main problem is proper determination of pore volume. The first group of methods such as mercury injection, gas expansion or imbibition/buoyancy method, is based on the extraction of a fluid from the sample or intrusion of a fluid into pore spaces. Imbibition method is based on the determination of a sample weight before, Wdry, and after imbibition, Wsat, in a perfectly wetting fluid of a known density, ρfluid. The bulk volume of the sample, V0, must be previously determined as well. Then, the volume of pores, based on the mass of liquid filling filter pores, can be calculated from physical relationships. However, typical filters for water purification do not absorb fluids, thus a weight measure of such a saturated filter would be pointless. For non-woven fibrous filter characterization there is a similar, more adequate method, the buoyancy method. The weight difference between the dry specimen and the immersed saturated sample divided by the fluid density results in the solid volume, and hence the volume of pores. In this approach, however, a saturated sample is suspended in a bath of the same fluid with which it was saturated to yield its suspended weight, Wsusp. The effect of the cradle must be taken away, hence the weight of the cradle 47

when suspended in the fluid up to the same level, Wcradle, must be taken into account in the final calculation. The porosity can be computed as: 𝑉0 −

𝜀=

(𝑊𝑑𝑟𝑦 −(𝑊𝑠𝑢𝑠𝑝 +𝑊𝑐𝑟𝑎𝑑𝑙𝑒 )+𝑊𝑐𝑟𝑎𝑑𝑙𝑒 ) 𝜌𝑓𝑙𝑢𝑖𝑑

𝑉0

(6.4.1.)

The accuracy of this method is determined by the efficiency with which the pores are filled by the impregnating fluid. In the European Standard EN 623-2 (BS EN 623-2:1993, 1993) an improvement of the impregnation is proposed as evacuating the sample before placing it into fluid and then re-pressurizing when fully submerged. Some researchers improve the imbibition using fluids with lower surface tension (Takata et al., 1992). In the next technique, which is based on gas expansion, the gas stored in a reference vessel is isothermally expanded into a sample vessel. After expansion, the resultant equilibrium pressure is measured. The method consists of placing a dry specimen into a container of volume Va connected with an evacuated container of volume Vb. The gas is introduced into the container with a sample and set to the pressure value P1. Next, the gas is released into the evacuated vessel and allowed to equilibrate throughout both chambers. The pressure decreases to a new stable value P2. Using the ideal gas law, the porosity can be measured as: 𝜀=

𝑉0 −𝑉𝑎 −𝑉𝑏

𝑃2 𝑃2 −𝑃1

𝑉0

(6.4.2)

In view of the above law, which is the principle of this method, the technique is sensitive to temperature variations and gas purity. Nevertheless, given a proper use of equipment, this method should give higher porosities than the buoyancy method due to better penetration of gas molecules inside pores that are difficult for the liquid to get into. Another popular method for porosity determination is mercury injection. This method measures the pore volume by forcing mercury into the pore space. Due to high pressure values it requires it is highly destructive and it is not suitable for porosity determination of fabrics. The second group of techniques used for porosity determination is based on image analysis. X-ray micro-computed tomography can reconstruct the complete internal 3-dimensional geometry of an item as a set of a number of images. Then, the basis of image analysis is made with professional computer tools. By setting a proper threshold to gray-leveled image, objects are extracted from their back-ground (pores) based on the degree of contrast. Thresholding 48

creates a binary picture from gray-leveled images by turning all pixels below the threshold to black regions in binary image and all pixels above the threshold to white ones. Afterwards, the percentage number of black pixels determines the porosity value. Such analysis is expensive and time consuming. It is also limited to a scale of a specimen down to the micron level (Saif et al., 2017). If an item is composed of smaller elements the analysis of images taken from scanning electron microscope should be performed. It enables the observation of a structure in nanometer scales (Desbois et al., 2011). Using stereological techniques (Lukas and Chaloupek, 2006) and images of representative plane sections the 3-dimensional structure of an object can be statistically extrapolated and a similar analysis of binary images can be implemented. Such extrapolation is also encumbered with errors due to the necessity of selecting a pore-shape model. The mentioned techniques are able to determine the porosity of a clean fabric. However, porosity of a fibrous structure decreased by the accumulated deposit is problematic. Techniques based on flow-through or immersion could destroy and relocate formed agglomerates, and thus produce false results. The only possibility of a non-destructive evaluation of this parameter is the use of X-ray tomography (Jackiewicz et al., 2015). However, as was mentioned above, in case of a submicron-sized contamination, the technique is limited to rather qualitative results. The quantitative measurement of porosity development inside a fibrous filter during the filtration process was never before a subject of detailed considerations, although it has a crucial impact on particle transport phenomena. In this work a quantitative description of filter porosity development based on the initial value of porosity, scanning electron microscope images and the overall filter mass was proposed. Initial porosity of a clean fabric was determined gravimetrically, based on its definition. To examine the porosity in a multilayer fibrous filter, its structure/volume was stratified into layers, i, of the same porosity and fiber diameter, based on the results presented in Sec. 6.1. Initial porosity of a clean fabric layer, ε0,i, was determined through the bulk volume of the material, V0,i, and the volume of fibers, Vfiber,i, defined from fabric mass, mfiber,i, and density, ρfiber, as: 𝜀0,𝑖 =

𝑉0,𝑖 −𝑉𝑓𝑖𝑏𝑒𝑟,𝑖 𝑉0,𝑖

=

𝑉0,𝑖 −

𝑚𝑓𝑖𝑏𝑒𝑟,𝑖 𝜌𝑓𝑖𝑏𝑒𝑟

𝑉0,𝑖

(6.4.3)

The values of porosities of the examined clean fibrous filters are presented in Table 6.4.1. They are averaged values of measurements for 4 filters of each type. The biggest standard 49

deviation of 0,0067 during measurements was insignificantly small, and therefore it was omitted in Table 6.4.1 below. Table 6.4.1. Average values of initial porosity of tested filters. Filter type

Number of the filter 1

2

3

MONO 2 µm

0,84

0,80

0,75

MONO 5 µm

0,85

0,81

0,75

MONO 10 µm

0,83

0,79

0,72

Number of the filter layer 1

2

3

4

5

6

STANDARD 1

0,74

0,80

0,79

0,80

0,82

0,85

STANDARD 2

0,73

0,79

0,81

0,81

0,80

0,85

STANDARD 3

0,68

0,76

0,80

0,84

0,78

0,86

MIXED-FIBER 1

0,72

0,77

0,81

0,82

0,85

0,84

MIXED-FIBER 2

0,69

0,76

0,78

0,77

0,82

0,85

MIXED-FIBER 3

0,67

0,75

0,77

0,79

0,82

0,81

The porosity of produced monolayer filters characterized by a particular fiber diameter distribution was 0,84; 0,80; 0,74 for filter types 1, 2, 3 respectively. MIXED-FIBER filters due to similar mass and volume of the filter layer were characterized by similar initial porosities as standard gradient filters with the highest difference up to 5 %. The last layer of the fabric, separating the finest contamination, was the most porous for STANDARD 3 and MIXED-FIBER 3 filters, and the least porous for STANDARD 1 and MIXED-FIBER 1 filters. In all multilayer filters, despite the character of fiber diameter distribution, the initial 50

porosity of fabric layers was the lowest on the filter inlet and the highest on the outlet. Between those layers porosity was changing diversely. During water purification the contamination deposit on the filter material initiated its structural changes. At first, solid particles adhere to a clean surface of the fabric. Due to the local fluid flow field near the fibers, particles deposit mostly on fiber intersections. These are the regions of momentum reduction and therefore offer favorable adhesion conditions. After a short time particles start to deposit on one another as can be seen in Fig. 6.4.1. Double layer interactions make solid particles create compact agglomerates with a value of particle packing density around 1.

Fig. 6.4.1. Fibrous filter loading with particles. For the verification of contamination penetration depth, monolayer filters were examined in an experiment performed on polydisperse contamination, according to a European standard (EN 13443-2:2005+A1:2007, 2007), until full clogging of the filter occurred. A description of the test procedure was made in Sec. 7. After the experiment, the filter was dried in a convection drier and sectioned into layers at 5 equal depths of the fabric. Then, pictures of front surfaces of these fabrics were taken. Results are presented in Figs. 6.4.2-4.

51

Fig. 6.4.2. SEM images of fibrous layers of filter MONO 2 μm 1 (ε0 = 0,84), 2 (ε0 = 0,80) and 3(ε0 = 0,75) after reaching 2,5 bar pressure drop during filter loading.

52

Fig. 6.4.3. SEM images of fibrous layers of the filter MONO 5 μm 1 (ε0 = 0,85), 2 (ε0 = 0,81) and 3 (ε0 = 0,75) after reaching 2,5 bar pressure drop during filter loading.

53

Fig. 6.4.4. SEM images of fibrous layers of the filter MONO 10 μm 1 (ε0 = 0,83), 2 (ε0 = 0,79) and 3 (ε0= 0,72) after reaching 2,5 bar pressure drop during filter loading. As can be noticed in Figs 6.4.2-4, the penetration of solids increases inversely proportionally to the initial porosity of the fabric. It is the most distant for filters with fabric initial porosity 54

of around 0,74. Agglomerates are present in the entire filter volume. However, it has to be emphasized that the initial structure of this material was noticeably soft and at the end of the experiment the outer diameter of these filters was reduced from 64 mm to 58 mm. Thus, the presence of solids could be the effect of structural damage and deposit relocation. In case of the filters characterized by initial porosity of ca. 0,80 agglomerates could be observed until 2/5 of the filter depth. Further on, rather single particles or small clusters could be noticed. During the filter loading the outer diameter of these filters did not change. Also filters of the highest porosity kept their initial dimensions. It might be due to the fact that a decrease in porosity and an increase in fiber diameter directly influence the amount of fibers which create the supporting rack preventing from deflections. Therefore, there is a down-limit value of porosity related with a specific value of fiber diameter below which fabrics are soft and prompt to structural damage during pressure increase. High separation efficiency of fibers of MONO 2 μm 1, 2 and 3 filters causes quicker clogging but also a controlled resuspension of the deposit as well. With the fiber diameter increase the ability to collect re-entrained particles decreases (Sec. 3). Moreover, in all filter types, despite size or packing density of fibers, most contamination was accumulated in the most front layer of the fabric. It concurs with results from process simulations (Zywczyk et al. 2015) where the authors theoretically evidence the optimum limit of filtration layer thickness. Most commercially available fibrous filters are in a structure of multilayer fabric, composed of layers differing in fiber diameter and porosity. Such a structure is more complicated than a monolayer filter and therefore was chosen to describe filter loading. During water purification with multilayer filters contamination accumulates at different depths of filtration fabric, depending on separation properties of each layer. Such deposition indicates non-uniform changes in porosity of the filter material. Porosity of a single fabric layer, εt,i, decreases with the growth of the deposit volume, Vdep,i, thus the deposit mass, mt,dep,i, and can be calculated from: 𝜀𝑡,𝑖 =

𝑉0,𝑖 −𝑉𝑓𝑖𝑏𝑒𝑟,𝑖 −𝑉𝑑𝑒𝑝,𝑖 𝑉0,𝑖

=

𝑉0,𝑖 −

𝑚𝑓𝑖𝑏𝑒𝑟,𝑖 𝑚𝑡,𝑑𝑒𝑝,𝑖 − 𝜌𝑓𝑖𝑏𝑒𝑟 𝜌𝑑𝑒𝑝

𝑉0,𝑖

(6.4.4)

where ρdep is the density of water contamination material. The mass growth of a dry filter layer after a precise time of the experiment indicates the mass of accumulated contamination. Its direct measurement for each layer of multilayer fibrous 55

filters is encumbered with errors. To consider layers separately, the filter has to be stratified into layers. Mechanical stratification causes some losses of the mass accumulated on fibers. Moreover, after a short filtration time the total mass growth of a filter divided into layers few millimeters thick is small for a precise measurement. Therefore it was decided to estimate the amount of accumulated deposit upon images from a scanning electron microscope. Porosity is a feature characterizing a 3-dimensional space. The flow through cartridge fibrous filters is in

the radial direction and particle transport and deposition are controlled by

structural changes mostly in a perpendicular plane. Due to the non-uniform distribution of deposit within the entire fibrous structure, a quantitative measurement of porosity involving full depth of the fabric does not inform about the dynamics of local condition changes. Clogging of the surface layer of the fabric mostly decides about the filter use, as could be seen in the example of monolayer filters. Despite reaching the value of 2,5 bar pressure drop during the filter loading, the main deposition was still spread among the first layers of the fibers (Fig. 6.4.2-4). Conditions in this part of the filter, the front surface of the filter layer, as well as dynamic changes of filter effectiveness decide about the filter longevity. For the purposes of a quantitative description of qualitative changes indicating filter performance, the porosity of the front surface of the layer volume was chosen as the most influencing parameter. Based on images, stratification filter into layers of the same structure did not affect the deposit accumulated in a plane perpendicular to the flow direction. Thus, the amount of the free space left on the layer surface was used in further analysis. Using a TM - 1000 scanning electron microscope manufactured by Hitachi Ltd., 10 images of randomly chosen locations of every layer of the tested filter after 0, 20, 40, 60, 80, 100 % of the loading time were performed. Images were taken in a magnification wherein a number of around 100 pores could be counted. Until this enlargement, the clearance of the sample was representative for the whole layer and some small amounts of deposit could still be noticed. The samples were previously coated by a 25 nm layer of gold, using a K550X sputter coater of Quorum Technologies Ltd., so that in images the fibers as well as the deposit were seen as bright images. By setting a proper threshold to gray-leveled images, objects were extracted from their back-ground based on the degree of contrast. A single pore was defined as a dark space in the image with an increased contrast, generated by around 5 top layers of the fibers. This number of layers should be adequate to create a constricted tube pore-shape, popularly used in theoretical considerations (Yang and Balhoff, 2017; Chaumeil and Crapper, 2014). 56

Deeper located fibers or deposit were treated as dark pixels. The clearance of the initial fibrous structure, P0,i, reduced by the structure of particle deposit was determined as the average percentage amount of black pixels in the image, Pt,i. A sample of image analysis is presented in Fig. 6.4.5.

