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Effect of particle electrostatic charge on aerosol filtration by a fibrous filter
Effect of particle electrostatic charge on aerosol filtration by a fibrous filter M.V. Rodrigues, M.A.S. Barrozo, J.A.S. Gonc¸alves, J.R. Coury PII: DOI: Reference:
S0032-5910(17)30250-4 doi:10.1016/j.powtec.2017.03.033 PTEC 12438
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Powder Technology
Received date: Revised date: Accepted date:
16 November 2016 7 March 2017 12 March 2017
Please cite this article as: M.V. Rodrigues, M.A.S. Barrozo, J.A.S. Gon¸calves, J.R. Coury, Effect of particle electrostatic charge on aerosol filtration by a fibrous filter, Powder Technology (2017), doi:10.1016/j.powtec.2017.03.033
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ACCEPTED MANUSCRIPT Effect of particle electrostatic charge on aerosol filtration by a fibrous filter
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M.V. Rodrigues1, M.A.S. Barrozo2* J.A.S. Gonçalves3 and J.R. Coury3
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1 Institute of Science and Technology -Federal University of Alfenas-Campus of Poços de Caldas, MG, Brazil 2 Faculty of Chemical Engineering, Federal University of Uberlandia, Uberlandia, MG, Brazil
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3 Department of Chemical Engineering, Federal University of São Carlos, Sao Carlos, SP, Brazil
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Abstract
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This study aimed to investigate the influence of the particle charge level on collection efficiency
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and pressure drop during aerosol filtration in a fiber filter. An Electrostatic Charge Classifier (ECC)
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measured the charge level of aerosol as a function of the particle diameter. The filter was made of polypropylene; its mass per area was 600 g/m2, its diameter was 0.047 m, and its thickness was 0.0026 m. Phosphate rock was the test dust (density: 3030 kg/m3; average Stokes diameter: 3.25 m). The aerosol was dispersed in air by a TSI Venturi type generator, model SSPD 3433. The particle charging was achieved by a corona charger. A relationship between the charge of particles and their diameter was identified. From the filtration results, it was analyzed the effect of the electrostatic charges in the particles on the performance of the filter (collection efficiency and pressure drop). The correlations from the literature did not adequately predict the experimental data behaviour. Thus, we proposed a new expression for the electrophoretic collection mechanism, which was consistent with the experimental results found in this research, as well as of other studies in the literature. Keywords: filtration, solid-gas separation, fibrous filters.
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1. Introduction
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Scientific and technological efforts have been dedicating the development of techniques to remove
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particles from the air, especially those smaller than 2.5 m, which can cause serious health problems. Researches on particulate control technologies have tried to find new, improved, cheaper and energy-
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saving structural materials and methods to collect small particles [1].
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*Corresponding author at: FEQ/UFU, Av. João Naves de Avila 2121, 38408-100, Uberlândia-MG, Brazil.
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Tel.: +55 34 996776099; +55 34 3230 9400. E-mail address: [email protected] (M.A.S. Barrozo)
Nanometer, submicron and micron-sized particles could be removed from gas stream by a group of
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devices, includes fibrous [2, 3, 4]; granular [5, 6] and ceramic filters [7], electrostatic precipitators [8] and
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wet scrubbers [9].
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The basic problem of the filtration theory is to express both pressure drop (P) and filter efficiency (E) as a function of the relevant variables and to describe the properties of the particles dispersion, medium, and filters [10]. Particularly, the electrostatic charge in the particles significantly contributes to the filter performance by affecting the collection efficiency and the pressure drop [11]. However, this phenomenon has not been comprehensively studied and ought to be investigated [12]. Electrical forces from a charged particle can far exceed gravitational forces and, in some circumstances, can even exceed aerodynamic forces in a moving air stream. As controlled handling of particles is exceptionally difficult to achieve [13], electrostatic particle charging is an important phenomenon related to powder handling [14]. Duarte Filho et al. [5] studied the filtration of electrified solid particles in a fixed bed of sand. The particles were electrified by impact. They performed the filtration tests with three bed heights (0.01, 0.02, and 0.04 m), three gas superficial velocities (0.07, 0.11, and 0.15 m/s), and four levels of particle 2
ACCEPTED MANUSCRIPT charging. The authors obtained a nonlinear response of both particle penetration and pressure drop with the particle charge.
