Polymeric microfilters by interference holography : development and applications

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Polymeric microfilters by interference holography :

development and applications

Citation for published version (APA):

Prenen, A. M. (2009). Polymeric microfilters by interference holography : development and applications. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR652646

DOI:

10.6100/IR652646

Document status and date: Published: 01/01/2009 Document Version:

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Polymeric microfilters by

interference holography:

Development and applications

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn, voor een

commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op maandag 12 oktober 2009 om 16.00 uur

door

An Maria Prenen

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prof.dr. D.J. Broer Copromotor:

dr.ing. C.W.M. Bastiaansen

A catalogue record is available from the Eindhoven University of Technology Library

ISBN: 978-90-386-2014-5

Printed by the Eindhoven University Press, the Netherlands. This research was financially supported by NanoNed

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In the past two decades, medical diagnostics have shifted their interest from the lab towards point-of-care testing. Biosensors have led to a tremendous progress in the development of new or strongly improved point-of-care tests. Two important components in a biosensor are microchannels and membranes. The microchannels enable the reduction of the sample volume, and a membrane can have various functions. For instance, its large internal surface can serve as substrate for the adsorption of biological species and of course it can also be used for the filtration of e.g. blood cells or platelets from a sample.

Numerous different types of membranes exist and usually they have a highly polydisperse pore size which limits efficiency and throughput. Mi-crosieves, or monodisperse microfiltration membranes, have an almost ideal geometry for efficient separation in combination with a high throughput. Nowa-days, several techniques are being developed for the fabrication of these mi-crosieves. Processes such as silicon micromachining, phase separation micro-molding, track etching all have their specific merits, but none are ideal and they are often very difficult to implement in biosensors. With interference holography, membranes can be produced with well-defined pore shapes, a high efficiency and a low pressure drop with the ease of fabrication and material properties of polymers. To achieve these, holography makes use of the in-terference pattern generated by two crossing, parallel polarized laser beams. The periodicity of this pattern can be tuned by changing the angle between the two laser beams. A chemically and thermally resistant photoresist, SU8, is used to digitally record the analogue interference pattern. SU8 allows for multiple exposures to an interference pattern due to its high glass transition temperature and the final structure is a simple addition of all exposure steps. A wide range of circular pore sizes (0.1 µm - 5 µm) was fabricated by tuning

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the angle between the interfering laser beams.

To investigate the geometrical parameters influencing the flux through a holographic membrane, finite element method simulations were executed. Simulations show that elongated, elliptical pores have a several advantages in comparison to the standard, circular pores. Due to their improved surface to volume ratio, the flow resistance induced by the presence of the pore wall is lower, resulting in a larger flux. Membranes with slit-shaped pores have the additional advantage that, in general, they have a larger porosity. It was shown that these slit-shaped pores can be produced by changing the angle be-tween the interfering laser beam bebe-tween the two exposure steps or by rotating the sample over an angle less than 90 degrees.

The pore wall reduces the throughput of a membrane and, consequently, membranes with pores with a low aspect ratio are usually preferred. Thin membranes have a lower flow resistance than thick membranes with the same selectivity, due to the no-slip condition at the pore wall. The membrane thickness is easily tuned by changing the thickness of the applied photoresist, either by adjusting the solid content in solution or by changing the spin coating conditions. Unfortunately, very thin membranes are mechanically weak and, therefore, a special processing route was developed to produce thin membranes with a small pore size on a mechanical support which is a thick membrane with a very large pore size.

The so-called Vena Contracta effect decreases the flux through the straight pores by restricting the effective flow diameter after a pore to a diameter slightly smaller than the actual pore diameter. Jet-shaped pores are known to decrease the loss in flux due to a Vena Contracta. A light intensity gradient over the film was induced by the addition of a UV absorber. This results in small pore diameters at the high light intensity side of the membrane, and large pore diameters at the low light intensity side, in combination with a continuous gradient in pore diameter. This effectively results in the desired jet-shaped pores, which reduce the Vena Contracta effect. On the other hand, the maximum obtainable porosity is also reduced and consequently an optimum is obtained for a membrane with a inlet pore diameter of 2 µm and an outlet pore diameter of 3 µm.

The above described membranes have several merits in classical filtering applications such as removal of particulate matter from exhaust streams. Nev-ertheless, incorporation of the membranes in microfluidic channels of a biosen-sor offers new opportunities in the design of e.g. protein microarrays.

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lamellae in a microchannel. Such lamellae are easily fabricated using either mask lithography of holography. In a new design of a protein microarray, groups of lamellae are positioned locally in a microchannel, forming adsorption sites for capture probes. In this way, several membranes can be put in series in a microchannel which results in a high signal-to-noise ratio and an excellent selectivity, while fulfilling the low sample volume requirement.

The flow between lamellae is laminar in nature, implying that the transport of biological agents to the lamellae walls relies on diffusion only, resulting in long assay times. To improve this, grooves are applied on the lamellae to induce a rotational flow and herewith enhance the transport of agents to the walls. These grooves are generated by a balanced combination of mask lithography and a holographic under-exposure.

So-called slanted-angle holography was developed to create membranes with in-plane pores that can be incorporated in a microchannel. These mem-branes are mechanically more stable than lamellar memmem-branes and they have a larger surface area. Again, the pore size and shape can be chosen by adjusting the angle between the laser beams and/or the tilt angle. In combination with a lithographic step, in-plane membranes are fabricated in situ inside a mi-crofluidic channel, providing a leak-free connection to the channel wall. When tested, these membranes show a low pressure drop and an excellent selectivity. Immobilization of antibodies is a crucial step in the development of mi-croarrays. The protein conformation needs to remain intact and the biological functionality of the protein has to be preserved. Physical adsorption is most frequently used as immobilization technique for proteins. However, covalent binding provides a much stronger attachment and is therefore preferable. Co-valent coupling techniques using amines or carboxylic acids on a surface have been developed to generate this strong binding. SU8 substrates were therefore provided with a coating of polyacrylic acid (PAA) or poly-L-lysine (PLL). Re-covery experiments were performed to test the binding of antibodies to these surfaces. Both plain SU8 and PLL showed a good recovery, PAA did not. The small difference between PLL and treated SU8 led to the choice for non-treated SU8 as substrate for subsequent biological experiments. A functional sandwich assay was performed on a flat surface of plain SU8. Preliminary re-sults showed a detection limit of 10 nM on a flat substrate. This is still rather high, but lower detection limits (pM) are expected when membranes will be used as a substrate.

Fluid flow through a biosensor is preferably not induced by external pump-ing devices. Often, capillary flow is used makpump-ing external pumppump-ing redundant.

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However, SU8 is known for its hydrophobicity which results in no capillary flux in a non-treated SU8 microchannel. The flow through microchannels was in-creased significantly by increasing the surface energy and the surface polarity of SU8 by a UV-ozone and/or and oxygen plasma treatment. This enables the use of capillary pressure as a driving force for fluid flow through a microchan-nel.