Fig. 6.4.5. Image of a filter layer loaded with solids before (a) and after (b) computer modifications for clearance determination – visibility limited up to 5 top layers of the fabric. On this point it has to be emphasized that tortuosity of a pore is established to be equal 1 and it is assumed that the deposit fills the fibrous fabric volume uniformly with the flow direction. Therefore the volume of the deposit could be measured based on this “2-dimensional porosity”. However, as it was proved above, the assumption about homogeneity of deposit alignment within the filter volume is far from reality. The front surface of the fabric layer, i.e. the surface from which the samples were taken, adsorbs most contaminations. Hence, the volume of the deposit accumulated on each layer of the filter can only decide about the proportion of the structure loading. Its direct conversion to a deposit mass would be overestimated. As a result, the true mass of contamination deposited within a single layer was determined including an increase of the total mass of a dry filter during the experiment, mt,dep, defined as: 𝑚𝑡,𝑑𝑒𝑝,𝑖 = 𝑚𝑡,𝑑𝑒𝑝 ∑6

𝑃0,𝑖 ∙𝑉0,𝑖 −𝑃𝑡,𝑖 ∙𝑉0,𝑖

𝑖=1(𝑃0,𝑖 ∙𝑉0,𝑖 −𝑃𝑡,𝑖 ∙𝑉0,𝑖 )

(6.4.5)

Then, the evolution of the filter structure was then determined from Eq. 6.4.4. Below are presented the outcomes of the method. Results of clearance measurements during filter loading are presented in App. 1. Figs. 6.4.6-8 present an increase of specific deposit, namely deposit mass accumulated within individual filtration layers of the multilayer filters. 57

The porosity evolution of each filter layer is presented in Figs 6.4.9-11. All results are shown as a function of time of a flow-through experiment performed until total clogging of the filter. Due to differences in test duration, time was normalized to a time of reaching 2,5 bar pressure drop on the filter.

(a)

specific deposit [kg·m-3]

180 150 1ˢᵗ layer

120

2ᵑᵈ layer

90

3ʳᵈ layer 4ᵗʰ layer

60

5ᵗʰ layer

30

6ᵗʰ layer

0 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-]

(b)


80

60 1ˢᵗ layer 2ᵑᵈ layer

40

3ʳᵈ layer

4ᵗʰ layer 20

5ᵗʰ layer 6ᵗʰ layer

0 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. 6.4.6. Evolution of specific deposit during loading of STANDARD 1 (a) and MIXEDFIBER 1 filters (b). 58

(a)



120

2ᵑᵈ layer

90


60

5ᵗʰ layer

30

6ᵗʰ layer

0 0,0

0,2

0,4

0,6

0,8

1,0


(b)


80


40


20


0 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. 6.4.7. Evolution of specific deposit during loading of STANDARD 2 (a) and MIXEDFIBER 2 filters (b).

59

(a)



120

2ᵑᵈ layer

90


60

5ᵗʰ layer

30

6ᵗʰ layer

0 0,0

0,2

0,4

0,6

0,8

1,0


(b)


80


40


20


0 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. 6.4.8. Evolution of specific deposit during loading of STANDARD 3 (a) and MIXEDFIBER 3 filters (b).

60

(a)

porosity [-]

0,85 0,80 1ˢᵗ layer 0,75

2ᵑᵈ layer

3ʳᵈ layer

0,70


0,65

6ᵗʰ layer 0,60 0,0

0,2

0,4

0,6

0,8

1,0


(b)

porosity [-]

0,85 0,80 1ˢᵗ layer 0,75

2ᵑᵈ layer 3ʳᵈ layer

0,70


0,65

6ᵗʰ layer 0,60 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. 6.4.9. Evolution of porosity during loading of STANDARD 1 (a) and MIXED-FIBER 1 filters (b).

61

(a)

porosity [-]

0,85 0,80 1ˢᵗ layer 0,75

2ᵑᵈ layer

3ʳᵈ layer

0,70


0,65

6ᵗʰ layer 0,60 0,0

0,2

0,4

0,6

0,8

1,0


(b)

porosity [-]

0,85 0,80 1ˢᵗ layer 0,75


0,70


0,65

6ᵗʰ layer 0,60 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. 6.4.10. Evolution of porosity during loading of STANDARD 2 (a) and MIXED-FIBER 2 filters (b).

62

(a)

porosity [-]

0,85 0,80 1ˢᵗ layer 0,75

2ᵑᵈ layer

3ʳᵈ layer

0,70


0,65

6ᵗʰ layer 0,60 0,0

0,2

0,4

0,6

0,8

1,0


(b)

porosity [-]

0,85 0,80 1ˢᵗ layer 0,75


0,70


0,65

6ᵗʰ layer 0,60 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. 6.4.11. Evolution of porosity during loading of STANDARD 3 (a) and MIXED-FIBER 3 filters (b). Specific deposit presents the mass of contamination accumulated within the filter volume. Standard SI unit is expressed through kg·m-3. Thickness of filtration layer in a multilayer filter is in a range of 10-3 m, as presented in Table 6.1.1. Therefore, such scale-up of a system

63

of 103 times, magnifies structural changes as well as resuspension of the deposit when some critical amount of solids accumulate on fibers. Porosity changes less rapidly than deposit mass due to calculations in scale of dimensions of the tested filters and non-uniform deposit distribution. As was mentioned earlier, the main deposition takes place only within a few front fiber layers. Deeper located parts of the layer are loaded sparingly. Therefore, despite differences in clearance of the front surface of the layers fluctuating up to 50 % with passing filtration time (App. 1), the calculated porosity values are diminished by compliance of the entire layer volume and should be treated as the average values for the entire layer. The maximum decline in porosity caused by deposit accumulation in standard gradient filters reached 6 % while in filters with bimodal distribution of fibers it was two times lower. It results from shortened time of exposure to contamination, affected by quicker clogging of the filter structure (Sec. 7). The analysis of specific deposit increase during the filter loading clearly indicates that the addition of nanofibers to the fibrous macrostructure changes deposit distribution within the filter volume. In Fig. 6.4.6.a deposit mass grows monotonically. Only 4th layer of STANDARD 1 filter reached its maximum in 80% of the filtration process time. An equivalent filter enriched by the addition of nanofibers, MIXED-FIBER 1 filter, showed clogging earlier (Fig. 6.4.6b). After 60 % of loading time a part of accumulated deposit was washed-out of the 2nd layer, which can be noticed from a decrease in the layer mass. It succeeded in a rapid increase in solid concentration in the flowing suspension. The broken deposit was efficiently collected by a subsequent layer, whose mass rapidly increased at the same time. Once the amount of deposit exceeded the maximum retention capacity of the 3 rd layer, resuspension of accumulated deposit occurred again to the following parts of the filter. Such contamination collection and release is the effect of variations in local conditions in microscale observations. Depth filtration is a process where pores of a filter material are larger than removed solids and separation results from effective particle transport inside the filter volume. Thus, no sieve effect can be noticed. In this work filtration under constant flow condition is considered. During suspension purification, solids deposit on fibers constantly decreasing the area for a liquid to flow through. To preserve the assumption of a constant flow, water velocity rises and so does the shear-stress on the contact surface. When the local shear stress rises to a critical value, due to a high viscosity of the liquid, further deposition of particles periodically leads to agglomerate burst and re-entrainment within or even outside the 64

filter structure. This phenomenon is common in water filtration and should be predicted on a filter design stage (Przekop and Gradon, 2016). A similar situation is presented in Figs. 6.4.7-8. Standard gradient structures were loaded mostly monotonically. The pores of MIXED-FIBER 2 and 3 filters are being built over more dynamically. Nanofibers attract particles more than micro sized fibers, therefore the addition of nanofibers to all filtration layers moved deposition to front layers and caused their quicker clogging. Also resuspended agglomerates seem to be captured more effectively, which can be concluded from the succeeding clogging of following layers. All of the above presented results lead to a conclusion that a good design of the filter fabric should foresee its structural loading. Calculations performed for a clean fabric are simple, well-known, but not enough (Tien, 2012). Moreover, the European standard of filter testing procedure (EN 13443-2:2005+A1:2007, 2007) requires filter validation during only the first minutes of the filter run. As was shown in this section of the thesis, only full experimental validation of fibrous filters gives information of non-steady state phenomena, i.e. deposit resuspension, which influence the quality of the filtrate. Therefore, only properly performed experimental research may provide basis of a good filter design.

65

7. EXPERIMENTAL VALIDATION The quality of a filter is determined by separation efficiency, generated pressure drop, lifetime and dirt holding capacity. Based on values of these properties obtained in a flow-through experiments, filters can be differentiated from each other.

7.1. Test stand Nowadays diverse procedures of filter testing are available and used by different companies (Hutten, 2016). In this work a standard EN 13443-2 (EN 13443-2:2005+A1:2007, 2007) was chosen as the reference. It specifies requirements relating to the construction, performance and methods of testing for mechanical filters designed for the removal of suspended matter in drinking water installations inside buildings. The standard requires validation of differential pressure during cartridge filter loading, under the constant flow rate specified by the manufacturer, until reaching a value of 1,5 bar. It also specifies a definition of separation efficiency and retention capacity of the fabric. Measurements should be performed in a test stand providing recycling of the filtered fluid. The procedure was modified to fulfill the main goals of this thesis. This work deals with filtration of nano- up to microsized particles. To maintain a constant contaminant concentration in the upstream of the filter, membrane separation should be applied during the fluid recycling step. Such an operation would be too expensive and therefore recycling was not ensured. A photo and a scheme of the modernized set-up is presented below.

66

Fig. 7.1.1. Schematic diagram of the experimental set-up. 1 – main reservoir of water, 2, 4 – pumps, 3 – particle contamination reservoir, 5 – filter to be tested, 6, 7 – decontamination filters, 8, 9 – pressure gauges, 10 – particle counter.

67

Fig. 7.1.2. Photo of the experimental set-up (a), filter housing (b) and reverse osmosis system (c). 1 – main reservoir of water, 2, 4 – pumps, 3 – particle contamination reservoir, 5 – filter to be tested, 6, 7 – decontamination filters, 8, 9 – pressure gauges, 10 – particle counter. The scheme of the test-rig presented in Fig. 7.1.1 was designed to examine filters in an industrial scale experiment. Therefore, filtration experiments were carried out under the constant flow conditions of 600 L·h-1, which is the value of nominal flow through the filters 68

of 10” in length (Amazon Filters, Ltd.). The basic medium used in the research was deionized water (1) produced in an external reverse osmosis installation. The contaminant slurry was prepared in a vessel (3), equipped with a magnetic mixer, and continuously injected into the main circuit by a peristaltic pump (4). The suspension combined with deionized water was pumped on the tested filter (5) using a centrifugal pump (2), so that the test concentration had an eligible value of cin. The pressure before (8) and after (9) the filters was measured using pressure gauges and the number of particles of a particular size was counted using a particle counter (10). The filtered water finally flowed through the decontamination filters (6) and (7) to the sewage system. Before every experiment the system was washed to a constant level of particle count. Filter loading was ended when a 2,5 bar pressure drop value across the tested filter was reached. The value is higher than that recommended in standards. The purpose of this enlargement was to examine filter behavior during the filter loading. A value of 2,5 bar is a commercially recommended value (Amazon Filters, Ltd.), which indicates clogging of filter pores, leading to filter replacement. Additionally, due to the increase of test time, more characteristic periods of the filter behavior could be noticed. Experiments were performed on 2 types of contamination. A mixture of various types of Arizona Test Dust typical for filter testing was used as a multi-sized contamination during filter loading analysis (7.2.1). In this type of experiment, separation efficiency, pressure drop, retention capacity were examined as time-dependent functions. A monodispersed-type contamination was used only in a precise separation efficiency measurement for comparison of filters characterized by uniform and bimodal distribution of fibers (Sec. 7.2.2).

7.2. Separation efficiency Separation efficiency generally describes the ability of a filter to remove various contamination types from fluids. It can be defined by the weight or number of particles. The gravimetric approach is considered to be simpler but also less precise. However, depending on the purpose of research both approaches were used.