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Mori et al. [15] studied the effects of a positive corona precharger on the performance of fabric
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filters in the air with controlled humidity. When the corona precharger was switched on, the charge of the particles did not vary according to the air relative humidity. On the other hand, when the corona
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precharger was switched off, the particle charge decreased with the increase in the relative humidity.
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He et al. [16] used a differential mobility analyzer (DMA) to measure the filter penetration. The authors observed that the presence of these multiply charged particles critically affects filter penetration
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measurements. The fraction of multiply charged particles upstream and downstream of the filter depends on the aerosol size distribution entering the DMA and the filter penetration characteristics.
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The effects of electrostatic fiber charge were quantified by by Sanchez et al. [17], comparing filter
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efficiencies for charged and uncharged filter media. The effects of particle charge were also quantified by
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using NaCl test aerosols in two electrostatic charge configurations: aerosol in the Boltzmann equilibrium charge distribution and uncharged aerosol, where all charged particles were removed in an electrostatic precipitator. A substantial increase in overall collection efficiency was observed when electrostatically charged filter media were used.
The problem of aerosol flow with charged particles in a dense array of spheres was studied by Zaripov et al. [18]. Velocity field of the carrier phase flow was found by solving the Navier–Stokes equations using CFD code ANSYS Fluent. Particle trajectories were calculated taking into account aerodynamic drag, gravity force and electrostatic force for single charge. The deposition efficiency of charged particles was quantified. The present paper aimed to investigate the influence of the particle charge level on the collection efficiency and the pressure drop during the first stages of filtration. We evaluated electrostatic forces,
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ACCEPTED MANUSCRIPT particularly image-dipole forces, between charged particles and uncharged fibers. Then, we proposed a
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model for total collection efficiency considering the dipole-image mechanism action.
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2. Filtration in fibrous filter and electrostatics effects
Filter performance is generally described in terms of total efficiency (E) and pressure drop (P).
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The total collection efficiency is the ratio of the number of particles collected by the filter to the number
n 2 - n1 n2
(1)
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E=
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of particles going to the medium:
Where n2 is the upstream concentration, and n1 is the downstream concentration of the filter.
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Penetration (P), defined by P 1 E , also characterizes the filter performance. Extensive studies
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on deep-bed filtration in granular and fabric filters have pointed out total efficiency as an exponential
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function of the filter thickness (H) composed of fiber collectors of diameters dc. The following equation [19] determines this variable:
4H(1 ) T P 1 E exp d C
(2)
Where is the filter porosity and T is the total collection efficiency of an individual collector. The total collector efficiency is the overall contribution of the efficiencies due to a number of collection mechanisms, which ideally represent the physical principles that promote the contact between the particle and the collector. Thus, the term T is normally considered as the sum of the individual efficiencies [5]. 2.1. Collection mechanisms
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ACCEPTED MANUSCRIPT The collection mechanisms responsible for most of particle collection in practical applications are mechanical or electrophoretic. Many equations describe the action of collection mechanisms in the
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literature. Table 1 summarizes the mechanical mechanisms: diffusional, gravitational, direct interception
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and inertial.
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Table 1
2.2. Electrophoretic mechanism
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Electrophoretic collection regards the presence of electrostatic charges in particles or in the collectors or in both. These charges can be generated by some phenomena inherent in the process (e.g.
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triboelectrification) or can be deliberately produced (by corona charging, for example). The attraction
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between particles and the collector occurs by several mechanisms [11]: (i) charged particle and an
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oppositely charged collector (Coulombic attraction); (ii) charged particle and an image dipole in a collector; (iii) charged collector and an image dipole in a particle; (iv) space charge repulsion; and (v) charged particle and a grounded collector. Kraemer and Johnstone [11] derived characteristic dimensionless groups for each of these mechanisms. For mechanism (ii), which is very relevant in this study, the image-dipole parameter KM was defined as: KM
c f FSq 2 2 c 2f 3 0d p dc2U
(7)
Where q is the particle charge, 0 is the permittivity of free space, and c and f are the collector and fluid dielectric constants, respectively.