Finally, contact between the analyzed body fluids and the outside environ-ment is usually unwanted in biosensors. Therefore, a cover that hermetically seals the microchannels is required. Glancing angle lithography was developed to solve this issue. Utilizing the non-discrete nature of a reflection interface, a thin area at the top of a photosensitive film (SU8) is activated. This activated area was crosslinked to form a cover layer during the postprocessing steps. The thickness of the cover layer is controllable by the angle of incidence, the exposure dose and the diffusion time of the photo-activated species. Com-bining this technique with the aforementioned techniques like slanted-angle holography, interference holography and classical lithography, a hermetically sealed functional biosensing device can be obtained.

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General introduction

Over the last 10 years, medical diagnostics have been shifting their focus from laboratory testing towards point-of-care diagnostics. Biosensors, devices that can perform laboratory tests on a chip that is smaller than a credit card, are extremely suitable for this task. The ultimate goal is to selectively detect mul-tiple types of species, preferably every molecule present in the analyte (sen-sitivity). This detection needs to be fast, using a very small sample volume, like the sample volumes obtained with a fingerprick. So, selectivity, sensi-tivity, speed and small sample volumes are key elements for biosensing. To meet these requirements, microfluidic channels and membranes are frequently used as building blocks for biosensors. A microfluidic device is often defined as a device containing at least one channel with a diameter smaller than 1 mm, which is very useful for dealing with small sample volumes. The fluids that are to be tested in the biosensor are usually complex mixtures that need pretreatments like filtration, mixing or chemical treatment. A membrane is often incorporated in a biosensor for microfiltration, turbulence induction or just for providing a large adsorption surface. The research performed in this thesis deals with the development of new technologies for the fabrication of microstructured elements and membranes for both standard microfiltration ap-plications as well as in microfluidic devices. A special emphasis is devoted to well-defined monodisperse microstructural elements, produced via interference holography, to obtain devices with a strongly enhanced performance in terms of selectivity and sensitivity.

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1.1 Miniaturization in medical diagnostics

About 2 decades ago, medical diagnostics started to shift its focus from labo-ratory testing towards point-of-care testing (POCT). Two factors led to this shift in approach of patient care: time to result and technological advances.

Firstly, it is beneficial for a patient if the time needed for a diagnosis in cli-nical situations is reduced[1, 2]_{e.g. in emergency services, intensive care units,}

etc. Rapid diagnosing enables a rapid treatment of possibly life-threatening conditions like in the early stages of a heart attack.[3] _{Secondly, the enormous}

technological developments in miniaturization of systems in the past years have made POCT feasible and practical. Pointofcare sensors called biosensors -should be able to compete with standard laboratory tests in terms of specificity and sensitivity, and preferably be faster, cheaper, use smaller sample volumes and be easier to use for non-specialized personnel.[4]

One of the best known examples of a biosensor probably is the glucose meter (figure 1.1), used by diabetics to measure the glucose concentration in their blood. By means of a fingerprick, a small amount of blood (∼1 µl) is sampled and applied onto a strip which is inserted into a reader. A few seconds later, the glucose concentration can be read from the LCD screen, and action (e.g. insuline injection) can be taken accordingly. This example illustrates some of the key features of biosensor: speed, selectivity and small sample volume.

Figure 1.1: The most well-known biosensor on the market: the glucose meter,

used to detect the glucose level in blood from a fingerprick.[5]

Glucose is a molecule that is relatively abundant in blood, in concentra-tions of approximately 80-110 mg/dl. However, markers for other condiconcentra-tions like troponin, an enzyme that is produced during cardiac failure, are only spo-radically present (ng/dl[6]_{) requiring a very sensitive detection device. These}

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low detection limits demand new approaches for the detection of biological markers.

Microfluidics[7–9]_{are often used to address the key requirements of a}

biosen-sor (speed, selectivity, sensitivity and sample volume). A microfluidic device is defined as a device containing at least one channel with a diameter smaller than 1 mm, of which some examples are shown in figure 1.2. Due to their small size, the required sample volume for the device is very limited, and a short time to result can be reached with this technology. However, the minia-turization of these biosensing systems has one major disadvantage: from the small amount of analyte the same amount of information or even more needs to be extracted.

Figure 1.2: Microfluidic chips.[10]

Biosensors realize detection by translating a specific nanoscopic interaction between receptors present in the sensor and the species to be detected in the analyte into a macroscopic signal. This signal can be optical, electrical, mag-netic, etc. and should be proportional to the amount of interactions that oc-cur.[11] _{Ideally the detection is performed in biological fluids like whole blood,}

saliva and urine. These fluids are usually complex mixtures that need various treatments like filtration/purification, mixing and chemical treatments.[12] _A

unit that is therefore often implemented in a biosensor is a membrane. Typ-ically, the membranes are used for the separation of particles from liquids, the induction of turbulence for mixing or providing a large specific area for adsorption of receptors or other chemical species.

Frequently, commercially available membranes are implemented in micro-fluidics.[12] _{Typically, these membranes are non-woven fabrics and exhibit a}

highly polydisperse pore structure and high porosity. Consequently, the appli-cation of these membranes results in a large pressure drop which restricts the throughput of the fluid in the device. Monodisperse microsieves have a low pressure drop but the actual implementation in a microfluidic device is compli-cated.[12] _{Therefore, an efficient way to fabricate monodisperse microfiltration}

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1.2 Microfiltration

Biological species like cells, pollen, bacteria[13] _{have dimensions in the order}

of micrometers, but also non-biological species like particulate matter (PM2.5,

PM₁₀[14]_{) are in that size range. To filter out contaminants of this size from a}

fluid, microfiltration is the commonly used filtration process. In microfiltration the fluid is passed through a microporous structure, a membrane, driven by an externally applied pressure. Physical separation takes place by size exclusion. The first person to develop a microfiltration filter was professor Sigmondy from the University of Goettingen in Germany in 1935. A couple of years later, the first membrane filters were commercially available, produced by Sartorius GmbH. Two principles of membrane filtration can be distinguished: dead end filtration and cross-flow filtration, (figure 1.3).

(a) Dead end

Membrane Membrane Retentate Permeate Feed Permeate (b) Cross flow

Figure 1.3: The two filtration modes: dead end (left) and cross flow (right).

The feed (fluid or gas with suspended species) is divided by the membrane into a retentate (species that are filtered out) and the permeate (filtered so-lution or gas). One of the problems in filtration is membrane fouling, which can be decreased by decreasing the transmembrane pressure drop. However, a reduction in pressure drop also reduces the flux through the membrane[15]

which reduces productivity and throughput of product. To compensate for this loss of flux, highly efficient membranes with a very low flow resistance are required.

Standard microporous membranes (figure 1.4) are usually random-network dense structures that have a large flow resistance due to the large pore size distribution.[13] _{The largest pores determine the selectivity of a membrane,}

while pores that are smaller increase the flow resistance.