69

7.2.1. Polydisperse contamination, mass efficiency Typical dusts recommended by the standard EN 13443-2 (EN 13443-2:2005+A1:2007, 2007) for filter evaluation are produced in accordance with ISO 12103-1 (ISO 12103-1:2016, 2016). Powder Technology, Inc. produces such powders. They are standardized in size distribution and chemical content limits. For verification of filter performance during its loading and to examine filter behavior on a broad range of particle sizes, a mixture of Arizona Test Dusts: Nominal 0-3 μm, A1 (Ultrafine) and A2 (Fine) was used. Test dust Nominal 0-3 μm is a special powder, the only one not specified by the ISO standard due to the size distribution. Nevertheless, its chemical composition is the same as the other 2 dusts, which is why it was chosen as a source of the nanosized matter. The most universal contamination in evaluation of ultrafine particle removal is A1 powder. Thus, its mass concentration was doubled in the test dust composition compared to Nominal 0-3 μm and A2. The size distribution of powder, based on data provided by Powder Technology, Inc., is presented in Fig. 7.2.1.1. For rationalization of the experimental operational time filter loading was carried out with 10 mg·L-1 mass concentration. 0,25

volume fraction [-]

0,20 0,15 0,10 0,05 0,00 0,5

1

2

5 10 20 particle size [μm]

40

80

120

Fig. 7.2.1.1. Particle size distribution of Arizona Test Dust used in the experiment. Due to irregularities in the shape of Arizona Test Dust particles, the definition of separation efficiency through

the number of particles up- and downstream of the filter with

commercially available particle counters gives faulty results (Wang et al., 2015). 70

Furthermore, to compare the removal of particles made of various materials, a hydrodynamic diameter, defined through , should be used. The hydrodynamic diameter is based on dynamical properties of a particle of density ρp suspended in a liquid of density ρ. It is an equivalent diameter of a sphere, of optical diameter d, that has the same settling velocity as that of the considered particle. As the Arizona Test Dust is a mixture of various chemicals, the comparison of fractional removal of particles differing in densities would be rough. Therefore, overall changes in filtration efficiency during the experiment were determined gravimetrically. After every 20 % of the total filtration time, tF, i.e. the time from the test beginning to reaching 2,5 bar of differential pressure, the filter element was dried and weighted. Based on the mass of the deposit accumulated within the fabric, mt,dep, during the filtration time, t, the efficiency of solid particle removal, ηt, was calculated as: 𝜂𝑡 = 1 −

𝑄𝑚𝑎𝑠𝑠 ∙𝑡−𝑚𝑡,𝑑𝑒𝑝

(7.2.1.1)

𝑄𝑚𝑎𝑠𝑠 ∙𝑡

where Qmass is the mass flow rate of the suspension. Results of effectiveness of solid removal by the examined multilayer filters, in a relationship to a non-dimensional time of filter life, defined as , are presented in Figs. 7.2.1.2-4.

separation efficiency [-]

1,0

0,8

STANDARD 1 MIXED-FIBER 1

0,6

0,4 0,0

0,2

0,4 0,6 0,8 non-dimensional time [-]

1,0

Fig. 7.2.1.2. Evolution of mass filtration efficiency during loading of STANDARD 1 and MIXED-FIBER 1 filters.

71

As can be noticed in the above graph, the separation properties of the multilayer fibrous filter are not constant during the loading process. Accumulation of solids within the filter material is positive due to the structure of loading under the constant contamination mass flow rate. However, after reaching some critical moment the increase slows down affecting the values of separation efficiency. It is the outcome of resuspension of accumulated deposit to the filtrate. Microscopic changes in particular layers, described in Sec. 6, sum together influencing the macroscopic behavior of the entire multilayer fabric. With passing time consequently more layers reach a maximum amount of specific deposit (Figs 6.4.6-11). Reaching the maximum specific deposit value indicates reaching the critical local shear stress within pores causing a subsequent release of the accumulated matter. In Fig. 7.2.1.2 above it is in approx. half of the loading time. As with time, the overall volume of the accumulated matter in the filter structure increases, the local shear stress increases as well. Thus, after reaching a particular mass of retained particles resuspension occurs more frequently, constantly decreasing the filtrate quality.


1,0

0,8 STANDARD 1 STANDARD 2 0,6

STANDARD 3

0,4 0,0

0,2


1,0

Fig. 7.2.1.3. Comparison of evolution of mass filtration efficiency during loading of STANDARD 1, 2, 3 filters.

72


1,0

0,8 MIXED-FIBER 1 MIXED-FIBER 2 0,6

MIXED-FIBER 3

0,4 0,0

0,2


1,0

Fig. 7.2.1.4. Comparison of evolution of mass filtration efficiency during loading of MIXEDFIBER 1, 2, 3 filters. The values of filtration efficiency founded on the increase of the filter mass are similar for filters composed of layers with uniform distribution of fiber sizes and their equivalents with bimodal distribution of fiber sizes. Thus, based on the data presented in Figs. 7.2.1.3-4, STANDARD 1 as well as MIXED-FIBER 1 achieved the highest separation efficiencies. They are characterized by the smallest macro-sized fiber diameters in the last layer of the fabric among all the examined multilayer filters. The nanostructure of MIXED-FIBER 1, 2, 3 filters was similar, between 0,6 – 0,7 μm. All the corresponding STANDARD and MIXEDFIBER structures had also similar porosities of the fabric layers. So the number of collectors in the structure of STANDARD 1 and MIXED-FIBER 1 was the largest. The number and size of filter elements directly influenced their performance. The last point of the experiment performed on MIXED-FIBER 3 filter was omitted in this analysis. As was mentioned before, the characterization of the filter separation properties based on the gravimetric approach is expected to be less precise than that performed on particle counting. The mass of nanoparticles, for which removal the MIXED-FIBER filters was designed, is incomparably smaller than the mass of micro-sized contamination. Thus, in Figs. 7.2.1.2-4 the difference between the corresponding multilayer STANDARD and MIXED-FIBER structures is small, reaching approx. 0,2 %. 73

7.2.2. Monodisperse contamination, fractional efficiency Among the most common standards of filter testing (ISO 16889:2008, 2008; EN 134432:2005+A1:2007, 2007) there are two variables defining the removal effectiveness of particles of different sizes during liquid filtration. “Beta ratio”, βd, describes the ratio of upstream particles to downstream particles, as: 𝑁𝑑,𝑢𝑝

𝛽𝑑 = 𝑁

(7.2.1)

𝑑,𝑑𝑜𝑤𝑛

where Nd,up and Nd,down is respectively up- and downstream cumulative concentration of particles of diameter d or greater. In the second method, filtration efficiency, ηd,cum, is expressed as a percentage of contaminant removed by the filter material: 𝜂𝑑,𝑐𝑢𝑚 =

𝑁𝑑,𝑢𝑝 −𝑁𝑑,𝑑𝑜𝑤𝑛 𝑁𝑑,𝑢𝑝

100

(7.2.2)

Usually both expressions are reported for all particles equal or greater than the particle size indicated by the subscript, d. The relationship between the above approaches is as follows: 𝛽𝑑 =

1 𝜂 1− 𝑑,𝑐𝑢𝑚

(7.2.3)

100

Tab. 7.2.1 presents an illustration of Eq. 7.2.3. Table 7.2.1. Comparison of β-ratio and percentage filtration efficiency. β-ratio [-]

Upstream

particle Downstream particle

Filtration efficiency

count [m-3]

count [m-3]

10 000

5 000

2

50,00

10 000

1 000

10

90,00

10 000

100

100

99,00

10 000

1

10 000

99,99

[%]

The minimum particle size for which a filter separates contamination with desired efficiency specifies the “micron rating” of the filter. It commercially differentiates filter structures from 74

one another. To illustrate the above, an absolute filter of 1 μm rating separates particles of 1 μm diameter and larger with 99,99% efficiency, thus 10 000 of β-ratio. This means that among 10 000 particles flowing through a filter only 1 particle of a size equal or larger than 1 μm passes over the structure directly to the filtrate (Tab. 7.2.1). β-ratio always refers to a cumulative particle count. Filtration efficiency can relate the cumulative as well as the fractional count of solids. Fractional efficiency, ηd, is defined by up, nd,up, and downstream, nd,down, concentration of particles of a specified size or size range groups as: 𝜂𝑑 =

𝑛𝑑,𝑢𝑝 −𝑛𝑑,𝑑𝑜𝑤𝑛 𝑛𝑑,𝑢𝑝

100

(7.2.4)

All the above separation efficiency calculations are based on the values of contamination concentration. The measurement of particle count and size in a liquid suspension can be performed by: -

Light extinction – fluid flows through a transparent tube located between a light source and optical sensor, which emits a specified electrical signal. Particles shadow sensor changing emitted electrical signal, which can be further related to the size of the particle. The number of changes defines particle count.

-

Electrosizing-zone technique – particles suspended in weak electrolyte are drawn through small aperture between 2 electrodes. In electrical field particles passing through the aperture produce a current proportional to their size. The number of particles is defined by monitoring such pulses in the elecrosensing-zone.

-

Laser diffraction – laser is passed through a suspension. Detectors measure the angle and intensity of scattered light. By coupling obtained data with mathematical algorithms a volume-based distribution of particle sizes is determined.

-

Microscopy – particles are defined and counted on an image of a specified volume of the sample.

-

Sieving – particles are graded by passing through a system of sieves characterized by decreasing sieve size. Size distribution is based upon the accumulated mass on each sieve.

All the techniques could be used in this work. Methods based on light extinction and laser scattering phenomena are able to perform online particle count and size analysis, which is 75

why they are recommended by procedures set by EN 13443-2 (EN 13443-2:2005+A1:2007, 2007). An SLS-1200 particle counter manufactured by Particle Measuring Systems, Inc. was used for determination of the filter up- and downstream suspension concentration. Its principle of measurement is based on laser diffraction phenomena. The biggest problem of this technique is detection of air bubbles in the submicron range in particular (Grant, 2004). Such additional counts should be avoided by degassing or heating the sample. On the other hand, every additional processing of a sample increases the risk of its pollution. Therefore, the considered test stand and methods of measurement were designed to avoid production of air bubbles. It appeared to be enough to avoid the problem. For this purpose mixing in the contamination reservoir as well as in the diluted sample vessel was adjusted on a speed under which no aeration occurred and mixing was sufficient. The noise of particle counter during the measurement performed for a clean test stand was on a constant level of 4 000 ml-1 particle count. Samples of up- and downstream fluid of the filter were carefully collected by a laminar stream poured on the vessel’s wall. Due to the upper limit of particle count of 10 000 ml-1, samples were sufficiently diluted by deionized water before measurement. To eliminate errors of faulty counts of the particle counter, the contamination used in fractional efficiency measurement were polystyrene latex microspheres produced by Magsphere, Inc. Due to the spherical size it was precisely reckoned by the instrument. The basic surface parameters of Arizona Test Dust and polystyrene latex particles were of the same sign so the electrical double-layer interactions as well as London-van der Waals forces were similar. Zeta potential was measured by Zetasizer 3000 of Malvern Instruments Ltd. The values of Hamaker constant were taken from literature. All the parameters are reported for pH of around 7,5 in Tab. 7.2.2. The examined spherical particles were of 0,3, 0,5 and 1 μm in size. Each size represents a domination of different particle transport mechanism inside the porous structure (Sec. 3). Table 7.2.2. Surface properties of the contamination used in the experiments. Hamaker constant [10-20 J]

Zeta potential [mV]

Arizona Test Dust

10.00 (Guo et al., 2002)

-30,0

Polystyrene latex

6.37 (Tsai et al., 2007)

-65,4

76

To perform measurement of fractional separation efficiency of the multilayer filter total filtration time, the time from the test beginning to reaching 2,5 bar differential pressure was divided into five equal time intervals. Then, the filtration experiment was performed again but on a clean filter of the same type until 20, 40, 60, 80, 100 % of the total filter lifetime expiration. After reaching the mentioned indicators of the process termination, the flow in the injection circuit was stopped. The particle contamination reservoir with a suspension of Arizona Test Dusts was replaced by a tank of deionized water, which injected by the peristaltic pump washed the injection circuit pipes for 30 min. Then, the system was sufficiently clean for the introduction of mono-sized contamination. Particles of 0,3, 0,5 and 1 μm in size were injected separately. Cleaning of the system was repeated after finishing the measurement for each size of spheres. It should be emphasized that all the stages of system preparation were performed continuously without changes of the flux through the tested filter. Every renewal of the flow could destroy the accumulated deposit structure while the aim of this experiment was to characterize solid removal by a partially loaded fabric. The measurement of particle count started after 1 minute of dosing the monodispersed slurry. Concentrated polystyrene latex particles were diluted so that their concentration in the upstream of the filter was similar, ca. 623 mln of particles per milliliter of a non-diluted sample. The valves ahead and after the tested filter were opened at the same time, washed for 5 seconds at the maximum flow. Then the flux through the valves was decreased for a proper simultaneous collection of both samples. The number of particles was measured 5 times. The averaged values were defined for up-, nd,t,up, and downstream, nd,t,down, of the tested filter. Fractional efficiency of particle removal, ηd,t, was determined for every period of the filter lifetime, t, as: 𝜂𝑑,𝑡 =

𝑛𝑑,𝑡,𝑢𝑝 −𝑛𝑑,𝑡,𝑑𝑜𝑤𝑛 𝑛𝑑,𝑡,𝑢𝑝

(7.2.5)

The experiment of polystyrene latex particle removal performed on a clean fabric characterized by bimodal distribution of fibers concurs with data obtained in computer simulations by Przekop and Gradon (Przekop, Gradon, 2008) (Fig. 7.2.2.1).

