Introduction
Background
As air pollution is one of the health hazards, engineers have designed varied air cleaning equipment, while governments have formulated comprehensive legislation to regulate the emissions of particles to improve occupational health in industries. In industrial settings, the application of fibrous filters has proved to be an effective method of cleaning the air. Nevertheless, fibrous filters do not effectively clean small particles with sizes ranging from 0.1μ to 1μ in different rates of airflow.
Therefore, depending on their efficiency, fibrous filters either have low efficiency or high efficiency levels. Course fibrous filters with diameters that range from 100μm to 1000μm have low efficiency, while fine fibrous filters with diameters less than 100μm have high efficiency (Bredin, Larcher & Mullins 2011). The use of filter fibers is advantagous because it is not only cheap but also exhibits a high level of efficiency in eliminating particles from varied forms of airflow.
The process of air cleaning has significant benefits to humans because it eliminates fine particles in the air to hinder them from penetrating lungs and blocking critical functioning of alveoli. Numerous studies have demonstrated that prolonged exposure to particles in air injure the respiratory system and contribute to the occurrence of cardiovascular disorders (Polichetti et al. 2009; Daz & Dominguez 2009; Binnig et al. 2011).
Legislation plays a central role in the prevention of air pollution because it stipulates the thresholds of occupational exposure. For example, within eight hours, diesel soot has a threshold of 0.1 mg/m3, whereas engine lubricant has a threshold of 5 mg/m3. However, diesel has unique properties because they comprise aerosols with a different mechanism of collection from solid particles. (Jaganathan, Tafreshi & Pourdeyhimi 2009). Comparatively, solid particles exhibit a higher filtration efficiency because they accumulate on the surface and form a secondary layer, while liquid particles have a lower filtration efficiency because aerosols amalgamate into huge droplets that flow easily through filters.
The analysis of the filtration process reveals that the existence of numerous factors or forces complicates it. Physical-chemical characteristics of the fiber, filter structure, sizes of particles, the nature of particle distribution, the flow rate of air, and physical conditions of airflow comprise factors that affect the process of filtration (Shahad 1989). In elucidating the mechanism of filtration and designing assorted types of filters, scientists have employed mathematical models (Jakab & Omastova 2005). As a structure, filter fibers constitute capillary tubes and pores, which discriminate the flow of particles according to their sizes.
However, particle deposition is a considerable problem in the filtration because it leads to the clogging of filters (Happel 1959; Kuwabara 1959). The problem of clogging requires constant regeneration of filters through the removal of solid particles that accumulate in filter membranes (Agranovski & Shapiro 2001). The analysis of literature reveals that researchers have elucidated the mechanism of clogging and designed effective technologies employed in the regeneration of clogged filters (Theodore & Buonicore 1988; Flagan & Seinfeld 1988; Cheremisinoff 1993). Thus, the literature review forms the basis of improving the use and efficiency of fibrous filters in air cleaning.
Research Objectives
The first objective of the report is to explain how the development of valid and empirical filter test methods offers more insights into the mechanisms of filtration processes, which are integral in improving the design and optimization approaches of fibrous fibers. The second objective is to investigate the effects of solid contaminants on the efficiency of fibrous filters in an outdoor environment. The third objective is to incorporate scientific knowledge in the design and manufacture of effective and efficient equipment employed in air cleaning.
Literature Review
Filtration
Filtration has proved to be an effective strategy for cleaning the air by removing solid particles and aerosols. Occupational health requires industries and hospitals to install air cleaning equipment and guarantee the safety of air the ambient environment (Hinds 1999). Given that cleaning equipment uses filters, they experience the problem of clogged pores, which diminish efficiency, decrease longevity, and increase operating costs of filters (Brown 1993). In this view, the frequency of regeneration and replacement of filters make companies incur extra costs in cleaning the air.
Type of Filters
The nature of membranes categorizes filters into surface filters and depth filters. Surface filters function by trapping particles on their surfaces to form a second layer that acts as a superfluous filter. In contrast, depth filters trap particles across the column matrix of the entire filter. The structure of depth filters comprises of fine isometric granules filled in a column (Tien 1989). These granules have appropriate attributes because they are inert, resistant to chemicals, and tolerant to high temperatures (Contal et al. 2004). Surface filters have smaller pores and lower porosity index when compared to granular filters (Hinds 1999; Zhao & Povitsky 2009). Nevertheless, surface filters are vulnerable to clogging and difficult to clean because their small pores resist the flow of air.
In addition to surface and depth filters, there are fibrous filters, which are distinctive because they comprise an assortment of fine fibers created from cellulose, plastics, glass, and stainless steel. The use of asbestos, a heat resistant material, in the manufacture of fibrous filters was not sustainable because it has harmful effects on health (Li & Marshall 2007). In the modern era, fibrous fibers made from ceramics and stainless steel have substituted the use of asbestos because they are not only safe but also resistant to heat and diverse chemicals (Peukert 1998).
Additionally, fibrous filters made from stainless steel and ceramics provide a higher level of filtration efficiency that meets required standards. Thickness and lengths are attributes that define varied sizes of fibrous fibers that measure less than the 100μm diameter (Wang, Kim & Pui 2008). Manufacturers normally strengthen fibrous filters by knitting, felting, or interlacing with more dense fibers.