The flow resistance of a membrane with a certain selectivity (size of the largest pore) is determined by its thickness, pore size distribution and poro-sity.[16] _{Microsieves, membranes with a well-defined pore geometry, pore size}

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se-(a) Isotropic (b) Anistropic

Figure 1.4: Schematic representation of isotropic and anisotropic polydis-perse membranes. Polydispolydis-perse membranes have a large flow resistance due to the irregular sizes and shapes of their pores.

lectivity and flow resistance.[15, 17] _{Recently, the production and properties of}

such monodisperse membranes have attracted considerable attention.[15, 18, 19]

Several rather elegant routes were proposed in the past to produce polymeric and monodisperse microsieves via, for instance, phase separation micromoul-ding,[20] _{track etching}[21] _{and silicon micromachining.}[22] _{In the above}

de-scribed studies, the prime objective is often to combine the ease of processing of polymers with the high performance of monodisperse porous media. Never-theless, the above described polymeric membranes also have limitations with respect to maximum porosity, material properties (mechanical strength) and freedom of design in pore geometry or in pore size.[23]

Monodisperse membrane fabrication techniques like phase separation mi-cromolding and micromachining are hard to integrate with biosensor produc-tion or it is even completely impossible. For instance, mounting such mem-branes to the microchannel with a leak-free connection is troublesome. As al-ternative fabrication method, possibly circumventing a number of these issues, we investigated holographic techniques for the in situ fabrication of membranes in microchannels. Therefore interference holography is discussed in some more detail in the next paragraph.

1.3 Holography

Holography is a photographic technique that has been known for over 60 years already.[24] _{In essence, it consists of capturing not only the brightness, but also}

the intensity variation between light passing through a photographic object and light from a reference beam. First, an interference pattern is created using coherent polarized light, usually from a laser. Then, this interference pattern is recorded in a photosensitive film. And lastly, the hologram is reconstructed

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using the diffraction of light by this film.[24]

In this research, the first two steps of the holographic process are used: the registration of an interference pattern in a photosensitive film. A microstruc-ture is obtained by removing the areas of the film that received a certain exposure dose (intensity × exposure time). Alternatively, a microstructure can also be generated with a so-called negative photoresist and then de unex-posed areas are removed by dissolving or etching. In fact, the major part of the research in this thesis is performed with such a negative photoresist (SU8). The creation of a regular interference pattern depends highly on the co-herence of the light source used for recording the hologram. Nowadays, lasers (Light Amplification by Stimulated Emission of Radiation, invented by T. Maiman[25]_{) are used as source for coherent light. During the recording of}

a hologram, the photosensitive film is placed on the intersection of the two interfering light beams.

Two types of recording geometries can be discriminated, depending on the orientation of the photosensitive film in the recording setup (figure 1.5). If the sample is perpendicular to the incoming beams, it is called transmission holography, from the fact that in a transmission hologram the object is recon-structed by the transmitted beam. If the sample is parallel to the incoming beams, it is called reflection holography. All structures presented in this thesis are created using transmission holography.

θ_/2 k1 k2 e_x ey k1 k2 θ_/2 θ_/2 Transmission Reflection

Figure 1.5: Recording geometries for transmission and reflection holography. In transmission mode, the two interfering laser beams are incident on the same side of the photosensitive film, in reflection mode they reach the sample from both sides.

In figure 1.6 an example is shown of the different processing steps for a photoresist. First, a thin layer of the photoresist is applied on a substrate,

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usually glass. After this, the sample is heated to evaporate residual solvents in which the resist was dissolved. The substrate is then exposed to an intensity pattern which can be induced by a mask or by the interference of laser beams (figure 1.6(b)). Usually, an additional heating step is needed to polymerize, in the case of a negative photoresist, or de-polymerize, for a positive photoresist, the material.

(a) Spin coating (b) Exposure

(c) Positive resist (d) Negative resist

Figure 1.6: Steps in the processing of photoresist materials.

SU8 (figure 1.7), a negative photoresist based on the cationic polymer-ization of epoxides, is used as recording material. SU8 is often used as chip material in microfluidics and micro-electromechanical systems (MEMS). It is known for its high aspect ratio patterning and produces very straight vertical side walls. Also, crosslinked SU8 is chemically and thermally resistant and biocompatible.[26] _{This all makes SU8 a very suitable material to fabricate}

membranes for biosensor applications.

O CC2H CH2 O CH3 H3C O C C2HCH2 O O CC2H CH2 O CH3 H3C O C C2H CH2 O O CC2H CH2 O CH3 H3C O C C2HCH2 O O CC2H CH2 O CH3 H3C O C C2HCH2 O H2 C H2 C H2 C

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As discussed previously, the combination of interference holography with suitable photoresist materials is potentially useful in the integration of mi-crostructured elements in the microfluidic channels of a biosensor. An illus-trative example of this is shown in figure 1.8. The microstructured elements are produced by interference holography, while the channel is fabricated using standard photolithography. The direct injection molding of a channel with such microstructural elements is impossible for instance because the aspect ratios of the structures are very high and/or because so-called undercuts are present. The separate production of the elements and the subsequent in-stallation in a preformed microchannel is or almost impossible or extremely laborious and expensive or both which illustrates the need for new processing schemes.

Figure 1.8: Example of the application of interference holography in the production of microstructured elements in a microfluidic channel.

1.4 Scope of the thesis

In chapter 2 a theoretical framework is established, in order to find the most ideal pore geometry for a microfiltration membrane. Finite Element Method (FEM) simulations are used to predict the pressure drop across monodisperse membranes and the flow through membranes with an emphasis on parameters such as pore shape, dimension, packing and cross-section. Chapter 3 is con-cerned with the use of holography for the fabrication of the above described membranes with pores perpendicular to the substrate. A wide range of pore geometries (round, slit-shaped) and pore arrays (square, hexagonal packing) are produced using holography, as well as different pore sizes (between 5 µm and 50 nm), according to the findings of chapter 2. Also, the simulation re-sults from chapter 2 are experimentally verified. Chapter 4 deals with the fabrication of in-plane membranes, i.e. membranes which have their pores parallel to the substrate. It will be shown that using this technique produces

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well-defined pores with a very small pore size distribution and that the pore geometry, size and packing is easily manipulated. Especially these membranes are extremely suitable for the in situ fabrication inside a microfluidic channel. Moreover, the membranes are evaluated in terms of selectivity and pressure drop. In chapter 5 holographic membranes are adopted for biosensor ap-plications. The usefulness of these membranes in protein microarrays will be elaborated. Additionally, blood cells will be filtered from a blood sample using in-plane membranes integrated in a microfluidic channel. Chapter 6 deals with the application of membranes in another type of filtration, namely using large adsorption area intrinsically provided by membranes for the adsorption of biomolecules without using the actual sieving properties of the membrane. These molecules would normally be too small to be filtered with a micro-filtration membrane. Different surface modifications, both chemical and physical i.e. the creation of relief structures on an otherwise flat surface and their effect on capture of biomolecules are subject of this chapter. An issue that is often faced when dealing with microfluidics, namely the sealing of mi-crofluidic channels to create a barrier between the fluids inside the device and the outside environment is the subject of chapter 7. A new exposure and sealing method, called glancing angle lithography is discussed, and differ-ent parameters affecting the film thickness of the cover layer are investigated. Finally, standard microstructural elements such as channels are sealed using this method.