77

Fig. 7.2.2.1. Results of water filtration obtained for the same flow conditions, 600 L/h: in computer simulations (Przekop and Gradon, 2008) (a) and after a filtration test with water contaminated by polystyrene latex particles, SEM image (b). Mainly thin fibers loaded with particles. Nanofibers attract particles higher than micro-sized fibers. Therefore, smaller particles are being captured even in front layers of the filter structure (Sec. 6). Thicker fibers are creating the rack for thinner fibers, which are mostly responsible for contamination removal. The obtained fractional filtration efficiency values confirmed these observations.

78

(a)


1,0 0,8 0,6 STANDARD 1 0,4


0,2 0,0 0,0

0,2


1,0

(b)


1,0 0,8 0,6 MIXED-FIBER 1 0,4

MIXED-FIBER 2 MIXED-FIBER 3

0,2 0,0 0,0

0,2


1,0

Fig. 7.2.2.2. Comparison of efficiency of 0,3 μm polystyrene latex particle removal by STANDARD 1, 2, 3 (a) and MIXED-FIBER 1, 2, 3 filters (b) during loading time.

79

(a)


1,0 0,8 0,6 STANDARD 1 0,4


0,2 0,0 0,0

0,2


1,0

(b)


1,0 0,8 0,6 MIXED-FIBER 1 0,4


0,2 0,0 0,0

0,2


1,0

Fig. 7.2.2.3. Comparison of efficiency of 0,5 μm polystyrene latex particle removal by STANDARD 1, 2, 3 (a) and MIXED-FIBER 1, 2, 3 filters (b) during loading time.

80

(a)


1,0 0,8 0,6 STANDARD 1 0,4


0,2 0,0 0,0

0,2


1,0

(b)


1,0 0,8 0,6 MIXED-FIBER 1 0,4


0,2 0,0 0,0

0,2


1,0

Fig. 7.2.2.4. Comparison of efficiency of 1 μm polystyrene latex particles removal by STANDARD 1, 2, 3 (a) and MIXED-FIBER 1, 2, 3 filters (b) during loading time. As could be noticed in Figs. 7.2.2.2-4 mainly the removal of particles of 0,3 μm in diameter was strongly affected by the addition of nanofibers to each filtration layer. The initial separation efficiency of 0,3 μm spheres increased from 4 to 30 % by adding nonofibers to the structure of STANDARD 1 filter. This over seven-fold enlargement is the result of an increase of Brownian diffusion effects near nanofibers that the particles of this size are 81

following. It appears that also for particles of 0,5 μm in diameter the diffusion coefficient is relatively high (4·10-13 m2·s-1) but due to higher particle mass the pathways are more strongly determined by fluid streamlines than by the motion of fluid molecules. Thus, the main transport results from advection effects, defined through the product of particle diameter and fluid velocity (3·10-9 m2·s-1). Convection movement is important in direct interception mechanism responsible for deposition of particles of 1 μm as well (Tab. 7.2.2.1). As the removal of larger particles was not significantly enhanced by the additional presence of nanofibers in every filtration layer, it can be concluded that the improvement of separation properties can be noticed only for particles, which follow Brownian diffusion. However, further research should be performed with nanosized particles of more diameters below 0,3 μm. Table 7.2.2.1. Comparison of parameters describing the strength of mechanisms determining transport of particles of 0,3, 0,5 and 1μm in size in a fluid flowing through the outer layer of STANDARD 1. The values were obtained for conditions under which the experiment was performed. 0,3 μm particle 0,5 μm particle

1 μm particle

Mechanism

Parameter

Interception

NR (Eq. 3.2.3) [-]

23·10-2

38·10-2

76·10-2

Inertia

NSt (Eq. 3.2.4) [-]

1·10-4

2·10-4

7·10-4

Sedimentation

NG (Eq. 3.2.5) [-]

1·10-5

4·10-5

15·10-5

Diffusion

NPe (Eq. 3.2.2) [-]

10736

17893

35786

The difference between the performance of STANDARD and MIXED-FIBER filters reduces with time and the deposition efficiency remains on a similar level for both filters (Fig. 7.2.2.24). This is the consequence of well-developed deposit agglomerates (Kubo et al., 2016; Choo and Tien, 1995), acting as additional collectors, on which deposition takes place when the clean filter surface is loaded. Because of high cost of spherical monodisperse contamination, relatively coarse particles were used for the loading process. Such particles are useful for reasonably quick loading, and a measured reduction of filter porosity. On the other hand, their

82

use smooths over the clear transport process of monodisperse submicron particles used for filtration efficiency testing. The removal of particles increases with the contamination size enlargement (Figs. 7.2.2.2-4). It corresponds with particle transport driven by particular mechanisms (Sec. 3). It was discussed on the example of standard multilayer filter performance. The initial value of fractional filtration efficiency obtained for the removal of smallest spherical particles was noted on a low and similar level for all the examined standard gradient structures. Higher efficiencies were noticed in the removal of larger particles. 0,5 μm diameter particles were removed with the initial effectiveness of 40, 23, and 28 %, and those of 1 μm with 53, 30, 51 % by STANDARD 1, 2, 3 filters, respectively. The influence of the minimum average fiber size in the structure, i.e. the properties of the outer layer of the gradient filter, is the cause of such behavior. Therefore, STANDARD 2 separated particles with the least values of fractional efficiency. On the other hand, filtration efficiency determined on the overall filter mass growth (Sec. 7.2.1) indicated the worst removal of the suspended contamination by STANDARD 3. Differences in filter design, which were mainly in the filtration layer thicknesses (Tab. 6.1.1), seem to be a direct cause of this disagreement. Such discrepancies clearly indicate the importance of filter design and its validation in a precise flow-through experiment.

7.3. Pressure drop Every filter material placed in a flow-through system causes flow resistance. Depending on the filter structure, i.e. the size of collectors, dc, their packing density/porosity, ε, the depth of the fabric, L, their resistance can be different. Kozeny-Carman’s equation (Carman, 1937) is the most widely used law for a description of the relationship. It relates flow resistance through a pressure drop, ΔP, as: −

∆𝑃 𝐿

(1−𝜀)2 𝜇𝑈

= 180 𝜀3 (𝜙

2 𝑠 𝑑𝑐 )

(7.3.1)

where U is the superficial fluid velocity and ϕs collector sphericity factor. The higher the pressure drop the more force is produced for fluid pumping, thus the process is more expensive. Pressure drop is measured as the pressure difference between the filter inlet and outlet. In the performed experiment it was measured by SEN-86 pressure sensors,

83

manufactured by Kobold Instruments, Inc. located directly ahead and after the tested filter. Results are presented in Figs. 7.3.1-3. 2,5

pressure drop [bar]

2,0 1,5 MONO 2 μm 3 MONO 5 μm 3

1,0

MONO 10 μm 3 0,5 0,0 0,0

0,2


1,0

Fig. 7.3.1. Pressure drop development during loading of MONO 2 μm 3 (ε0 = 0,75), MONO 5 μm 3 (ε0 = 0,75), MONO 10 μm 3 (ε0 = 0,72). 2,5

pressure drop [bar]

2,0 1,5 MONO 2 μm 1 MONO 2 μm 2

1,0

MONO 2 μm 3 0,5 0,0 0,0

0,2


1,0

Fig. 7.3.2. Pressure drop development during loading of MONO 2 μm 1 (ε0 = 0,84), 2 (ε0 = 0,80), 3 (ε0 = 0,75). 84

The relationship between the initial pressure drop across the monolayer filter and the filter fiber diameter (Fig. 7.3.1) as well as packing density (Fig. 7.3.2) clearly show that the larger the collectors and the more of them are present, the higher flow resistance the structure produces. The character of the pressure drop growth during filter loading time was similar for all MONO filters. All the monolayer fibrous structures exhibited a stable increase until clogging of the filter pores. Further build-up of pore spaces resulted in a sudden growth of upstream pressure and with time in structural damage of the cartridge. Therefore, loading of the filter after reaching its critical retention capacity should be avoided. The exemplary performance of the examined multilayer filters is presented below.

pressure drop [bar]

2,5 2,0 1,5 STANDARD 1

1,0

MIXED-FIBER 1 0,5 0,0 0,0

0,2

0,4 0,6 normalised time [-]

0,8

1,0

Fig. 7.3.3. Pressure drop development during loading of STANDARD 1 and MIXED-FIBER 1 filters. A profile of the pressure drop curve of STANDARD 1 and MIXED-FIBER 1 filters, presented in Fig. 7.3.3, is related to the loading development of the filter structures described in detail in Sec. 6. Around a halfway through the experiment time the inner layers of MIXEDFIBER 1 started reaching their maximum retention capacity (Fig. 6.4.6). Due to local changes of physical conditions, resuspension of the deposit started to occur more frequently. The inflection point can be noticed in Fig. 7.3.3. Clogged pores were partially washed out, which enabled further work of the filter. The re-entrained deposit was efficiently captured by the following layers of the filter structure. In Fig. 7.3.3 the initial resistance caused by the structure enriched by the addition of nanofibers was almost 3 times lower than that of the standard gradient filter. Initial porosities 85

of the fabrics were comparable (Tab. 6.4.1), but 10 % of the filter mass was composed of nanosized fibers. Thus, according to Eq. 7.3.1, the flow resistance of the filter with a higher fraction of nanosized fibers indeed should be lower. Taking into consideration the similar profile of the pressure drop development for all standard fabrics, characterized by uniform fiber size distribution, the lower the initial pressure drop the longer the filter lifetime in filters of the same type. In below section analysis of this issue is presented.

7.4. Retention capacity and filter lifetime During a depth filter loading with contamination, particles accumulate within the filter material. The deposition of the suspended matter on the surface of the material’s elements can be different, depending on the structural properties as was shown in Sec. 6. The maximum mass of the solid matter effectively retained by the filter when the final differential pressure, a value of 2,5 bar in our case, is reached defines retention capacity, R. It can be easily determined from the gravimetric measurements, as: 𝑅 = 𝑚𝑡 − 𝑚0

(7.4.1)

where m0 is the weight of a clean filter and mt – a mass of a dry filter after loading with contamination. The time of reaching the final pressure difference across the filter material directly indicates the value of retention capacity. The shorter the time the filter is being loaded, the less suspended matter will be accumulated within the structure. Thus, these two values are considered together. Filters of mono- and multilayer structures were loaded with a suspension of Arizona Test Dust, specified in Sec. 7.2.1, until reaching 2,5 bar pressure drop. The time of the experiment was measured and the retention capacity was defined using an AS 310.X2 analytical balance, manufactured by Radwag. To compare the results in some characteristic scale the deposit growth rate was used. It describes an increase of the filter mass per unit of loading time.

86

Table 7.4.1. Comparison of lifetime and retention capacity of the examined filters. Time [h] Filter type

Retention capacity [g]

Growth rate [g·h-1]

1

2

3

1

2

3

1

2

3

MONO 2 μm

4,1

3,0

1,7

6,2

12,4

15,2

1,5

4,1

8,9

MONO 5 μm

5,7

4,2

3,5

5,3

17,5

21,5

0,9

4,2

6,1

MONO 10 μm

13,2

6,2

5,1

16,8

17,3

21,9

1,3

2,8

4,3

STANDARD

15,0

17,2

16,5

67,3

72,0

56,2

4,5

4,2

3,4

MIXED-FIBER

5,1

6,4

6,9

22,6

26,9

30,3

4,4

4,2

4,4

From the above presented results (Tab. 7.4.1) it can be concluded that clogging of the filter pores, defined through the particular differential pressure, occurred after the longest time during verification of the multilayer standard gradient filters. Compared to equivalent filters enhanced by the presence of nanofibers in every filtration layer, the average increase was 2,7 times faster. Shortening of the filter lifetime influenced the total amount of the retained deposit, although the rate of solid accumulation was on a similar level for most multilayer filters. STANDARD 2 was characterized by a structure with the highest longevity, and therefore retention capacity. However, among all the multilayer filters the deposition rate was the highest for the filter with the highest separation efficiency (Sec. 7), i.e. STANDARD 1. The operational time of monolayer filters was incomparably short. Structures characterized by the highest solidity, thus those marked 3, separated the suspended matter with the highest rate. The maximum value was achieved by the filter composed of 2 μm fibers. Its dense structure efficiently captured particles as a sieve on the surface of the fabric preventing from depth penetration (Fig. 6.4.2). Such surface filtration caused rapid clogging of the filter and the test termination. All the above observations result from deposit distribution within the entire filter structure. The suggested application of filters uniform in the entire structure is to collect rather monosized contamination for which the structure was designed for. Multilayer fabrics enable 87

capture of particles of various sizes at different depths. The addition of nanofibers to every filtration layer moves deposition to earlier layers of the material, although it accelerates the layer clogging. Despite the lower initial differential pressure these filters work for a shorter time. Thus, the application of multilayer filters with bimodal distribution of fibers should be used for removal of particles characterized by either mono- or polydisperse size distribution but of nano-diameters. Such particles are still efficiently separated only by membranes. The mixed-fiber structure reduces the flow resistance of dense membranes or monolayer fabrics preserving high efficiencies of nanoparticle removal. It also effectively prevents from resuspension of the deposit to the filtrate, thus it seems to be a solution to the liquid mechanical depth-filtration problems. Based on the obtained results of experimental filter validation, examination of local conditions influencing the macroscopic behavior of filters, a model of a depth filtration process was defined.

