Hutten describes four major influences that affect the separation by depth filtration mechanism.[3]
Particles carried by the fluid transported through the filter medium generally follow the streamlines of the fluid. However, if a particle gets into contact with the material of the filter medium, it usually gets deposited due to physical attractive forces. Figure 1.12 displays the major influences leading to particle deposition that will be introduced in the following. The inertial impaction (a) refers to particles that exhibit an inertia too high to be carried around an intersecting fiber. Therefore, the particle collides with the fiber and is deposited. The second way of particle deposition is given by interception (b). A particle does not particularly collide with a fiber, but approaches the fiber to the point where attractive forces capture the particle.[3,99]
Figure 1.12: Schematic representation of influences contributing to particle deposition by depth filtration mechanism. (Figure is based on ref[3])
Deposition by diffusion (c) is mainly based on the Brownian diffusion of small particles that allows for motion away from the streamlines of the fluid resulting in contact with the fibrous filter material. The last influence is given by electrostatic attractions (d) of the filter material and the particles. However, depending on the particle sizes, different influences in depth filtration dominate the separation process. Large particles with diameters of around 300 nm and higher are usually separated by interception, whereas particles with diameters of way below 100 nm are captured by diffusion. In most cases, filter media based on depth filtration exhibit the largest penetration of particles in the
Flow streamlines
Fiber Diffusion Inertial impaction
Interception Electrostatic attraction a)
b)
c)
d)
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intermediate region of particle diameters between the two influences. Figure 1.13 displays a schematic correlation between the particle diameter and the penetration of a filter medium. The particle size corresponding to the most penetration is referred to as the “most penetration particle size” (MPPS).[3]
Figure 1.13: Correlation between the diameter of filtered particles and the penetration of a filter medium. Depending on the particle size, either interception or diffusion processes dominate the particle deposition. The combination of these influences yields the resulting penetration. The location of the most penetration particle size (MPPS) depends on the linear velocity of the filtration process.
(Figure is based on ref[3])
The particle size of the MPPS depends on many factors such as the flow velocity of the fluid during filtration or the material the particles are composed of. Apart from the particle deposition, additional effects like reentrainment have to be considered, whereas this process corresponds to the detachment of particles that where already captured by the filter medium due to mechanical forces of the fluid medium on the particle.[3]
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Among others, filter media are usually characterized by two main properties. The percentage of particles removed from the fluid is referred to as filtration efficiency (f) and corresponds to the quality of separation that can be achieved by the selected filter medium. Values are typically given for defined particle diameters and are generally calculated according to equation 1.1. By investigation of the filtration efficiency of particles with different diameters, typically particle size dependent filtration efficiency curves are displayed.
f = (1 − N
N0) ∙ 100% (1.1)
N corresponds to the number of particles that penetrated the filter medium and N0 refers to the number of all particles that were applied to the filter.
The second property corresponds to the resistance of the filter to the fluid during the filtration process.
The flow of the fluid through the filter medium requires some kind of driving force. Therefore, normally a pressure difference is applied to the filter to start the filtration process, which can be induced either by gravity, vacuum or utilization of a pump. In theory, the flow through a filter is sometimes compared with the flow through individual capillaries representing the individual pores. However, in many filter media, such as nonwovens, the so-called pores are rather void spaces inside the porous medium without a regular cross-section.[3,95]
One of the simplest approaches to describe the flow of a fluid through a porous medium is based on work by Darcy, who performed series of experiments of water flowing vertically through an iron pipe filled with sand representing a porous structure. The relationship between flow velocity and a permeability constant is given by equation 1.2.[95]
u = −k
ì ∙dp
dz= −k
ì ∙ ∆p (1.2)
u represents the linear flow velocity of the fluid measured in m/s. k is the permeability constant and μ is the viscosity of the fluid. dp refers to changes in pressure over a porous medium with thickness dz, which can also be written as a pressure difference Δp before and after the filter. For nonwoven media, most systems can be described by Darcy’s law. However, the exact form of the permeability constant is not clear and has to be investigated for each material separately. One of the most important information obtained by equation 1.2 is that the linear flow velocity u is directly proportional to the difference in pressure before and after the filter medium. Therefore, comparison between two different filter media is often difficult due to differences in setup and testing conditions. The so-called quality factor was established to allow for the evaluation and comparison of different filtration systems. The quality factor QF is given by equation 1.3. Here, N is the number of particles that
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penetrated the filter medium, N0 refers to the number of all particles that were applied to the filter and Δp is the differential pressure before and after the filter.
QF = −ln(𝑁 𝑁⁄ 0)
∆𝑝 (1.3)
By taking into account the filtration efficiency of a filter and the corresponding differential pressure at defined operating conditions, different filters can be compared.
Applications of filters
Filtration systems are applied in a variety of different technologies of the everyday life. In solid gas separation, filters can be found for example in living and working space purification systems, industrial dust removal or respirators. In liquid filtration, one of the most prominent examples for the application of filtration systems is the treatment of ground and surface water to obtain safe drinking water.[101] In addition, one of the most widespread technologies containing many different filters are automobiles involving the filtration of the air intake, fuel filtration and cabin air filtration.[3]
The choice of a suitable filter for a specific application mainly depends on the particles that have to be removed from the fluid. Figure 1.14 provides an overview of contaminations that are often removed by liquid filtration applications. These applications are generally classified into four different filtration processes depending on the size of particles that need to be removed from the fluid. These are microfiltration, ultrafiltration, nanofiltration and reverse osmosis.[3] In general, the removal of small particles is associated with a higher differential pressure during operation of the filter, whereas less pressure is needed in filtration systems separating larger particles.
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Figure 1.14: Schematic overview of contaminations with different particle sizes removed by reverse osmosis, nanofiltration, ultrafiltration and microfiltration. (Figure is based on ref[3])
Based on the topics discussed in this chapter, the following chapters will present the work performed in the course of this thesis. In contrast to conventional top-down approaches, the self-assembly of small molecules provides a bottom-up approach for the preparation of supramolecular nanofibers. The influence of processing parameters on the morphology of the fibers was investigated under defined self-assembly conditions. In addition, prepared nanofibers were employed into support structures to obtain composites that were suitable for air- and liquid filtration applications.
Reverse osmosis