1.5 References

[1] N. Drenck. Point of care testing in critical care medicine: the clinicians

view. Clin. Chim. Acta, 307, (2001) 3–7.

[2] M. Fleisher. Point-of-care testing: Does it really improve patient care? Clin. Biochem., 26, (1993) 6–8.

[3] D. Eccleston, C. Reid, A. Brennan, J. Miels, N. Andrianopoulos and H. Krum. Point of care biomarker assays are superior to clinical

assess-ment for diagnosis of heart failure in australian emergency departassess-ments: Triaged study. Heart Lung Circ., 17 (Supplement 3), (2008) S155 – S155.

[4] P. St-Louis. Status of point-of-care testing: promise, realities, and

possi-bilities. Clin. Biochem., 33 (6), (2000) 427–440.

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[6] B. Oosterlynck, J. D. Knock and P. Bouckhout. Dringende medische

hulpverlening door verpleegkundigen. Acco Medical (2008).

[7] D. B. Weibel and G. M. Whitesides. Applications of microfluidics in

chemical biology. Curr. Opin. Chem. Biol., 10, (2006) 584–591.

[8] C. Hansen and S. Quake. Microfluidics in structural biology: smaller,

faster...better. Curr. Op. in Struct. Biology, 13, (2003) 538–544.

[9] C. Situma, M. Hashimoto and S. A. Soper. Review: Merging microfluidics

with microarray-based bioassays. Biomol. Eng., 23, (2006) 213–231.

[10] http://www.micronit.com.

[11] T. Vo-Dinh and B. Cullum. Biosensors and biochips: advances in

biolog-ical and medbiolog-ical diagnostics. J. Anal. Chem, 366, (2000) 540–551.

[12] J. D. Jong, R. Lammertink and M. Wessling. Membranes and

micro-fluidics: a review. Lab Chip, (6), (2006) 1125–1139.

[13] R. Baker. Membrane technology and applications. Wiley, 2 edition (2004).

[14] Council directive 199/30/ec. Official journal of the European

Communi-ties (1999).

[15] S. Kuiper, C. van Rijn, W. Nijdam and M. Elwenspoek. Development

and applications of very high flux microfiltration membranes. J. Membr.

Sci., 150, (1998) 1–8.

[16] S. Kuiper, C. van Rijn, W. Nijdam, O. Raspe, H. van Wolferen, G. Kri-jnen and M. Elwenspoek. Filtration of lager beer with microsieves: flux,

permeate haze and in-line microscope observations. J. Membr. Sci., 196,

(2002) 159–170.

[17] L. J. Heyderman, B. Ketterer, D. Bchle, F. Glaus, B. Haas, H. Schift, K. Vogelsang, J. Gobrecht, L. Tiefenauer, O. Dubochet, P. Surbled and T. Hessler. High volume fabrication of customised nanopore membrane

chips. Microelectron. Eng., 67-68, (2003) 208–213.

[18] C. van Rijn, W. Nijdam, S. Kuiper, G. Veldhuis, H. van Wolferen and M. Elwenspoek. Microsieves made with laser interference lithography for

micro-filtration applications. J. Micromech. Microeng., 9 (2), (1999) 170–

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[19] S. Kuiper, H. van Wolferen, C. van Rijn, W. Nijdam, G. Krijnen and M. Elwenspoek. Fabrication of microsieves with sub-micron pore size by

laser interference lithography. J. Micromech. Microeng., 11, (2001) 33–37.

[20] M. Giron´es, I. Akbarsyah, W. Nijdam, C. van Rijn, H. Jansen, R.G.H.Lammertink and M. Wessling. Polymeric microsieves produced

by phase separation micromolding. J. Membr. Sci., 283, (2006) 411–424.

[21] I. M. Yamazaki, R. Paterson and L. P. Geraldo. A new generation of track

etched membranes for microfiltration and ultrafiltration. part i. prepara-tion and characterisaprepara-tion. J. Membr. Sci., 118 (2), (1996) 239–245.

[22] C. van Rijn and M. Elwenspoek. Micro filtration membrane sieve with

silicon micro machining for industrial and biomedical applications. IEEE

Proc. MEMS 1995, page 83.

[23] M. Ulbricht. Advanced functional polymer membranes. Polymer, 47, (2006) 2217–2262.

[24] G. Saxby. Practical holography. IOP, Bristol, 3 edition (2004).

[25] T. Maiman. Stimulated optical radiation in Ruby. Nature, 187, (1960) 493–494.

[26] G. Voskerician, M. S. Shive, R. S. Shawgo, H. von Recum, J. M. Anderson, M. J. Cima and R. Langer. Biocompatibility and biofouling of MEMS drug

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Flow through holographic

membranes

For the development of efficient microfiltration membranes, the critical design parameters need to be known. From a theoretical viewing point, it is clear that the porosity (open surface/total surface) has a major role in the flow resis-tance of a microsieve. Also the pore shape, round or slit-shaped, has a large influence on the flow behavior. Slit-shaped pores have a larger volume to sur-face ratio than round pores and thus less flow resistance induced by the no-slip conditions at the wall of the pore. Another important parameter is the as-pect ratio of the membrane. Ideally, the ratio between the pore diameter and the membrane thickness is between 0.5 and 1, to decrease the flow resistance. Prevention of the Vena Contracta effect is another issue in the optimization of membrane performance. This is a well-known effect that occurs after ori-fices which decreases the flux through an opening. It is known that this can be decreased by using jet-shaped pores. This shape causes the flow to follow the pore walls such that the effective flow through the pore is increased. The theoretical models illustrate that flow through membranes can be designed with a very low pressure drop and high throughput provided that the membrane has a high porosity and the pores are short, slit-shaped and tapered.

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2.1 Introduction

A membrane acts as a semi-permeable barrier layer between two phases. Some components can pass through the membrane (permeate) and others are re-tained by it (retentate). Membranes are neutral or charged, and the driving force for separation can be concentration, chemical or electrical gradients or pressure. However, sieving is the main particle retention method in the mi-crofiltration regime (0.5 - 5 µm). Many techniques are being used to fabri-cate polymer microfiltration membranes,[1] _{like stretching, track etching}[2] _and

phase separation micromolding.[3]

Microfiltration membranes can be subdivided into membranes with a poly-disperse and monopoly-disperse pore diameter. Polypoly-disperse membranes are often manufactured with phase separation techniques and their properties are often far from ideal i.e. the selectivity is determined by the largest pores and the flow resistance is dictated by the smallest pores.[4] _{A far more ideal situation}

is obtained with monodisperse membranes such as those produced via phase separation micromolding and by interference holography (see later).