88

8. FILTRATION MODEL Simulation of a filtration process is an important part of filter design. A worthy computer model can save time and money spend on experimental investigation of the filter performance. Analysis performed in previous sections showed that deposition of solids within filter media causes changes in microstructure influencing macroscale effects. Accumulated matter changes filter porosity. Porosity affects local velocities within the porous structure and thus transport mechanisms, deposit accumulation and detachment. The increase of packing density due to accumulated solids causes growth of flow resistance and so the differential pressure. Depending on the character of the system analysis, two types of process simulations were developed (Keir et al., 2009): -

Macroscopic models - describe local phenomena related to macroscopic behavior of the filter via changes in a representative infinitesimal volume of the system. Calculations base on conservation equation, equation of deposit growth rate and equation relating differential pressure at any position and time.

-

Microscopic models - follow the fate of each individual particle that enters the system. They can be divided into Eulerian and Lagrangian approaches. Eulerian methods are concerned with calculating the concentration distribution of particles in time and space. The convection-diffusion equation is used to describe particle transport and deposition. The solutions are based on analytical efficiencies for separate attachment mechanisms causing deposition on the collector (Yao et al., 1971). Lagrangian methods determine filtration rates from particle trajectories obtained in force and torque balances (Payatakes, et al., 1973). Deposition occurs once a particle comes into a contact with the collector. Whether Eulerian or Lagrangian method is used a selection of an appropriate model for a filter structure representation has to be chosen as well as a suitable flow field. The analysis can be performed for a single collector (Kuwabara, 1959; Happel, 1958), or in a series of unit bed elements (Rege and Fogler, 1988; Payatakes et al., 1973).

Macroscopic models are empirical in nature, thus prior knowledge of physical and chemical conditions under which the solutions were obtained is crucial. It determines the usefulness of the model in a desired case. The empirical parameters governing the filter behavior are considered to have no physical interpretation. Theoretical considerations founded on laws determining the mechanisms of particle transport and deposition are present in microscopic 89

models. However, to improve an agreement between the theory and experiment some correcting factors have to be introduced (Altoe et al., 2006; Bai and Tien, 2000). Both approaches are limited in utility. So far macroscopic models are less rigorous. Knowledge about transport and deposition mechanisms of suspended matter is not necessary. Generally they are simpler thus more commonly used in filter design, which is why this approach was used in this work. To eliminate the accusation of the absence of theoretical background, the observations of microscopic effects, such as deposit structure, its development and resuspension, were enclosed in a macroscopic description of a non-steady filtration process. All analysis was performed for a standard gradient filter as a representative of the most commonly used structures on the market.

8.1. Separation efficiency The main purpose of a filter material is to purify a liquid from contamination. Thus, a desired quality of the filtrate is demanded for the whole period of the filter lifetime defined through reaching a critical differential pressure. That value is specified by the filter’s manufacturer. Due to mechanisms of particle separation the biggest problem of depth filtration of liquids refers to resuspension of accumulated matter (Przekop and Gradon, 2016; Heuzeroth et al., 2015). Optimization of the filter structure with computer simulations should help in solving this problem. By the application of macroscopic modeling into a filter design, the performance of various structures can be predicted. In case of a multilayer filter design, computer calculations have to be done for each layer separately, as each one of them has a different structure. The effluent of the previous layer becomes the influent to the subsequent layer. The basic information about the initial suspension concentration, C0, has to be known to predict the filter lifetime. The foundation of computer simulations is mass balance whose general form for one dimensional transport in a flow direction, z, (Fig. 8.1.1) is: 𝜕𝜎 𝜕𝑡

+

𝜕𝜀𝐶 𝜕𝑡

+

𝜕𝑢𝐶 𝜕𝑧

−

𝜕 𝜕𝑧

(𝐷

𝜕𝐶 𝜕𝑧

)=0

(8.1.1)

where σ is specific deposit, defined as the amount of mass deposited in a unit of filter volume [kg·m-3], C - concentration of a suspension [kg·m-3], u - local velocity [m·s-1], D - dispersion coefficient [m2·s-1]. As the analysis is performed for an infinitesimal filter depth, dz, in Fig. 8.1.1 a cylindrical filter structure was simplified through a flat-sheet system by relating local

90

velocity with current position on a filter radius, Rz, via 𝑢 = 𝑈

𝑅0 𝑅𝑧

, where R0 is the outer radius

of the cartridge filter element.

Fig. 8.1.1. Graphical representation of the analyzed system. The first term of Eq. 8.1.1 describes the kinetics of mass accumulation on the fiber surface, the second one defines the rate of suspension concentration changes due to the development of agglomerates. The next terms describe advection and dispersion transport, respectively. The initial condition concerns cleanliness of the filter at the beginning of analysis and boundary conditions refer to the influent and effluent concentration values. All are defined as follows: -

for 𝑡 = 0, 𝑧 ≥ 0, 𝐶 = 0, 𝜎 = 0

(8.1.2)

-

for 𝑡 > 0, 𝑧 = 0, 𝐶 = 𝐶0

(8.1.3)

-

for 𝑡 > 0, 𝑧 = 𝐿, 𝜕𝑧 = 0

𝜕𝐶

(8.1.4)

To simplify the above equations a few remarks regarding fibrous filters can be made. A typical assumption for depth filtration process implies that temporary changes in the concentration of particles within pores are negligibly small, compared to mass accumulation. The flow around fibers is laminar as the Reynolds number value is of the order of 10-3 - 10-1. Dispersion, D, of particles flowing through the porous media is a sum of Brownian movement of particle, DB, and its transverse and longitudinal displacement caused by the disturbance of suspension flow around the obstacle (fiber in our case) (Bijeljic and Blunt, 2007; Levenspiel, 91

1962). The second term of the dispersion coefficient is proportional to the product of approach velocity of the liquid, U, and obstacle characteristic size, df. Taking into account the range of particle diameters in the suspension, DB is of the order of 10-14 - 10-13 m2·s-1. The approach velocity of water in the filter in our experiment was 10-3 m·s-1 and characteristic diameter of the fiber was of the order of 10-5 m. Thus, the second term of the dispersion coefficient is also very small. The dispersion of particles in the transport process through the 𝐷

fibrous structure can be omitted ( 𝑈𝐿𝐵 ~10−5 ). Furthermore, single layers of the fabric were thin and highly porous so the assumption of a constant local velocity within a single layer was made. With the above assumptions, Eq. 8.1.1 may be simplified to an expression: 𝜕𝜎 𝜕𝑡

𝜕𝐶

= −𝑢 𝜕𝑧

(8.1.5)

To complete the description, the filtration rate, i.e. the rate of a specific deposit growth,

𝜕𝜎 𝜕𝑡

, is

required. Iwasaki (Iwasaki, 1937) was the first researcher who proposed a description of particle concentration profile throughout a filter via a logarithmic law: 𝜕𝐶 𝜕𝑧

= −𝜆𝑐

(8.1.6)

where λ [m-1] is known as the filter coefficient. By combining Eq. 8.1.6 and 8.1.5 the filtration rate can be determined. In the work of Iwasaki (Iwasaki, 1937) the filter coefficient remained constant. This assumption is true only for the initial stage of the process. Its physical meaning describes a number fraction of retained particles per unit of bed length. It depends on the current growth of the accumulated matter and the correcting factor, α, determining deviation from the above logarithmic law. In general, it can be expressed as: 𝜆 = 𝜆0 𝐹(𝜎, 𝛼)

(8.1.7)

where λ0 [m-1] is the initial value of filter coefficient and F(σ, α) [-] is the correcting function. The value of λ0 can be calculated by fitting the predicted effluent concentration history to the experimental data at initial times. The exemplary values for defined systems were listed by Hendricks (Hendricks, 2006). Based on the form of the function F(σ, α) different behavior of the filter can be described. In Tab. 8.1.1 a list of the most popular expressions is presented (Tien, 2012).

92

Table 8.1.1. List of expressions for the correcting function. Author

Model

Parameter

𝐹 = 1 + 𝐴𝜎

A

(8.1.8)

𝐹 = 1 − 𝐴𝜎

A

(8.1.9)

𝜎 𝜀0

-

(8.1.10)

𝜎 𝜎𝑢𝑙𝑡

-

(8.1.11)

A, B

(8.1.12)

A

(8.1.13)

Mackrle et al. (1965)

𝐴𝜎 𝐵 𝜎 𝐶 𝐹 = ( ) (1 − ) 𝜀0 𝜀0

A, B, C

(8.1.14)

Ives (1960)

𝐵𝜎 2 𝐹 = 1 + 𝐴𝜎 − 𝜀0 − 𝜎

A, B

(8.1.15)

Ives (1969)

𝐴𝜎 𝐵 𝜎 𝐶 𝜎 𝐷 𝐹 = (1 + ) (1 − ) (1 − ) 𝜀0 𝜀0 𝜎𝑢𝑙𝑡

A, B, C, D

(8.1.16)

Iwasaki (1937) Stein (1940) Ornatski et al. (1955) Shekhtman (1961) 𝐹 = 1− Heertjes and Lerk (1967) Maroudas and Eisenklam

𝐹 =1−

(1965)

Mehter et al. (1970)

𝐵 1 𝐹=( ) 1 + 𝐴𝜎 𝐴

Deb (1969)

𝜙(𝜎)

𝐹=( ) 𝜎 𝜙0 (𝜀0 − 1 − 𝜀 ) 𝑑

Models listed in Tab. 8.1.1 are still frequently used in depth filtration investigations (Babakhani et al., 2017; Li and Davis, 2008; Sykes, 2009; Wojciechowska, 2002). The difference between them is within the character of correction function, thus filtration rate dynamics. All models were founded on experiments performed in various conditions, with several filter materials and contamination. In a model of Iwasaki (Iwasaki, 1937), every 93

growth of deposit mass accumulated within the filter caused an increase in filtrate clearance. A contrary situation was observed by Ornatski (Ornatski, 1955). Ives (Ives, 1969) tried to incorporate accumulation and resuspension in a complex description. Thus, the first term of Eq. 8.1.16 takes into consideration an increase of the specific surface of filter elements resulting from deposition. The second one accounts for a decrease in porosity and the last term includes detachment of the accumulated deposit. All the authors described loading of the filter through a single equation, as a one-step process. As could be seen from Figs. 6.4.6-8 more phases in a fibrous filter performance characterizing a different description of the process should be identified. For example, in STANDARD 1 the 4th layer of the structure reached a peak before the test ended (Fig. 6.4.6a). After reaching the maximum value of specific deposit, thus critical shear stress within pore spaces, a burst of accumulated agglomerates could be noticed in the final weight of this layer in a filter loaded 20 % longer. While using filters with higher separation efficiencies, i.e. filters characterized by bimodal distribution of fiber diameters, even more phases could be noticed. After deposit destruction, agglomerates are being successfully rebuilt by the constantly upflowing suspension (2nd and 3rd layer of MIXED-FIBER 1; Fig. 6.4.6b). It is expected that further loading is in the scheme of accumulation (ripening) and resuspension (breakthrough) stages occurring subsequently in all fibrous filter structures until process termination. Thus, accumulation process is conceived as reversible one. As the transition moment influences filtrate quality, such transition should be designed for the moment when the filter reaches its maximum differential pressure (STANDARD 1) or should be predicted to occur in earlier parts of the filter so that the released matter would be efficiently captured within the filter fabric (MIXED-FIBER 1). In microscopic models, due to the fact that analysis of the process in a reduced scale of size of a pore or a collector, deposit resuspension is easier to describe as a series of attachmentdetachment processes. The current list of models was provided by Babakhani et al. (Babakhani et al., 2017). In the macroscopic approach such multistage kinetics requires process fragmentation for periods of similar filter behavior and a separate description of each phase. Adin and Rebhun (Adin and Rebhun, 1977) were the first who differentiated, in a phenomenological approach, the initial ripening stage from working and breakthrough ones. The authors provided a definition of a “breakthrough curve”. Hence, a detailed description only of the working stage of the process was delivered. 94

Bai and Mackie (Bai and Mackie, 1995) proposed an explanation of the loading process according to: 𝜕𝜎 𝜕𝑡

𝑢𝐶(𝐴 + 𝐵𝜎)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡0 < 𝐶 ≤ 𝐶𝑐𝑟 ={ 𝑢𝐶(𝐴 − 𝐵𝜎)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝐶 > 𝐶𝑐𝑟 ⁡⁡⁡⁡

(8.1.17)

The “early” and “latter” stages were distinguished by fitting experimental data. A, B and C were parameters achieved in a linear regression of test results. Eq. 8.1.17 described the dynamics of polyvinyl chloride removal from water in a column filled with ballotini glass beads of 0,6 – 0,71 mm diameter. The size of contamination ranged between 0,5 to 15 μm. Another phenomenological approach of multistage kinetics of deposition was developed for the removal of kaolin clay particles suspended in water by a sand filter of approx. 1,05 mm grain size by Gitis et al. (Gitis et al., 2010). The size of particles was between 0,05 – 0,2 μm. It concerned a full description of all 3 phases of the separation process: ripening, efficient filtration/operable and breakthrough individually as. 𝜕𝜎 𝜕𝑡