The Basic Theory Elucidating Aerosol Deposition
The mechanism of filtration is mainly dependent on the nature of particles in the air targeted by filtration. Theories of filtration hold that different airflow systems consist of gas, liquid, and solid phases that form aerosols system. The process of the formation of aerosol systems involves a homogenous mixture of solids, liquids, and suspension of particles in streams of airflow. The reaction of gases due to the condensation of aerosols causes the formation of supersaturated vapors and production of non-volatile soot (Myojo, Kanaoka & Emi 1984).
Comparatively, dispersion aerosols are coarser than condensation aerosols because of the different processes involved in their formation. Packing density, diameter, thickness, temperature, pressure, moisture, fiber length, condensing vapor, and electrostatics are factors that determine the deposition of particles on fibers.
Theory of Filtration
The Navier-Stokes equations elucidate the mechanism of filtration using the principles of fluid motion. Based on the principles of the second law of Newton relating to the forces of moving bodies, viscous drag of fluids, and the prevailing pressure, researchers formulated these equations. According to the second law of Newton, the rate of fluid’s flow has direct relationships with the forces that act on particles at a given pressure.
However, equations that elucidate the filtration process are complex owing to partial and non-linear trends of airflow. The effective application of these equations requires consideration of assumptions of aerosols mechanics, frictional forces, adhesive forces, and external forces that act on particles. Moreover, consideration of the compressible fluids is critical in the application of the Navier-Stokes equation.
Reynolds Number
Reynolds number is the ratio between different forces, viscous and inertial forces, which operate between particles in the air. A fluid that meets Newton laws has a momentum that behaves as an incompressible solution. For instance, the Reynolds number of gases that flow through the filter has a positive relationship with the flow velocity, the diameter of the fiber, and gas density, but has a negative relationship with the dynamic viscosity. The analysis of Reynolds numbers shows that values less than one display the laminar flow, while values greater than 2300 indicate the turbulent flow. The transition from the laminar flow to the turbulent flow is a gradual process that is dependent on the viscosity of fluids.
Uniform Particle Motion in a Fluid
Due to the complexity of non-linear flow rates, Navier-Stokes equations require further simplification of expressions. The elimination of extremely high values omit the effects of inertia and transform Navier-Stoke equations to linear expressions that resolvable. (Brown 1993). Therefore Stokes’ Law indicates that drag force is directly proportional to the velocity of flow, the diameter of the particle, and the dynamic viscosity of the fluid. The addition of the correction factor explains the frictional force that particles experience. This factor is common in small oil droplets and solids with radii less than 50nm.
Single Fiber Efficiency Theory
The use of a single fiber approach in the assessment of the filtration efficiency is crucial due to the complex process of fibrous filtration (Kasper et al. 2009). The elucidation of the mechanism of particle deposition effectively predicts penetration and filtration efficiencies of fibrous filters. Hence, single fiber efficiency is directly proportional to the packing density, the filter penetration, and the filter thickness but inversely proportional to the diameter of the filter.
However, the use of single fiber efficiency needs an independent flow of air, laminar flow of aerosols, and stable collection of particles for effective elimination (Hinds 1999). In the filtration mechanism, the efficiency measures the number of particles that the filter collects, whereas the degree of penetration scales the amount of particles that go into the filter. Comprehensive consideration of single fiber efficiency needs the assessment of inertial impaction, Brownian diffusion, and interceptive forces.
Cell Model and Filtration Mechanism
Cell model provides a practical method of determining the mechanism of filtration. Kuwabara (1959) and Happel (1959) explain that the cell model simplifies the mechanism of filtration by providing a real geometry, a similar flow field, and a feasible prediction of the airflow rate and particle collection. Given that the cell model has proved to the best approach employed in the explication of fluid flow, researchers have continued to apply it in the filtration realm (Davies 1973; Lee & Liu 1982; Brown 1984; Brown 1993). By applying the cell model, Kuwabara (1959) created the velocity profile of fiber and described the two-dimensional flow of viscous fluids.
Brownian Diffusion
The coefficient of diffusion, derived from the Brownian diffusion, provides a precise method of quantifying the momentum and explaining why particles stray from their streamlines in motion. In an elaborate equation, Einstein demonstrated that the mean displacement of a particle has a positive relationship with the slip correction factor (Cc = 1 + Knp (1.257 + 0.4e-1.1/Knp), the Boltzmann constant (σ=1.3810-23 (m2kgs-2K-1), and the ambient temperature but a negative relationship with the viscosity and the diameter of the particle.
The Eulerian approach further simplifies the mean displacement of a particle by incorporating the convective-diffusive equation, which defines the concentration of the particles. As the equation does not apply in an experiment, the incorporation of a new coefficient is essential. Lee and Liu (1982) evaluated the total efficiency by disregarding the effects of inertia in particles that penetrate easily into filters. The addition of the diffusion and the interception formulas to variable coefficients gives a new practical equation.
Therefore, Lee and Liu (1982) suggested the use of Etot (EtotPeR) as a novel parameter in instances where the interception value is greater than three and the total efficiency is lower than 0.3. Overall, equations show that the numerical determination of the Navier-Stokes equations using the finite volume technique is the primary step (Patankar 1980) and the Eulerian approach is the secondary step.
Inertial Impaction
Since particles possess inertial force, they tend to resist filtration when trapped in filters. In essence, the presence of inertia makes particles experience inertial impaction, which is a force that causes them to deviate from their flow streams. Depending on Stokes numbers, inertial impaction can be of a high, medium, or low level. Therefore, by using Stokes numbers, one can evaluate the single-fiber efficiency of particles and determine the inertial impaction.
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