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ACCEPTED MANUSCRIPT Nielsen and Hill [11] derived a relation between KM and the efficiency for individual collectors, for the case of inertialess particle of negligible size collected by isolated spheres. The correlation is given
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by: (8)
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E K M
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Coury [11] obtained experimental values for ηE as a function of KM in a granular bed filter operating to remove fly ash from air streams. The following correlation represented the best fitting for this
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author’s experimental data:
(9)
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E 8.246(K M )1 / 2 Where: 10-6 < KM < 10-4.
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Lundgren and Whitby [23] verified the influence of electrostatic charge on particle removal from
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gas by a fibrous filter. The authors used methylene blue as the test aerosol. They concluded that the image force can be the primary mechanism responsible for the removal of aerosol particles by a fibrous filter.
a cylinder:
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The authors proposed the following equation to fit the experimental data obtained for viscous flow around
E 1.5(K M )1 / 2
(10)
Where: 10-6 < KM < 10-2.
2.3. Combined filtration mechanism In the process of deposition on fibers, particles can be subject to the simultaneous effect of all deposition mechanisms, playing different roles under different filtration conditions [10]. Usually, only one or two deposition mechanisms play a dominant role. In general, researchers assume that the total collection efficiency of a fibrous filter is given by the sum of the individual efficiencies; however, in
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ACCEPTED MANUSCRIPT reality, the effects can overlap each other. A general practice in this case is to add the predicted values for each individual mechanism using Eq. (11).
T D I DI G E
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(11)
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Fig. 1 presents the collection efficiency of an individual collector as a function of the particle
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diameter in a granular bed filtration. In this case, the filtration velocity was 0.11 m/s.
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Figure 1
2.4. Filter pressure drop
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The classical correlation proposed by Davies [24] is usually used for estimating the pressure drop evolution (P) of a clean fibrous filter with filtration velocity (U):
1 561 3
d C2
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3/ 2
(12)
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1 P 64U L
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Where L is a filter thickness, U is filtration superficial velocity, is gas viscosity, dC is the fiber diameter and is the filter porosity.
3. Experimental methodology
3.1. Charge particles measurement
The particle charge distribution was measured using the Electrostatic Charge Classifier (ECC). This device has been extensively used to measure particle charge distribution [25, 26]. A full description of the apparatus and the techniques used to measure distribution, magnitude, and polarity of the charge carried by the airborne particles is given elsewhere [11, 14, 27].
3.2. Experimental apparatus and filtration rig
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ACCEPTED MANUSCRIPT Fig. 2 presents a schematic view of the experimental apparatus used in this study. The experimental apparatus included an aerosol generator, an aerosol charger, an aerosol charge meter (ECC),
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a filtration rig, the filter media, a flowmeter, valves, a vacuum pump, and a particle diameter analyzer
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(TSI APS 3320). In the present work we have used particles in the range of 0.5 to 20.5 m, with a Stokes
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mean diameter of 3.25 m.
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Figure 2
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A particle-free air stream, kept dry by passing through a silica gel column, was fed to a TSI Powder Disperser, model 3433, which disperses small quantities of powders from a rotary table by means
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of an aspirator in the form of a Venturi nozzle. Then, the loaded stream was directed to the particle
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charger and fed into the ECC, for charge measurement, or the filtration rig. Fig. 3 details the filtration rig,
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which presents a downward flux. The increase in the voltage of the corona charger gradually raised the charge level. A micromanometer (Furness FC012) monitored the pressure drop across the filter. We tested aerosol penetration by isokinetic sampling with an Aerodynamic Particle Sizer (APS 3320 by TSI), which counted the number of particles before and after filter within five ranges, from 0.5 to 20.5 µm. We conducted filtration tests with three gas superficial velocities (0.05, 0.08, and 0.12 m/s) and three levels of corona charging (0, -3, and -6 kV).
