3.1 Introduction
The recent rapid development of modern industry has created serious environmental pollution issues.The large amount of industrial exhaust emissions have drastically increased the suspended fine particulate matter (such as PM2.5) in the air,which is harmful to the environment,climate,equipment life,product quality and public health [1-2].Therefore,the effective means are required to prevent the harmful particles from diseases.
Fibrous filters are relatively inexpensive,simple and particularly efficient means to capture the suspended particles in the air flow.Filtration performance is most broadly reflected by the air pressure drop and filtration efficiency,which are mainly determined by the filter's internal microstructure and gas-solid interaction.The primary trapping mechanisms for particles include the Brownian diffusion,interception and inertial impaction [3-4],as well as other mechanisms due to external forces such as electrostatic force and gravity.In order to reduce the design time and product cost of fibrous media,Maze et al.noted that it was critical to explore an effective way to predict the performance of fibrous media [5].During the past half-century,many pioneering studies on the filtration characteristics of single fiber or arranged fibers have been reported.Researchers have been attempting to develop mathematical formulations to predict the performance of fibrous filters and build the foundation of current filtration theories,which were originally developed assuming a single fiber by Kuwabara [6] and Happel [7],and later extended to the effects of neighboring fibers [8-10].These theories were initially developed to study the flow field around perfectly clean fibers by a numerical solution.
Particle deposition can lead to the formation of complicated dendrites on the fiber surface,which alters the flow field inside a filter.The first numerical study of simulating the effects of particle deposition on the pressure drop and collection efficiency of the filter was conducted by Payatakes and Chi [11].These authors simulated the growth of chain-like dendrites on a fiber in a Kuwabara cell.Later,Kanaoka et al.[12-13] studied the growth mode of particle dendrites in the two dimensional charged single fiber using a Monte Carlo method and a Lattice-Boltzmann (LB) method,respectively.Chen et al.[14] and Cheung et al.[15] studied the collection efficiency and particle deposition in the electret filter with rectangular split-type fibers.Maschio and De Arruda compared the simulation data with experimental X-ray computerized tomography digital images.They concluded that larger particles can form bridges and improve the collection efficiency,and smaller particles tend to result in a more pronounced pressure drop [16].Przekop et al.[17] and Wang et al.[18] numerically analysed the effects of particle deposition morphology of a single fiber on its filtration characteristics using the LB method.Additionally,Wang et al.simulated the filtration mechanisms of the multi-fiber model using the LB method and analysed the dynamic impact of structural [19].Li and Mashall used a discrete element method (DEM) to simulate the micro-particle deposition on the cylindrical fiber [20].Qian et al.used a CFD-DEM method to simulate the gas-solid flow characteristics in fibrous media and investigated how porosity,face velocity,and particle size affected filtration performance [21-22].Lin et al.proposed a LB-CA model to investigate the effect of pore size on particle-fiber collisions in a laminar free-stream flow over a semi-infinite array of clean elliptical fibers [23].Tamadate et al.simulated the random motion and deposition of highly charged nanoparticles on a single fiber by employing the Langevin Dynamics (LD) method [24].Lambert et al.proposed a lubrication model for a coupled volume penalization method and discrete element method solver that estimated the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow [25].Kerimov et al.developed a numerical framework to simulate the trapping of fine particles in porous granular media with the prescribed host particle size,shape and distribution [26].Yang and Hogan found that collisions in shear were complicated because particle inertia influenced the differential motion in the gaseous media [27].
Previous studies provided theoretical and practical foundation for developing filtration theories and improving the filtration performance of filters.Théron et al.evaluated the influence of pleat geometrical parameters on the pressure drop and air velocity field at the vicinity of pleated fibrous filters [28].Feng et al.found that the electrostatic effect could significantly increase filtration efficiency of a fibrous filter [29].Joe et al.found that an external electric field that applied on the filter could improve its collection efficiency [30].Rodrigues et al.found that the penetration decreased substantially with the increase of the particle charge level [31].Karjalainen et al.found that the filtration efficiencies were strongly dependent on the particle size and the filtration efficiency of an electrostatic precipitator (ESP) increased as a function of the particle size [32].Gac et al.used a numerical model to analyse the formation and dynamics of solid deposits during consecutive solid-liquid or liquid-solid aerosol filtration [33].Huang et al.investigated the growing process of particle dendrites on elliptical fibers and found that particles will mostly deposit on the windward of the elliptical fibers [34].Rastegar et al.found that the fiber capture efficiency increased in the presence of Brownian excitation,which was far more significant for smaller particles [35].Chen et al.demonstrated that the penetration efficiency curves for the test fibrous filters rendered a U-shaped curve for particle sizes from 70 nm to 500 nm,and the most penetrating particulate size decreased over time [36].Maddineni et al.demonstrated that the filtration efficiency of the oil-treated filter media would increase owing to the mechanism that particle rebound could be suppressed by oil treatment [37].Some researchers invented high-performance air filters.Liu et al.developed a transparent air filter with a high filtration efficiency for PM2.5 [38].This filter has a specific microstructure to achieve a transparent texture,high air flow and a high filtration efficiency.Kim et al.developed a novel electrostatic precipitator-type small air purifier with a carbon brush ionizer and an activated carbon fiber filter [39].Nemoto et al.proposed a simple freeze-drying procedure to produce nanocellulose and high-performance air filters.Although the previous theoretic achievements have demonstrated good applications to experimental manufacturing,further studies pertaining to the fibrous filtration are still relevant [40].More realistic computing models,more optimized microstructures,and a better compromise between air flow and filtration efficiency remain to be explored.
The previous studies have showed the tendency of the pressure drop and filtration efficiency to change with different fibrous structures,solid volume fractions,and other external factors such as face velocity and particle size.Furthermore,some studies have investigated and developed the particle rebound mechanism theories.Dahneke suggested that only when a colliding particle did not have sufficient energy to escape the potential well,will it be trapped by a solid surface [41].Gallily and La Mer found that micrometer-sized particles often rebounded when collided with a smooth surface with an approach velocity on the order of 10 m/s [42].Dahneke reported that the rebound properties depended on several parameters including the incident velocity,particle size,particle and surface geometry and orientation,particle and surface materials,surface contamination,temperature,and so on [43].Lehmann et al.simulated the growth by particle deposition for different values of the restitution coefficients [44].Kasper et al.introduced a new particle rebound parameter,which was associated with Stokes number (Stk),interception parameter (R=dp/df),and conduct good measurements of the morphology and packing density of particle deposition [45].This work simulated particle movements with considering particle rebound during the filtration stage.It distinctly showed the effects of the flow field and particle size on rebound,which led to the redistribution of particle deposition,and obtained new results of filtration efficiency.
Particle trajectories and filtration efficiency of various fibrous structures were investigated in our previous study [46].This chapter investigates the dynamic performance of particle rebound and statistically analyzes the deposition/accumulation of particles on a fiber surface.A 2D model is developed,which can successfully simulate and demonstrate the efficiency of fiber filtration to a certain extent reported by previous studies [47-48].We use the CFD method to calculate the inertial flow field around a row of fibers.Then,we utilize an adherence criterion for the particle rebound,and simulate the particle trajectory and deposition around one of the fibers using a self-developed solver in Fortran code.Effects of the face velocity and particle diameter on the particle rebound and accumulation are investigated.The trajectories and accumulation of particles on the fiber surface are visually presented.Finally,the filtration efficiency of one single fiber is compared with published results of existing particle trapping mechanisms.