Here, Finite Element Methods are used to model the flow rate and pressure drop of monodisperse membranes. Obviously, parameters like porosity and pore shape have a large influence on the flow characteristics of the membrane, but also the aspect ratio of the pores and their conicalness are investigated. Especially the ratio between the pore diameter and the membrane thickness (aspect ratio) is expected to have a large effect on the flow. Furthermore, it is well-known that jet-shaped pores can decrease the Vena Contracta ef-fect, which inevitably occurs at the membrane pores. By simulating different tapered pore shapes, the most ideal conical pore shapes are obtained.

Before moving on to the finite element method simulations, the basic theory of microsieve fluid dynamics is presented in a short review.

2.2 Flow theory

Four main flow regimes exist: continuum flow, slip flow, transition flow and free molecule flow. The dimensionless parameter that describes which flow regime is applicable, is the Knudsen number.[5] It is related to the Reynolds number and to the Mach number. The Knudsen number is defined as:

Kn = a

L (2.1)

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scale of the physical system, also in [m]. In air, the mean free path is about 68 nm, which results in a Knudsen number between 0.34 and 6.8 × 10−3 for pore diameters between 0.2 and 10 µm. In figure 2.1 the flow regimes with the corresponding Knudsen numbers are schematically depicted.

0 Kn 10-3

10-2 ₁₀-1 ₁₀0 ₁₀1 _Kn _∞

Continuum Flow

Slip Flow Transition Flow Free molecule Flow Navier- Stokes Eqns

Slip Conditions No-slip

Euler

Eqns Burnet Eqn Boltzmann Eqn

Figure 2.1: Flow regime classification based on Knudsen number.

From this figure it can be found that for holographic membranes in the size range of 0.2 to 10 µm, the continuum flow theory with either slip or no-slip conditions will hold.[6, 7] _{For liquids the mean free path is shorter,}

therefore also in liquid filtration, the continuum flow model will apply and the use of Navier-Stokes equations therefore is legitimate. In later paragraphs, the validity of FEM simulations using the Navier-Stokes equations will be experimentally verified since entrance effects are expected to have an influence when considering membranes instead of single pores.

The basic equation in continuum fluid dynamics is the well-known Navier-Stokes equation, in its most basic form:[5]

ρdv

dt = −∇ · P + F (2.2)

with v the vectorial speed in [m s−1_{], ρ the density in [kg m}−3_{] and F the} combinatorial force vector of all forces working on the fluid in [N m−3_{]. P is} the generalized pressure in [Pa] and ∇ is the nabla-operator. Or, in a simpler, vector-form: Inertia z }| { ρ³ ∂v ∂t + v · ∇v ´ = P ressure z }| { −∇p + V iscosity z }| { µ∇2v +

Other body f orces z}|{

f (2.3)

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pres-sures below 10 kPa this is usually the case[5] _{- and that the gravitational forces}

can be neglected compared to the applied pressure difference. Finally, the as-sumptions of a steady state and no-slip conditions in a cylindrical channel, lead to following simplified form of the N-S equation:

Q = Z _2π 0 dθ Z _R 0 r dr vzr = πR 4 8µ ∆P lz (2.4)

also known as Poiseuille’s equation. Here Q is the volumetric flow in [m3_s−1_{] through a cylindrical channel with radius R [m] and length l}

z [m].

µ is the dynamic viscosity of the fluid in [Pa s] and ∆P the transmembrane

pressure in [Pa]. In membrane applications Q is multiplied by the membrane porosity to obtain the average volumetric flow through the membrane area. This is the simplest approximation, but it is inaccurate for small length scales and does not take into account entrance or slip effects nor the pore array. Since these effects do play an important role in the flow characterization of microsieves, Poiseuille’s equation is not accurate enough for this application. Aspect ratio (t/d), porosity (β), pore shape and Reynolds number (Re) should be considered when developing a model for membrane fluidics. Dagan[8]

sug-gests following expression for the pressure drop over an orifice with finite thickness and an aspect ratio of t/d:

∆P = µQ (d/2)3 h 16 π ³ t d ´ + 3 i (2.5) This equation applies for very low porosities β → 0, but since our goal is to fabricate membranes with a high porosity, it is not applicable in this case. Tio & Sadhal[9] on the other hand provide a model for the pressure drop of a thin array of pores:

∆P = µQ (d/2)3 h 1 − f (β) i (2.6) Q is the throughput per pore in [m3s−1]. P is the transmembrane pressure (TMP) in [Pa], the viscosity in [Pa s], R the pore radius in [m], β the porosity and f(β) a function of the porosity defined as:

f (β) = ∞ X i=0 aiβ( 2i+1 2 ) (2.7)

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of circular pores, a1 = 0.3389, a2 = 0.1031, a3 = 0.0558 and a4 = 0.0364 for

a hexagonal array of circular pores. Van Rijn combined equations 2.5 and 2.6 into:[10] Q = ∆P η R 3 " 1 16t πd + 1 # · 1 1 − f (β) ¸ (2.8)

From equations 2.8 and 2.7 it follows that a low aspect ratio and high porosity are required for a high throughput at a given pressure drop and selectivity. The porosity is defined as:

β = πab

Λ1Λ2sin α

(2.9) with a, b, Λ1 and Λ2 as in figure 2.2.

a b

Λ1

Λ₂

Figure 2.2: Definition of parameters to determine the porosity. The figure represents one unit element of a larger array.

All theories give a good indication for the flux through a membrane with a certain porosity. The theory of van Rijn however, describes best the flow through a microsieve, which will be elaborated by comparing the flow theories described above with finite element method simulations. FEM simulations have the advantage that modeling the third dimension (in depth of the mem-brane) is readily done, while incorporation of more advanced pore shapes in an analytical model is laborious.

2.3 Flow simulations

It is generally accepted that FEM simulations are a reliable way to obtain information on the behavior of fluids around and inside structures.[11] _{So as}

to come to an understanding of the parameters that have a significant influence on the throughput and pressure drop of a membrane, FEM simulations (using Comsol Multiphysics) will be utilized in this paragraph.

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2.3.1 Basics of FEM simulations

The Finite Element Method (FEM) approximates a partial differential equa-tion (PDE) problem with a discretizaequa-tion of that original problem. The FEM method starts from a mesh, which is the division of a chosen geometry into small units with a simple shape, the mesh elements, with the same dimen-sionality as the geometry itself.

Figure 2.3: FEM mesh generation.

For modeling a physical problem, three classes of parameters need to be known: material properties (density and viscosity of the fluids), initial condi-tions and boundary condicondi-tions. A set of partial differential equacondi-tions governing the physical phenomenon that is modeled is solved using these parameters. The initial conditions set a starting point for the calculations. Boundary con-ditions specify the values the solution needs to have on the boundaries of the domain, e.g. no-slip (flow velocity = 0) at the pore wall. Typically these constraints are imposed on dependent variables (velocity, pressure,...).

When modeling a flow through a microfiltration membrane, a momentum balance needs to be solved. The Navier-Stokes equation (equation 2.3) is the governing equation. Since normally a membrane will be operated at a constant flow, steady-state conditions apply. In Comsol Multiphysics, the Chemical Engineering module offers the opportunity to model a steady-state momentum balance using Navier-Stokes equations, which will be the standard model used in this study. Before solving the momentum balance, a schematic drawing of the problem, the geometry, needs to be made.