𝑘𝑟 𝑢𝐶⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡0 < 𝜎 ≤ 𝜎𝑟 = { 𝑘𝑎 𝑢𝐶 − 𝑘𝑑 𝜎⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝜎𝑟 < 𝜎 < 𝜎𝑢 0⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝜎 = 𝜎𝑢 ⁡⁡⁡⁡

(8.1.18)

where kr, ka, kd, were ripening, attachment and detachment constants, respectively. The model assumes that during the ripening stage a nonreversible layer of deposit is formed. It is described by a value of σr. Further specific deposit increase begins an operable stage during which accumulated matter creates a reversible deposit. Accumulation continues until reaching a value of σu, initiating a stage of a breakthrough. The model is precise as it reflects realistic conditions of the experiment via adapting a full advection-dispersion mass balance (Eq. 8.1.1). The last approach was put forward in 2014 by Wang et al. (Wang et al., 2014). Deposition and release of kaolinite particles, of a size between 1,7 – 40 μm, during the flow through a column filled with sand of a median diameter of 410 μm were described as: 𝑘𝑎 𝜕𝜎 𝜕𝑡

𝜌𝑝

= {𝑘

𝑎

𝜌𝑝

𝐶(𝜀0 − 𝜎)𝜙(𝜎)𝜃(𝑧)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝜏 < 𝜏𝑐𝑟 𝐶(𝜀0 − 𝜎)𝜙(𝜎)𝜃(𝑧) − 𝑘𝑑 𝜎 (1 −

𝜏𝑐𝑟 𝑛 𝜏

(8.1.19)

) ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝜏 ≥ 𝜏𝑐𝑟

where the dimensionless function ϕ(σ) accounts for time local dependent retention and θ(z) for depth-dependent retention. n is an empirical parameter. The distinction between the stages of attachment and detachment is based on a function of the local hydraulic shear stress: 95

𝜏=

∆𝑃 𝐿

√(𝜀

2𝐾 0 −𝜎)

(8.1.20)

where K is the permeability of the bed. Combination the local shear stress within pores and the filtration rate is theoretically correct, although the form of dimensionless functions ϕ(σ) and θ(z) is strongly related to experimental conditions. In the revised literature, no phenomenological model developed particularly for fibrous filters was found. All the above mentioned ones were developed in experiments performed with granular filters. In fibrous filtration the specific surface area of filter elements is higher due the decreasing of the collector diameter, which is why the depth of the filter material can be reduced (Sec. 3). Such a reduction of the filter depth affects the control of resuspension phenomena. The thinner the material is the shorten is the way of the re-entrained particles to the filtrate. Furthermore, only four last cited models deal with the multistage character of the process. Based on our observations presented in Sections 6-7, the filtration process within fibrous filters can be treated as a two-stage operation. Initially, in a clean fabric, most pore spaces have the shape of a trapeze or a triangle. As was mentioned above, particles fill the pore space starting from its corners. Loading of the structure with contamination causes a conversion of this shape to elliptical one. When a pore plane reaches a circular shape, i.e. when the fabric layer accumulates a critical deposit mass, σcr, it is assumed that the second phase of the filtration process begins. Filter loading is considered under constant flow conditions. A decrease in pore size increases local fluid velocity. When the local shear stress rises to a critical value, further deposition of particles periodically leads to agglomerate burst and re-entrainment within the filter structure. During this stage the filter layer generates particles influencing suspension concentration in deeper parts of the filter. Thus, when the filter layer reaches σcr, the contamination accumulates less rapidly than in the beginning of the process or this increase becomes negative. Summarizing the above, the kinetic equation of deposit accumulation is proposed as: -

while: 𝜎 < 𝜎𝑐𝑟 :

-

while: 𝜎 ≥ 𝜎𝑐𝑟 :

𝜕𝜎 𝜕𝑡 𝜕𝜎 𝜕𝑡

= 𝑘1 𝑢𝐶(𝜎𝑚𝑎𝑥 − 𝜎)

(8.1.21)

= 𝑘1 𝑢𝐶(𝜎𝑚𝑎𝑥 − 𝜎) − 𝑘2 𝜎

(8.1.22)

where σmax is the theoretical maximum value of specific deposit which could clog filter pores.

96

During the first stage, named the ripening phase of the filter performance, it is assumed that contamination can only be accumulated within the filter. No detachment occurs. The rate of solids deposition on the fiber surface depends only upon the initial structure properties determining particle transport mechanisms, which is represented by a constant k1 [m2·kg-1], further called an attachment constant. The driving force of the process is described through the amount of free space available for deposition, defined as a difference (𝜎𝑚𝑎𝑥 − 𝜎). The second stage of the filtration process is called the breakthrough stage. Its complex character results from continuous particle inflow and deposit re-entrainment. Eq. 8.1.22 incorporates both, attachment and detachment of solids. This phase is determined mostly by the value of hydraulic gradient caused by the accumulated solids, embodied in a detachment constant k2 [s-1]. In case of filter structures where most contamination deposits in earlier filtration layers, after a phase of a breakthrough a ripening stage might occur again. However, in gradient structures, the deposit is assumed to be distributed uniformly in the entire volume of the fabric. Thus, filter design should foresee clogging of the outer layers while reaching 2,5 bar differential pressure across the entire material. Blocking of earlier filter parts means that an additional pre-filter should be used. The values of mass accumulated during the specified time intervals within the filter layers of STANDARD 1, 2 and 3, obtained in Sec. 6.4, enabled the solution of Eqs. 2-5, 21, 22 with the 4th order Runge–Kutta scheme. The values of attachment and detachment constants, k1 and k2, were evaluated with the method of least-squares linear regression. Their universal meaning was proposed. A comparison of the experimental data with computer simulation is shown below.

97


1st layer 150 100 50 0 0,0

0,2

0,4 0,6 non-dimensional time [-]

0,8

1,0

0,8

1,0

0,8

1,0


2nd layer 200 150 100 50 0 0,0

0,2



3rd layer 120 80 40 0 0,0

0,2


98


4th layer 150 100 50 0 0,0

0,2


0,8

1,0

0,8

1,0

0,8

1,0


5th layer 150 100 50 0 0,0

0,2



6th layer 150 100 50 0 0,0

0,2


Fig. 8.1.2. Specific deposit development determined in the experiment (data points) and the model (solid line) for STANDARD 1 filter. In Fig. 8.1.2 an example of the model application was shown for STANDARD 1. The last point in 2nd layer validation was neglected, as it is assumed to be directly before the phase transition. As can be noticed from Fig. 8.1.2, the increase in a specific volume within a single 99

filter layer is uniform until the critical value is reached. The line inclination depends on the layer number, hence the initial fiber diameter, df,i, and packing density, (1 − 𝜀0,𝑖 ). Therefore, the constant k1 represents transport mechanisms responsible for particle capture. By linear regression of achieved data, its universal form was proposed for a quick determination of the single laye behavior during its ripening: 𝑘1 = 0.000934 ∙ 𝜀0,𝑖 −0.423 ∙ 𝑑𝑓,𝑖 −0.285

(8.1.23)

As can be noticed from the values of exponents, the attachment constant is a decreasing function of the initial porosity of the fabric layer as well as its fiber diameter. Such dependence is obvious as thin fibers are strong collectors even for nano-objects and the more densely the collectors are packed the higher probability of particle-fiber contact. The contamination used in the experiment was characterized by a broad size distribution, between 0,5 – 80 µm of particle diameter, to simulate natural conditions of filtration process. From Eq. 8.1.23 it can be concluded that the biggest impact on particle transport to the fiber surface had direct interception and inertia, which agrees with results from the previous chapter (Sec. 7). The second stage of the loading process initiates the inhibition of the growth of specific deposit seen in Fig. 8.1.2, as the moment of transition of the pore cross-sectional shape. From this moment, within the filter layer periodically the resuspension of the deposit occurs. As this phenomenon has a local occurrence and the broken agglomerate can be relocated within the same layer or to a next part of the material, it is hard to predict in macroscopic simulations. Thus, a value of detachment coefficient was calculated as the mean value of obtained constants: 𝑘2 = 0,0008⁡𝑠 −1 The average standard deviation was equal to 0,0008 s-1.

100

(8.1.24)


(a) 1,0

0,5

0,0 0,0

0,2


0,8

1,0


(b) 1,0

0,5

0,0

0,0

0,2


0,8

1,0

0,8

1,0


(c) 1,0

0,5

0,0 0,0

0,2


Fig. 8.1.3. Separation efficiency determined from the experiment (data points) and the proposed model (solid line) for STANDARD 1 (a), 2 (b) and 3 (c). 101

The separation efficiency presented in Fig. 8.1.3 is a sum of effects measured and modeled within individual filter layers for standard gradient fabrics. The values of predicted and measured filtration efficiency are consistent at the beginning of the filtration process for all the multilayer filters (Fig. 8.1.3). The discrepancies, which are initially rather small, increase with the time of filtration. It arises from specific deposit development, and the moment of stage transition, i.e. the critical value of specific deposit. Due to the cost and time of the experiments the amount of time intervals, in which the structure of the filter material was examined, was limited to five. If the number of tests was doubled, a better concurrence between the model and the test could be achieved or even more stages of the loading process could be defined. Moreover, the simplification of the mass balance from Eq. 8.1.1 to Eq. 8.1.5 reduces the complexity of phenomena but also results in some disagreement between the model and experimental validation. Size distribution of contamination was not included in the analysis as the filter’s micron rating practically defines also the maximum size of removed solids. The manufacturers (Amazon Filters Ltd.) recommend removal of contamination of the maximum size 100 times larger than the size indicated by the micron rating. The chemical composition of contamination used for the filter loading (Arizona Test Dust) was mainly composed of quartz. Thus, the application of this model to simulate for example purification of natural waters from sands broadens its use. The proposed 2-stage model is simple, thus useful in designing multilayer fibrous filters. Incorporation of the microscale effects in macroscopic observations was successfully performed through the attachment and detachment constants. With the proposed equations, the quality of the filtrate can be predicted for the entire cycle of filtration process. Furthermore, the constants k1 and k2 defined by Eqs. 8.1.23-24 provide the specific deposit increase within the filter, hence a porosity value, essential in pressure drop prediction.

8.2. Pressure drop An effect of the presence of the porous medium in a flow-through system was first described by Darcy in 1856, who studied the flow of water through sand filters (Darcy, 1856). Ever since its empirical formulation it has been the base of either micro- or macroscopic models. The most common form of Darcy’s law refined by Muskat (Muskat, 1937) is given by: 𝑄=−

102

𝐾𝐴𝛥𝑃 μL

(8.2.1)

According to the above relation, the volumetric flow rate Q [m3·s-1] is proportional to the permeability of the bed, K [m2], its cross section, A [m2], and pressure difference between the surface and the base of the bed, ΔP [Pa]. μ [Pa·s] is the dynamic viscosity of the liquid and L [m] defines the bed’s width. Eq. 8.2.1 applies mostly to laminar-flow systems (Lasseux et al., 2017). As the Reynolds number for the analyzed experiments performed on multilayer filters was in the range of 10-3 - 10-1, Darcy’s law can be adapted to our case as well. Based on the description of the coefficient K, different models were developed. Two are the most commonly used in the literature – Kozeny Carman (Carman, 1937) and Ergun equations (Ergun, 1952). In 1927 Kozeny (Kozeny, 1927) made theoretical investigations on a flow through porous material treated as an assembly of capillary tubes for which Navier-Stokes equation was used. The model was later verified by Carman (Carman, 1937) in an experiment performed on water flowing through a packed bed. This led to the formulation of the Kozeny-Carman equation, as: −

Δ𝑃 𝐿

= 𝑘1

(1−𝜀)2

𝜇𝑈

𝜀3

(𝜙𝑠 𝑑𝑔 )

(8.2.2)

2

where k1 [-] is a constant, U – superficial velocity [m·s-1], dg – filter grain diameter [m], ρ – density of the liquid [kg·m-3] and ϕs – sphericity factor of the filter grain, defined as the ratio of the surface area of a sphere, with the same volume as the given grain, to the actual surface area of the grain. By far it is the most popular equation of a detailed description of the flow through porous media (Eker et al., 2016; Qin and Pletcher, 2015; Haji et al., 2015). Ergun’s equation (Ergun, 1952) was based on a gas flow through a packed column. It can be expressed as: −

∆𝑃 𝜙𝑠 𝑑𝑔 𝜀 3 𝐿 𝜌𝑈 2 1−𝜀

= 𝑘1 (1 − 𝜀) 𝜙

𝜇

𝑠 𝑑𝑔 𝑈𝜌

+ 𝑘2

(8.2.3)

However, with proper values of constants k1 and k2 it is widely used for water-flow description as well (Hoyland, 2017; Rodriguez de Castro and Radilla, 2017; Boccardo et al., 2014). The above models are able to predict the pressure gradient across the filter element only during the phase of its constant growth. Recently it was proved (Tien and Ramarao, 2013) that the approaches generate overestimated values even in similar conditions as in the basic