Due to the symmetric layout of the holographic membranes and the pos-sibility to define symmetry boundaries in Comsol, the flow behavior can be deduced from the simulation of a single membrane pore. An axi-symmetric 2D geometry is chosen to simulate the flux through a membrane pore. The simulated pore geometry consists of an inlet, the pore itself and an outlet as depicted in figure 2.4. The width of the inlet is determined by the porosity of the membrane.

The boundary conditions that apply to this geometry are defined as follows. In figure 2.4, A is the rotational symmetry axis, over which the geometry needs to be rotated over 360◦ _{to obtain a three-dimensional pore. As mentioned}

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A

Outlet, P = 0 Inlet, P = ∆P

Membrane

S_in S_out

Figure 2.4: Schematic representation of the geometry for flow simulations. An inlet and outlet are added to the pore to simulate entrance and outlet effects.

The inlet width is determined by the porosity of the membrane. Sin and Sout

are symmetry boundaries.

earlier, no-slip conditions apply at the pore walls. Sin and Sout are symmetry boundaries that ensure a continous connection between adjacent pores. The transmembrane pressure drop ∆P is applied between the inlet and the outlet. Only the two fluids that most likely will be filtered using holographic mem-branes will be simulated: air and water. The choice for those 2 fluids is rather self-explanatory: air resembles most gases that are filtered with microfiltra-tion and water is the major component of most biological fluids. These two applications are of interest for this research. In principle all membrane flow problems are three dimensional, however, due to the symmetric layout of the microsieves, the problem can be simplified to two dimensions, which is bene-ficial for the calculation speed.

To justify whether it is correct to used 2D axi-symmetric simulations in-stead of the time-consuming full 3D simulations, the velocity field of 2 identical pores is compared for both geometries. A pore with a diameter of 2 µm and a length of 2 µm (aspect ratio 1) is considered. An inlet and outlet are as-sumed to have a length of 2 µm and a diameter of 4 µm corresponding to a porosity of 25%. At the inlet an air flow due to a pressure of 1000 Pa is applied (at these low pressures, incompressible N-S apply), at the surface of the membrane, no-slip conditions apply. On the interface between the pores a symmetry condition is imposed. The resulting velocity fields are shown in figure 2.5.

From this figure it is clear that the results from both simulations are iden-tical, and therefore the axi-symmetric simulation is legitimate to replace the elaborate 3D simulations. In the subsequent simulations, therefore mainly axi-symmetric geometries will be simulated. Only for the comparison of pore

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0.0 0.5 1.0 1.5 2.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 V e l o c i t y f i e l d ( m / s )

Distance from center pore ( m)

2D

3D

Figure 2.5: Velocity fields at the outlet of a pore with a diameter of 2 µm, length of 2 µm and an inlet and outlet of respectively 2 µm length and 4 µm width. The solid line represents a 2D axi-symmetric geometry, the dashed line is the 3D geometry, no significant difference can be observed.

shapes, 3D simulations will be used, since for elliptical pore shapes the rota-tional symmetry argument no longer holds.

The last step before adopting FEM to compare membrane geometries, it needs to be investigated whether the simulation results correspond with results of analytical models. These models have been evaluated experimentally many times.[12] _{To find out whether the FEM simulations match the flow models}

described in section 2.2, the flux at a certain transmembrane pressure for a typical membrane is calculated and simulated.

Let us consider a membrane with a porosity of 40%, a pore diameter of 1

µm and a pore length of 5 µm. A porosity of 40% in practice means a

peri-odicity of 1.4 µm, for a square array of circular pores. In an axi-symmetric geometry, this corresponds to an inlet and outlet width of 0.7 µm. Using equations 2.4, 2.5, 2.8 and Comsol to calculate the throughput at pressures between 0 and 3 kPa, graph 2.6 was obtained. The simulation results approx-imate the theoretical outcome, and therefore give a good description of the flow behavior of microfiltration membranes.

For membranes with straight, circular pores in any array, analytical models provide a direct computational method for the determination of flow through the membrane. However, when elongated pores, tapered pores or other shapes need to be compared, FEM simulations are much simpler and versatile in use.

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0 1000 2000 3000 0.0 0.2 0.4 0.6 0.8 Poiseuille Dagan Van Rijn Comsol F l u x ( 1 0 -1 2 m 3 / s ) Pressure (Pa)

Figure 2.6: Comparison of flow theories.

2.3.2 Round vs slit-shaped pores

Several microfiltration applications are used for the separation of rather un-deformable nearly spherical particles, e.g. dust particles[13] _{or bacteria.}[14]

For these applications, it is possible (and feasible) to change the pore shape from circular to slit-shaped, without affecting the separation selectivity. Slit-shaped pores have some important advantages over circular pores. The flow resistance of a slit-shaped pore is significantly lower than that of a circular pore.[15] _{Moreover, slits cannot be completely blocked by a spherical particle,}

allowing fluid to keep flowing and making the membrane less susceptible to fouling. It also results in a smaller contact area between the particle and the membrane which facilitates cleaning of the membrane.

To investigate the actual decrease in flow resistance R upon stretching a circular pore into an elliptical pore, a three dimensional FEM simulation for a membrane with a porosity of 25% and a selectivity (pore diameter) of 2

µm is executed. The pressure drop over the membrane is chosen to be 1 kPa

(air), and the membrane thickness is 2 µm giving an aspect ratio of 1. The porosity is chosen constant to simplify the comparison of the flow resistance, since it is known that elliptical pores can be packed to a larger porosity than circular pores. The flow resistance is derived from the flow (Q, in m3_s−1_{) and} the pressure drop (∆P in Pa):

R = ∆P

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In figure 2.7, the flow results for elliptical pores with a small diameter of 2 µm and a large diameter ranging from 2 µm to 4 µm are shown.

2.0 2.5 3.0 3.5 4.0 0 2 4 6 8 10 F l o w r e si st a n ce ( a . u . ) Large diameter ( m)

Figure 2.7: Flow simulations for a 1 kPa flow through a membrane with a porosity of 25%, for an increasing large diameter of the elliptical pores. Starting point is a round pore with a diameter of 2 µm.

It is found that a slit-shaped pore with an a/b ratio of 2 (figure 2.2) has a flow resistance that is 3 times lower than circular pores with the same diameter, for a constant porosity. This is a significant improvement in flux, which is expected to become even more meaningful when pores with a larger aspect ratio (diameter/membrane thickness 1) are considered.

2.3.3 Aspect ratio

One of the parameters that is easily accessible and does not influence the selectivity of the membrane, is the aspect ratio of membrane pores. The aspect ratio of a pore is defined as the ratio between the pore diameter and the thickness of the membrane. Since the thickness of a membrane is easy to tune, as will be shown in the experimental part, the only thing to be determined is aspect ratio that results in the largest flux.

Finite element method simulations are used to show the trend that is ob-served when applying a certain pressure (1000 Pa in all simulations performed in this paragraph) over a pore with a certain geometry (aspect ratio). The standard 2D axi-symmetric pore geometry is used, the inlet and outlet are 2 µm long, and 2 µm in diameter. On the pore walls a no-slip condition is imposed, and a pressure of 1000 Pa is applied over the pore. Simulations are carried out for air and water. For a fixed pore diameter, the length of the pore

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0 1 2 3 4 5 0 5 10 15 A i r f l u x ( 1 0 -1 2 m 3 / s ) Aspect ratio (a) Air 0 1 2 3 4 5 0.0 0.1 0.2 0.3 W a t e r f l u x ( 1 0 -1 2 m 3 / s ) Aspect ratio (b) Water

Figure 2.8: Flux simulations for different membrane aspect ratios for a pore diameter of 1 µm. (a) Air flux, (b) Water flux. The air flux is significantly larger than the water flow, due to the lower viscosity.

is gradually increased, and the flux is calculated. In figure 2.8 two graphs showing the flux as a function of the aspect ratio for both air and water are displayed. A strongly decreasing trend is observed with increasing aspect ra-tio, which is the same for both materials. From equation 2.8 it can be deduced that the flux is inversely proportional to the aspect ratio. However, there is a more intuitive explanation for this behavior. A higher aspect ratio implies that a pore is longer and therefore that more pore wall is present. Since pore walls only add to the flow resistance of the pore (no-slip conditions apply), it is evident that the longer the pore is, the more flow resistance it has, and therefore a lower flux will be observed. This behavior is universal for all pore diameters in the 50 nm to 10 µm range.

It is therefore concluded that the lower the aspect ratio is, the larger will be the flux through the membrane. Ideally, a membrane would thus be infinitely thin, which is in practice not achievable. Infinitely thin membranes are also infinitely weak. Keeping in mind both the practical execution and optimization of the flux, a most ’ideal’ aspect ratio is chosen to be between 0.5 and 1. This means that the fluid only has contact with the membrane over a very short time, causing the fluid to leave the membrane very quickly.

2.3.4 Vena Contracta

Streamlines and/or flows are not able to change direction in a discrete step. Therefore, after an orifice or a membrane pore, the streamlines that converged when entering the pore will only gradually diverge after the pore, in a smooth

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way. This causes the flow diameter to contract to an effective diameter, smaller than the actual pore diameter. The place where this flow diameter is minimal is called the Vena Contracta (Torricelli 1643, figure 2.9). At very high troughput, flow instabilities can occur at the end of the straight channel. The net result is that the transmembrane pressure drop increases. It is well-known that this effect can be reduced using tapered or jet-shaped pores. In order to get a better insight in the parameters that play a role in the Vena Contracta effect and to find the optimum pore geometry to decrease this effect, FEM simulations are performed.

Membranes with the same selectivity (same pore diameter at the inlet side) and same pore length are simulated. For a transmembrane pressure drop of 1 kPa, the flow through membranes with different conical pores are simulated. Again, one pore is simulated and from this, the membrane characteristics are calculated.

An important aspect that needs to be taken into account is the fact that when tapered pores are used, the maximum achievable porosity decreases. This is due to the fact that at the outlet side of a membrane with tapered pores, the effective pore diameter is larger than at the inlet side. It is not possible to pack these larger pores as closely together as the small pores, which effectively causes the porosity of the inlet side to be lower. Therefore, for the different pore geometries, always a ’maximum achievable porosity’ needs to be taken into account. In figure 2.10, a schematic drawing of the geometry used in the FEM simulations is shown. The maximum porosity is calculated by using the minimum pore periodicity. In figure 2.10, this corresponds with the case that the pore wall thickness at the outlet side (W) is zero.

The inlet pore diameter (din) is kept constant while the outlet pore

di-Vena Contracta

Figure 2.9: Schematic representation of the Vena Contracta effect. The effective flow diameter is decreased after passing an orifice.

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Membrane Outlet Inlet Outlet Inlet Outlet W d_in d_out Pore

Figure 2.10: Geometry for simulations of tapered pores.

ameter (dout) is varied, for a constant pore length and applied pressure. In figure 2.11, the uncorrected throughput as a function of outlet pore diameter for different pore lengths for a selectivity of 2 µm is shown.

5 10 15 20 25 30 0 100 200 300 400 500 U n co r r e ct e d f l o w ( a . u . ) Outlet diameter ( m) 2 m 4 m 6 m 8 m 10 m

Figure 2.11: Flow versus outlet diameter of the pores. Larger outlet diameter of the pores results in a larger flux.

As was expected, the throughput of one pore increases with increasing opening angle of the pore. However, as indicated before, it is not correct to conclude from this that the wider the pore diameter at the outlet side, the higher the flux through the membrane. Therefore, in figure 2.12, the flow corrected for the maximum achievable porosity is depicted.

From this graph it is evident that a maximum in the flux through a mem-brane (for a fixed pressure drop) exists at a rather small outlet diameter. This optimal geometry is observed at an outlet pore diameter of 3 µm. In para-graph 3.4.3, a method to produce membranes with this pore geometry will be presented. Nevertheless, it appears that the actual influence of the Vena Contracta effect is rather small if corrections are made for maximum porosity.

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2 3 4 5 6 7 0 10 20 30 40 C o r r e ct e d f l o w ( a . u . ) Outlet diameter ( m) 2 m 4 m 6 m 8 m 10 m

Figure 2.12: Simulation results for flow through tapered pores, corrected for maximum achievable porosity for increasing outlet diameter. An optimum is observed at an outlet diameter of 3 µm.

Now, the design requirements for an efficient microfiltration membrane are understood. In the next chapter, a new technique using interference hologra-phy combined with a negative photoresist will be introduced, and an attempt will be made to fabricate membranes meeting these requirements in a practical way.

2.4 Conclusions

The control over pore geometry and dimensions is essential in the fabrication of high performance polymeric membranes. Finite element method simula-tions based on solving Navier-Stokes equasimula-tions on discrete elements provide an insight in the important parameters for membrane design. The main char-acteristics are pore size distribution, porosity, pore shape, aspect ratio and conicalness of the pores.

Since the largest pores determine the selectivity of the membrane and all smaller pores only contribute to the flow resistance of the microsieve, the pore size distribution should be very narrow. From the equations derived by van Rijn (equation 2.8), the requirement for a high porosity follows. A large open surface increases the efficiency of the membrane enormously. Slit-shaped pores provide a geometry that opens the opportunity for high density packing of the pores, combined with a better surface to volume ratio than their round counterparts. Slits also have the advantage that they exhibit the same selectivity, determined by their small diameter. In addition they have a

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lower flow resistance, due to the larger open surface. This pore shape is less susceptible to fouling and easier to clean.

Long pores also contribute to the flow resistance, caused by the no-slip conditions at the pore wall. Therefore it is beneficial to produce very short pores, preferably with an aspect ration between 0.5 and 1. The weakening of the membrane by decreasing its thickness remains an issue which will be addressed in the next chapter.