103

experiment. The application of these models to fibrous filtration generates faulty results as well (Rosenholm, 2015). Thus, an alteration of these equations was proposed. It is known from experimental research (Sec. 7.3) that the process of filter loading with particles influences a steady growth of the structural resistance to the flow. Periodical local resuspension of the deposit within the structure does not influence the overall pressure gradient. With time pores are being consequently built-up. When the filter structure reaches the critical retention capacity, the resistance to the flow starts to rise more rapidly until the filter’s damage. Such changes in the dynamics impose also a two-stage description, with a transition moment defined for a global filter structure. Due to the multilayer construction of the filters and assumed utility of the model it was decided to govern the development of the filter’s flow resistance through the average porosity within the filter structure, . The porosity of single layers is influenced by solid accumulation and resuspension. A properly designed fibrous system composed of a few layers is considered by the filter’s user as one object which during its loading should not experience deposit release. Based on results presented in Sec. 7.3, changes of the pressure drop on the loading filter were described as the function: (1−𝜀̅ )2

𝐴 ⁡⁡⁡⁡⁡𝑓𝑜𝑟⁡𝜀̅ > 𝜀̅𝑐𝑟 ∆𝑃 = { 𝜀̅⁡3 ⁡𝐶 𝐵 ∙ 𝜀̅ ⁡⁡⁡⁡⁡⁡⁡𝑓𝑜𝑟⁡𝜀̅ ≤ 𝜀̅𝑐𝑟 ⁡

(8.2.2)

where: 𝜀̅ =

∑6𝑖=1 𝜀𝑡,𝑖 ∙𝐿𝑖 ∑6𝑖=1 𝐿𝑖

(8.2.3)

where Li is the layer thickness. The first formula in Eq. 8.2.2, which is valid for the initial period of filtration, is inspired in dependency upon void volume fraction by Kozeny-Carman equation (Eq. 8.2.2), according to which: 𝜀̅ ⁡3

𝐾 ∝ (1−𝜀̅)⁡2

(8.2.4)

By linear regression of data acquired for standard multilayer gradient filters, presented in Sec. 7.3, the universal form of differential pressure increase during loading of a fibrous filter was determined as:

104

(1−𝜀̅ )2

2.38 ∙ 105 ̅ ⁡3 ⁡⁡⁡𝑓𝑜𝑟⁡𝜀̅ > 𝜀̅cr 𝜀 ∆𝑃 = { 0.0017 ∙ 𝜀̅⁡−67 ⁡⁡⁡⁡⁡⁡⁡𝑓𝑜𝑟⁡𝜀̅ ≤ 𝜀̅cr

(8.2.5)

pressure drop [kPa]

(a) 300 200 100 0 0,18

0,2

0,22 packing density [-]

0,24

0,26

0,24

0,26

0,24

0,26

pressure drop [kPa]

(b) 300 200 100 0 0,18

0,2


pressure drop [kPa]

(c) 300 200 100 0 0,18

0,2


Fig. 8.2.1. Pressure drop across the loading filter determined from the experiment (data points) and the proposed model (solid line) for a filter with absolute filtration efficiency of (a) 0.5 µm, (b) 1 µm and (c) 3 µm particles according to packing density, (1 − 𝜀̅). 105

A comparison between data obtained in experiment and computer simulations was presented in Fig. 8.2.1. The value of porosity averaged for the entire filter material was similar for all three experimentally verified filter types so the prediction of the presented model was similar despite the filter number. The long stage of a slow growth of differential pressure proceeded its rapid increase. The major difference was in time necessary to reach particular values, which can be obtained from calculations from the previous subsection. A change in the dynamics of flow resistance growth appeared when the average porosity reached . Further loading of the filter should be continued cautiously. The two-stage character of the process description offered in Eq. 8.2.5 is adequate for the description of the entire filter lifetime. It is based on the average porosity development, thus retention capacity of the multilayer filter. The suggested model does not concern the characteristics of the individual layers of the filter. The research performed for a wide range of monolayer filter types should be provided for this purpose. Fibrous filter performance is generally described through its temporary separation efficiency, preserved on a required level, and, defining the filter lifetime, the maximum pressure drop and retention capacity. It all determines the filter use through the deposit alignment within the filter volume. The obtained empirical correlations of kinetics of deposit accumulation and the pressure drop development are helpful in filter design. Local phenomena, i.e. the agglomerate structure, spatial distribution and resuspension were widely explained and generalized to global, macroscopic conclusions. The proposed description of the structural loading of the multilayer filter is simple, reliable and can help in preliminary estimation of the filter structure. Afterwards, the final parameters, such as fiber diameter and packing density, can be fine tuned in experimental research.

106

9. BIOFOULING This thesis primarily concerns the aspects of clarification of abiotic suspensions. However, as the removal of solid particles from water is always accompanied by retention of organic matter as well, additional research about separation of biotic contamination was included in this section. The major problem with water purification processes is that the feed stream is organically and permanently loaded. Organic matter filtration is often associated with operational problems, such as loss of flux and shortening of filter life (Sun et al., 2017; Umar et al., 2017; Deng et al., 2016). It is due to the additional factor of microbial growth kinetics, , present in a mass balance of the system: 𝜕𝜎 𝜕𝑡

+

𝜕𝜀𝐶 𝜕𝑡

+

𝜕𝑢𝐶 𝜕𝑧

𝜕

𝜕𝐶

𝜕𝑃

− 𝜕𝑧 (𝐷 𝜕𝑧 ) + 𝜕𝑡 = 0

(9.1)

The rate of microorganism growth can be described for example by the Monod equation (Solimeno and Garcia, 2017). If the deposit contains bacteria, e.g. in the growth phase, clogging of the filter occurs not only from the up-flowing contamination but also from multiplying bacteria. Such filter surface blockage by organic matter is called a biofouling. It is a common problem in membrane filtration (Saeki et al., 2017). In deep bed filtration, contaminations are removed by deposition throughout the filter medium. However, both literature (Selomulya et al., 2005) and our own findings show that the front surface of the outer fabric adsorbs most contaminations either abiotic (Sec. 6.4) or biotic (Fig. 9.1). In the deeper parts of the material single agglomerates of solid particles or distinct microorganisms can be found. A high concentration of microorganisms accumulated in front layers of the filter connected with their ability to reproduction result in shortening the lifetime of the filter and so more frequent changes of the filter element. Proper antibacterial modifications of the filter surface could reduce the biofouling effect, extend filter longevity and make the filtrate free of various bacterial contamination.

107

Fig. 9.1. CLSM images of a STANDARD 1 fibrous filter tested on natural river water. (a) outer layer, (b) – 1 mm deep, (c) – 5 mm deep. Fibers are seen in white, pores in black and organic matter in color. Water bacteria are very diverse organisms. To date, no universal antibacterial chemical has been found. However, the antibacterial properties of ZnO and Ag nanoparticles are known and have been verified by many researchers (Andrade et al., 2015; Mg et al., 2013). They can act on different organisms (You et al., 2011) and, as a result, were used to create a filter that would exhibit antibacterial properties over a broad range of bacteria types. In this chapter, the performance of two multilayer filters made of pure polypropylene (PP) and a composite of polypropylene, 1 %vol ZnO and 0,1 %vol Ag nanoparticles (PP+ZnO+Ag) was analyzed. Both filters were produced using the melt-blown technology process. Their structure was the same in geometry, diameter and packing density of fibers as that of STANDARD 1 filter. Antibacterial tests were performed in both laboratory and industrial scale experiments.

9.1. Formation of a deep-bed filter structure modified with ZnO and Ag Nanoparticles of ZnO and Ag manufactured by Nanostructured & Amorphous Materials, Inc. were used for the formation of composite fiber and composite deep-bed filter. The filter raw material was granulates of polypropylene, with an appropriate concentration of nanoparticles in the mixture.

108

Fig. 9.1.1. Production of polypropylene-nanoparticle composite (Sztuk and Gradon, 2016). Granulates used in the mixture are produced in the technological system shown in Fig. 9.1.1. Granulates of pure propylene (1) are introduced into a twin-screw extrusion cylinder (3), which is then melted and transported into another section of the extruder. The powder consisting of a uniform mixture of ZnO and Ag particles (2) is batched in a controlled amount into the extruder, mixed with the melted polypropylene and transported to a die (4). Here, the monofilament (5) is formed. The monofilament has a uniform mixture of nanoparticles. After cooling in the water bath (6), it is introduced to a rotating knife system (7) where granules (8) are produced. Granules of polypropylene that consist of ZnO and Ag nanoparticles with a 4 %mass concentration, are used as raw material for the production of composite filters using the melt-blown technique. The final concentration of nanoparticles in polypropylene used for filter production is controlled by diluting the concentrated granulates with pure polypropylene granulates. After manufacturing the composite granulate, the filter cartridge is produced using the meltblown technique. The production principles were described in Sec. 4.

109

Fig. 9.1.2. Formation of the single fiber in the die nozzle. Fig. 9.1.2 presents the formation of the single fiber in the nozzle. The molten polymer leaving the die cylindrical hole, is exposed to the stream of the hot air. The shear stress on the boundary of polymer filament causes fiber extension. The inside filament mechanical stress and temperature distribution (Gradon et al., 2005) result in nanoparticle displacement towards the fiber surface. Finally fibers with nanoparticles on their surface are formed. A sample of fibers with nanoparticles is shown in Fig. 9.1.3.

Fig. 9.1.3. SEM Image of modified filter fibers with nanoparticles (bright spots). 110

The advanced melt-blown technique, which is equipped with a twin-screw extruder, is the most promising method for composite fiber production. Given proper process controls, the direct introduction of desired antibacterial nanoparticles towards a fiber surface during a standard fiber formation process is possible.

9.2. Movement of bacteria near the fiber The separation of abiotic and biotic contamination in depth filters is driven by various mechanisms. The trajectory of motion for solid particles inside a fibrous structure is characterized by well-defined equations resulting from the force balance acting on the particle (Sec. 3). Bacterial movement depends on the bacterial type because some of them, such as Pseudomonas putida (Jost et al., 2010), exhibit motility. The self-induced random movement of motile microbes, mostly caused by flagella, is known as chemotaxis (Berg and Brown, 1972). Non-motile bacterial movement is similar to that of abiotic particles.

Fig. 9.2.1. Movement of bacteria and solid particles near the fiber. The literature contains no practical field applications of bacterial removal by fibrous filters. Although some authors have tried to model the deposition of particular bacteria types (Gac and Gradon, 2015), their calculations are based on idealistic assumptions. In fact, almost every feed stream contains more than one type of bacteria. Many studies state different deposition mechanisms, even for the same strain of bacteria, e.g., Escherichia coli D21 and Escherichia coli D21f2 (Ong et al., 1999). Therefore, because of lack of comprehensive data, it is hard to predict the behavior of many bacterial strains in the natural environment. 111

9.3. Antibacterial/bacteriostatic test As the antibacterial filters are highly demanded product on the market, quantitative test methods to determine their antibacterial activity were developed and standardized (ASTM E2922-15, 2015; ISO 20743:2013, 2013). For example an ISO 20743:2013 standard is directly dedicated to all textile products, including nonwoven filters. It recommends 3 inoculation methods: •

Absorption method – test bacterial suspension is inoculated directly onto specimens.

•

Transfer method – test bacteria are placed on an agar plate and transferred onto specimens.

•

Printing method – test bacteria are placed on a filter and printed onto specimens.

The produced filter materials made of the polymer and its composite with ZnO and Ag nanoparticles were first verified in laboratory scale experiments in a scheme similar to the transfer method. The quantification of colony plate count was not performed as the purpose of this research was the qualitative comparison of modified and non-modified materials. Because the bacterial environment is extremely diverse, antibacterial and bacteriostatic tests were performed on common bacterial strains in the aqueous environment. Escherichia coli PCM 2560 and Bacillus subtilis PCM 2021 were chosen as representatives of gram-negative and gram-positive bacteria, respectively. The antibacterial/bacteriostatic tests were carried out in plate assays, on Petri dishes. The Escherichia coli was grown in the differentiating medium, while the Bacillus subtilis was grown in 1 % Luria-Bertani agar (LB). In the case of both fabrics (the non-modified polypropylene filter fabric and the filter modified with ZnO and Ag nanoparticles) samples were taken from the front layer, at 1/3 and 2/3 depth, and outer surface of the filter structure. It has to be emphasized that each sample differed in fiber diameter. The fiber diameters were decreasing with the flow direction as the structure of the examined filters was a multilayer gradient. Each sample was put on plates covered with a suitable medium and incubated for 24 h at 37°C. In the test, the antibacterial and bacteriostatic properties of the material are reflected by the halo emerging around the fabric samples. The data presented below show that the polypropylene and polypropylene composite (with ZnO and Ag nanoparticles) filter materials are characterized by different properties.

112

Fig. 9.3.1. Antibacterial and bacteriostatic plate test: (a) - on E. coli on differentiating medium incubated for 24 h at 37°C, (b) – on B. subtilis on LB medium incubated for 24 h at 37°C. PP – pure polypropylene. 1, 2, 3, 4 – layers of modified fabric from different material depths, starting from the filter inlet. Plate tests on the Escherichia coli and Bacillus subtilis, presented in Fig. 9.3.1, confirmed the antibacterial properties of ZnO and Ag nanoparticles. The clear zone, which is visible only around the modified material, shows inhibited growth. This suggests that bacteria will not grow near the fibers. The same zone is wider for Bacillus subtilis. In the case of Escherichia coli, a bacteriostatic effect can be noticed instead. Results of experiments performed on samples taken at different depths of the analyzed material were similar. Hence, despite the differences in fiber size, antibacterial and bacteriostatic properties were achieved on the surface of the entire fibrous structure. The antibacterial action mechanisms of ZnO and Ag are still not fully understood (Andrade et al., 2015; Mg et al., 2013). Some maintain that their properties are mainly associated with ion diffusion. Others claim that their toxic effect is the result of direct contact between bacteria and the nanoparticles. Based on our experiments, it is hard to define which mechanism was dominant.