A last important factor that determines the throughput of a pore is the conicalness of the pore. Due to an effect called the Vena Contracta, the flux is limited by a decrease in effective flow diameter, the Vena Contracta. Jet-shaped pores are known to prevent this from happening. For a model mem-brane with a selectivity of 2 µm, the optimum outlet diameter is determined to be 3 µm in the ideal case.

2.5 References

[1] R. Baker. Membrane technology and applications. Wiley, 2 edition (2004).

[2] I. M. Yamazaki, R. Paterson and L. P. Geraldo. A new generation of track

etched membranes for microfiltration and ultrafiltration. part i. prepara-tion and characterisaprepara-tion. J. Membr. Sci., 118 (2), (1996) 239–245.

[3] M. Giron´es, I. Akbarsyah, W. Nijdam, C. van Rijn, H. Jansen, R.G.H.Lammertink and M. Wessling. Polymeric microsieves produced

by phase separation micromolding. J. Membr. Sci., 283, (2006) 411–424.

[4] M. Ulbricht. Advanced functional polymer membranes. Polymer, 47, (2006) 2217–2262.

[5] P. K. Kundu and I. Cohen. Fluid Mechanics. Academic press (2002).

[6] X. Yang, J. M. Yang, Y.-C. Tai and C.-M. Ho. Micro machined membrane

particle filters. Sensor Actuator, 73, (1999) 184–191.

[7] R. Perry and T. Green. Perry’s chemical engineers handbook. 7 edition (1999).

[8] Z. Dagan, S. Weinbaum and R. Pfeffer. An infinite-series solution for the

creeping motion through an orifice of finite length. J. Fluid Mech., 115,

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[9] K.-K. Tio and S. Sadhal. Boundary conditions for stokes flows near a

porous membrane. Appl. Sc. Res., 52, (1994) 1–20.

[10] C. van Rijn and M. Elwenspoek. Micro filtration membrane sieve with

silicon micro machining for industrial and biomedical applications. IEEE

Proc. MEMS 1995, page 83.

[11] X. Yang and Y.-C. Tai. Micromachined particle filter with low power

dissipation. J. Fluids. Eng., 123, (2001) 899–908.

[12] S. Kuiper, C. van Rijn, W. Nijdam and M. Elwenspoek. Development

and applications of very high flux microfiltration membranes. J. Membr.

Sci., 150, (1998) 1–8.

[13] Council directive 199/30/ec. Official journal of the European

Communi-ties (1999).

[14] D. Wild. The Immunoassay Handbook. Elsevier, 3 edition (2005).

[15] S. Kuiper, C. van Rijn, W. Nijdam, O. Raspe, H. van Wolferen, G. Kri-jnen and M. Elwenspoek. Filtration of lager beer with microsieves: flux,

permeate haze and in-line microscope observations. J. Membr. Sci., 196,

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Fabrication of holographic

membranes

Interference lithography is a well-known process for the fabrication of micro-structures. Combining this technique with a negative photoresist (SU8) which has an excellent mechanical and chemical resistance provides a method to pro-duce monodisperse membranes. The periodicity of the interference pattern induced by two crossing, parallel polarized beams is tunable by adjusting the angle between the beams. SU8 has a non-linear optical response which enables digital recording of an analogue interference pattern. Parameters like porosity, pore diameter, aspect ratio, pore shape and conicalness are easily addressed. The glassy state of the photoresist at room temperature permits the use of several consecutive exposure steps. Exposing a photosensitive layer twice to a line pattern, rotated 90 degrees with respect to each other, generates a grid-like structure in which the pores are formed. Using holography, a wide variety of pore shapes (round or slit) and pore sizes (100 nm - 5 µm) in different arrays can be fabricated. To reduce the Vena Contracta effect, jet-shaped pores are a necessity. Addition of a UV absorber to induce an intensity gradient over the photosensitive material, results in a pore diameter gradient over the thickness of the membrane, and thus tapered pores are obtained. The membranes pro-duced are also used for the experimental verification of the theoretical predic-tions in chapter 2. Simulated fluxes correspond well with the measured fluxes, confirming that the assumption that simulating one pore suffices to predict the behavior of an entire membrane, is correct.

This chapter has been partially published as A.M. Prenen, J.C.A. van der Werf, C.W.M. Bastiaansen and D.J. Broer, Adv. Mater. 21, 2009 pp 1751-1755.

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3.1 Introduction

The removal of particles from liquids and gasses using membranes is a widely used separation process. A large variety of membranes is commercially avai-lable[1–3] _{and the properties of these membranes are extensively tuned to the}

desired size-selectivity, throughput and pressure drop.[4] _{Often, these}

mem-branes are produced via solvent induced phase separation processes which invariably results in membranes with a rather large polydispersity in pore size and a tortuosity which is far from ideal.[5]

High performance separation membranes should have a narrow pore size distribution, a high porosity, a low tortuosity and a good selectivity and per-meability.[4, 5] _{Recently, the production and properties of such monodisperse}

membranes have attracted considerable attention.[6–8] _{Commercially available}

monodisperse microsieves are usually inorganic and possess an excellent chem-ical and thermal resistance. These membranes are produced using lithographic techniques similar to those used in the semiconductor industry. The produc-tion of these membranes is rather laborious and involves a sequence of process-ing steps such as coatprocess-ing, illumination, developprocess-ing, etchprocess-ing and strippprocess-ing.[6–9]

Not surprisingly, the cost of these membranes is very high which limits their usefulness and this despite their excellent performance.

Several rather elegant routes were proposed in the past to produce poly-meric and monodisperse microsieves via, for instance, phase separation mi-cromolding[10] _{and track etching.}[11] _{The prime objective is often to combine}

the ease of processing of polymers with the high performance of monodis-perse porous media. Nevertheless, the above described polymeric membranes also have limitations with respect to maximum porosity, material properties (mechanical strength), or freedom of design in pore geometry or in pore size.[5]

In this chapter, a new method for the production of monodisperse mem-branes with a wide range of well-controlled pore sizes, pore geometries and pore packings is described. The main distinction with existing polymeric mi-crosieves is the processing route (interference lithography) and materials used (densely crosslinked thermosets). Interference holography[12] _{is used to obtain}

a straightforward process with a few processing steps. Interference lithogra-phy is a well-known process for creating micro- and nanostructures for various applications, including nano-pillars,[13] _{nanostructured substrates}[14] _{and 3D}

photonic crystals.[15] Densely crosslinked thermosets are used to enhance the chemical resistance and high temperature performance of the membranes.

Polymeric microfilters by interference holography : development and applications

Polymeric microfilters by interference holography :

development and applications

Polymeric microfilters by

interference holography:

Development and applications

Contents

Polymeric microfilters by interference holography:

Development and applications

Summary

General introduction

1.1

Miniaturization in medical diagnostics

1.2

Microfiltration

1.3

Holography

1.4

Scope of the thesis

1.5

References

Flow through holographic

membranes

2.1

Introduction

2.2

Flow theory

2.3

Flow simulations

A

Membrane

2.4

Conclusions

2.5

References

Fabrication of holographic

membranes

3.1

Introduction