113

The preliminary positive effect of biofouling at the local parts of the filter layers made allowances for testing the modified filter under real filtration conditions.

9.4. Composite filter behavior during loading Ten-inch long cartridge filters, i.e. filters of commercially available size and geometry, made of pure polypropylene and its composite, were tested in conditions typical for water filtration. Filtration experiments were carried out using Chriesbach (Dübendorf, Switzerland) river water. The average water quality was characterized as having a turbidity of 1,3 ± 0,2 NTU and a temperature of 12,7 °C. The amount of bacteria per milliliter of river water was constant during the experiments, at approximately 700 000 of total bacteria, and 550 000 of live bacteria in the flow-through buffer tank. Biofilms grown on the Chriesbach water surface were analyzed using the amplicon pyrosequencing. It contained substantial amounts of the following bacterial species (with a relative abundance > 2 %): Niastella sp., Arcicella sp., Acidobacterium sp., Devosia insulae, Bradyrhizobium sp., Reyranella massiliensis, Maricaulis sp., Agrobacterium tumefaciens, Methylibium petroleiphilum, Sphaerobacter sp., Rhodoplanes sp., Giesbergeria sinuosa, Acidovorax sp., and Desulfomicrobium orale, Chondromyces sp. All these bacteria are gram-negative and some are motile. A diagram of the filtration set-up is schematically shown in Fig. 9.4.1. The filters were tested under nominal flow conditions of 600 L·h-1. The experiments were carried out until a 2,5 bar pressure drop on the filter was reached. This critical value commercially indicates the clogging of filter pores, which leads to a rapid pressure drop and filter damage.

Fig. 9.4.1. Diagram of the experimental set-up. 114

During the experiments, the following parameters were measured: the pressure drop on the filter, and the number of bacteria upstream and downstream of the filter. The number of bacteria deposited or grown/killed on the fibers was determined based on the difference between the quantities upstream and downstream of the filter. The amounts of total and live cells were counted separately and determined using a CyFlow Space flow cytometer, Sysmex Partec GmbH. SYBRR Green and Propidium Iodide (diluted 100 times in DMSO) were used, respectively, according to literature (Van der Merwe et al., 2014). The number of dead bacteria was determined as the difference between the total and the live cells. Industrial-scale experiments conducted on natural river water, which was contaminated by many types of bacteria, also showed performance improvement. The results shown in Figs. 9.4.2-3 indicate that both pressure drop and the inhibition of bacterial growth are significantly affected by the implementation of ZnO and Ag nanoparticles to the fiber surface.

dead / live bacteria number [-]

1,6

1,2

0,8

PP

PP+ZnO+Ag 0,4

0,0 0

20

40

60

80

100

time [min] Fig. 9.4.2. Relationship between the number of captured dead and live bacteria during the filtration process for standard (PP) and modified filters with 1 % zinc oxide and 0,1 % silver nanoparticles (PP+ZnO+Ag). Fig. 9.4.2 describes the ratio between the number of dead and live bacteria as separated by the filters. This proportion declines for the standard polypropylene filter and the amount of live 115

bacteria captured by the filter is higher compared to the removal of dead bacteria. The composite filter separation properties developed differently. The ratio between the filtrated dead and live bacteria increased during the process. After some time, the proportion reversed, indicating that the amount of dead bacteria stopped by the filter was higher than the removal of live bacteria. The number of bacteria upstream was constant. Therefore, the growing number of dead bacteria, which accumulated on the fibers, along with the decrease in living bacteria, must be the consequence of bacteria killing. 2,5

pressure drop [bar]

2,0

1,5 PP 1,0

PP+ZnO+Ag

0,5

0,0 0

20

40

60

80

100

time [min] Fig. 9.4.3. Pressure drop on the filter during filtration process for standard (PP) and modified filters with 1 % zinc oxide and 0,1 % silver nanoparticles (PP+ZnO+Ag). The initial pressure drop across the filter is equal for both filters (Fig. 9.4.3) because they have the same fibrous structure, porosity and fiber diameter. After a short filtration time, the suspended contamination deposits on the previously deposited matter, and creates agglomerates. At this point, non-steady state filtration starts. The initial porosity decreases with time. Initially, it refers to a clean fibrous fabric, but after a short time, filter pores build over with deposited particles, thereby changing the porosity of the filtrating structure. In addition, the deposited bacteria start to reproduce, which also affects the pore sizes. This growth increases especially when microorganisms deposit on solid surfaces. Because these 116

are fixed cultures, they are less strongly affected by changes in environmental conditions (Lazarova and Manem, 1995). Consequently, the resistance for the flowing fluid increases, as shown in Fig. 9.4.3. At the same time, the growth for the composite filter is slower. This may be the effect of ZnO and Ag nanoparticle supplementation. The natural river water flowing in the riverbed with the velocity over 0,4 m·s-1 contains bacteria at different stages of growth kinetics. ZnO and Ag nanoparticles located on the fiber surface inhibit the growth of bacteria. If fewer bacteria are reproduced, the clogging of the filter results only from the upflowing contamination. Porosity changes are less rapid in this case. The lifespan of the filter and the profile of the pressure drop are the main factors defining economics of the process. The main operating cost, M, is connected to the expenditure of energy for pumping suspensions through the filter at a particular flow rate, Q. During filtration time, tF, this cost can be calculated as: 𝑡 𝑐𝑃𝐸 ∙𝑄∙∆𝑃(𝑡) 𝑑𝑡 𝜂𝑃

𝑀 = ∫0 𝐹

(9.4.1)

where cPE is the unit price of energy, ηp denotes the mechanical efficiency of the pump, and ΔP(t) is the momentary pressure drop across the filter. For a fixed price of electricity, flow and pump quality, the energy consumption for filtration is directly connected to the pressure drop profile in a filter during loading: 𝑀=

𝑐𝑃𝐸 ∙𝑄 𝜂𝑃

𝑡

𝐹 ∫0 ∆𝑃(𝑡)𝑑𝑡

(9.4.2)

Taking into account Eq. 9.4.2, the ratio of the costs of water pumping through both, modified (PP+ZnO+Ag) and non-modified (PP) filters, m, can be calculated as: 𝑡

𝑚=

[∫0 𝐹 ∆𝑃(𝑡)𝑑𝑡]

𝑃𝑃+𝑍𝑛𝑂+𝐴𝑔 𝑡𝐹 [∫0 ∆𝑃(𝑡)𝑑𝑡] 𝑃𝑃

(9.4.3)

Comparing the effect of filter loading, the value of tF is defined at the moment when one of the filters reaches the pressure drop of 2,5 bar. In this work, it was 105 min for the nonmodified filter. The calculated results based on the ΔP(t) profiles (Fig. 9.4.3) gave the value of m equal to 0,68. This means that the cost of pumping for the modified filter versus the regular filter was reduced by 32 %.

117

Even small concentrations of antibacterial compounds (1 %vol ZnO and 0.1 %vol Ag nanoparticles) greatly increased the working time of the filter. Therefore, the cost of the filtration process was significantly reduced, while the expenses on the filter material production increased by just a few percentage points. The final price of the modified filter due to the composite production and the antibacterial compounds purchase should increase up to 20-25 %. Most significantly, these composite filters improved bacterial removal, although total removal was not achieved. Nevertheless, it should be taken into consideration that ZnO and Ag nanoparticles do not exhibit antibacterial activity for every bacterial type. Further tests investigating the leaching speed would deepen our understanding of the process mechanism. The development of a production method for antibacterial composite fibrous filters marks a groundbreaking milestone in the field of low-pressure filtration.

118

10. CONCLUDING REMARKS This thesis presents the results of extensive theoretical and experimental studies on water filtration in fibrous filters. The investigations were conducted using various types of suspended matter and different kinds of fibrous filters. A melt-blown technology process was developed to manufacture filters characterized by various properties. Results clearly indicate that filters described by various initial structures, i.e. fiber diameter and porosity distributions in the filter layer, are loaded differently. The evaluation of their behavior based only upon their performance at the initial stage of the process, as recommended by EN 13443-2:2005+A1:2007 standard (EN 13443-2:2005+A1:2007, 2007), does not provide any practical information about the filter quality. Filters separating the same particles better or even similarly during their initial stage of operation, in fact, might clog after a short time due to the incorrectly designed structure. Thus, only a verification of the filter performance in the entire non-steady state filtration cycle determines the filter class. A procedure of filter testing proposed in this work gives comprehensive information about the separation efficiency, retention capacity, lifetime and pressure drop across the filter. The method can be used for a reliable filter characterization. It was shown that a distribution of particle deposits within the filter structure determines the filter performance. The proposed model of kinetics of solid accumulation within a fibrous structure depends on the filter initial structure, including fiber diameter and porosity of a clean fabric. The model includes agglomerate break and resuspension through a two-step process. These phenomena are the most problematic ones in depth filtration.

Local

occurrences, such as deposit structure, deposit location within a single pore as well as in the entire filtration material were included in the macroscopic description of the process via filter porosity development. Porosity was chosen as the parameter most influencing the filter behavior. A suggested technique of its determination in a partially or totally loaded fabric is simple and does not require microscopic assumptions about the shape or the number of pores/collectors. Models founded on obtained porosity profile may help in prototyping the construction of filters for solid-liquid mechanical separation. Filtration efficiency, pressure drop and filter lifetime calculated with the proposed simplified macroscopic equations give rough expectations from the chosen fibrous structure during its use, which later can be examined and fine tuned in experimental research.

119

Yet, fibrous filtration challenges the removal of nano-sized contamination, which so far was possible only with membrane techniques. To increase separation properties of standard fibrous structures in efficient filtration of such objects, a novel structure of a fibrous fabric was designed and produced in a modified melt-blown technology process. Throttling the flow of polymer in some parts of the extruding die enabled fabrication of nano- and micro-sized fibers in parallel, thus making the fabric layer being characterized by bimodal distribution of fiber diameters. Such a mixed-fiber structure verified in an experimental research, when compared with the standard fibrous structure characterized by uniform distribution of fiber diameters, performed with higher efficiency of nanoparticle removal, whose movement was mainly driven by the Brownian diffusion motion. Therefore, a mixed-fiber filter material, designed for removal of particular particle sizes lowers the limits of depth filtration and the filter micron rating. With the progress made in this work, a design of a fibrous structure dedicated for not only water clarification, but also water polishing under a normal pressure condition and with relatively high capacity is possible. The general aim of this work was related to the issues of solid fibrous filtration. However, as the water medium is constantly organically loaded, the biofouling effect was additionally analyzed. A solution to intrinsic bacterial growth on filter surface was proposed through the material modifications of a surface of the filter elements during the process of filter production. A twin-screw extruder was projected to support the construction of granules of polypropylene containing antimicrobial nanoparticles. The granules were further used as the substrate in the production of antibacterial filters. Once the granulate was ready, a properly designed traditional melt-blown extrusion process enabled manufacturing of fibrous filters made of the polypropylene and desired nanoparticles on the fibrous surface. The bacteriostatic and antibacterial properties of filters made of the polypropylene and ZnO and Ag nanoparticles were confirmed in laboratory and industrial scale experiments. The filters performed longer than the standard filters made of pure propylene. When filter replacement is problematic, the use of such composite filters is highly beneficial. Structural and material modifications are the future of the improvement of fibrous filters. With a good filter structural design and the method of filter production proposed in this work, the limitations of depth filtration process disappear. Knowing the characteristics of suspension contamination, fibrous filters can be now designed for water clarification as well as polishing, and used as an inexpensive alternative to membrane mechanical filters. 120

Presented results may be an inspiration for researchers to change the normative requirements concerning the classification of nonwoven filter media.

121

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APPENDIX 1

0,8

clearance [-]

0,6 1ˢᵗ layer 2ᵑᵈ layer

0,4

3ʳᵈ layer 4ᵗʰ layer 5ᵗʰ layer

0,2

6ᵗʰ layer 0,0 0,0

0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. A.1. Evolution of specific deposit during loading of STANDARD 1 filter.

0,8

clearance [-]


0,4


0,2


0,2

0,4

0,6

0,8

1,0


132

0,8

clearance [-]


0,4


0,2

6ᵗʰ layer 0,0

0,0

0,2

0,4

0,6

0,8

1,0


0,8

clearance [-]


0,4


0,2


0,2

0,4

0,6

0,8

1,0

non-dimensional time [-] Fig. A.4. Evolution of specific deposit during loading of MIXED-FIBER 1 filter.

133

0,8

clearance [-]


0,4


0,2

6ᵗʰ layer 0,0

0,0

0,2

0,4

0,6

0,8

1,0


0,8

clearance [-]


0,4


0,2


0,2

0,4

0,6

0,8

1,0


134