Figure 3
3.3. Filtering media The polypropylene filter [28] used in the experiments, supplied by Gino Cacciari Ltd., was 2.6 mm thick and had a weight per unit face area of 660 g/cm2. Its dielectric constant was 2.4 [29] and its porosity 8
ACCEPTED MANUSCRIPT was 0.752 0.07 (determined by Aguiar et al. [30, 31]). Fig. 4 displays a sample of the micrograph of the polypropylene filter surface. The micrographs were analyzed in the Image Pro-Plus 3.0 software, and the
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fiber diameters measured were 23.0 1.8 m.
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Figure 4
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3.4. Aerosol generator
The TSI Powder Disperser (3433) produced the poly-dispersed aerosol. It is an appropriate device
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to disperse small quantities of dry powder with diameters between 1 and 50 m using the Venturi aspiration technique [32]. We placed the powder over the surface of a rotating disc, and a brush spread it,
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forming a uniform layer, which was then aspirated by the Venturi through a capillary tube. The lower and
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upper sections of the capillary tube were very close to the surface of the rotating disc and to the narrow
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portion of the Venturi, respectively. The increase in the air velocity in the narrow portion of the Venturi created a low-pressure zone, and, consequently, the particles were aspired by the capillary tube.
3.5. Corona charger
Fig. 5 shows the corona charger used in the experiments. It consisted of a cylindrical PVC tube with tapered ends to facilitate the connection with the aerosol generator and the ECC. The main body had a grounded cylindrical copper electrode with an inner diameter of 4.8 cm and length of 10 cm. The space between wire and cylindrical electrode is 2.4 cm. The discharge electrode was located at the central portion of the charger (Fig. 5). It consisted of a 0.25-mm-diameter stainless steel wire. This wire was connected to a high voltage supply, Exactus model EAT 22 2012-B. This source can apply an electric potential ranging from 0 to -20 kV and a current from 0
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ACCEPTED MANUSCRIPT to 10 mA. It produces positive corona currents, as well as negative ones. For the present study, the
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potential applied was -3 and -6 kV.
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Figure 5
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3.6. The test aerosol
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A phosphate rock concentrate [33-35], non-cohesive and non-hygroscopic powder, was the test material. Its density was 3030 kg/m3, its sphericity was 0.60, its dielectric constant was 6.5, and Stokes
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mean diameter was 3.25 m. Table 2 presents the chemical composition of the concentrate
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Table 2
4. Results and discussion
4.1. Particle charge measurements
All tests were performed under controlled laboratory conditions. The air humidity and temperature were kept at 443% and 232 oC, respectively. The Electrostatic Charge Classifier (ECC) measured the charge level of the aerosol as a function of the particle diameter. Three levels of charge were carried out: (a) the charges acquired by the particles naturally derived from the aerosol generation procedure without using any additional charging method (corona 0 kV); (b and c) the particle charging was achieved by a corona charger as a supplementary method (corona -3kV and corona -6 kV, respectively).
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ACCEPTED MANUSCRIPT Fig. 6 shows the particle charge distribution of the phosphate rock concentrate (median charge and standard deviation) in the three conditions evaluated. All cases indicated a linear dependency between the
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particle charge and its diameter. The increase in the voltage of the corona charger (0, -3, -6 kV) gradually raised the charge level. The measurements indicated that the median charge of particles increased from -
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1.3×10-17C to -4.1×10-17C in case (a); from -2.2×10-17C to -8.4×10-17C in case (b), and from -3.4×10-17C to
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considerable amount of particles was positively charged.
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-12.5×10-17C in case (c). In addition, in all cases, although the median charges were negative, a
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Figure 6
The data were treated by multiple regression technique. Eq 13 shows the obtained relationship (r2 =
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0.88) between the particle charge (q), in Coulombs, the corona voltage (V), in kV, and particle diameter
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(dp) in m .
q 3.13 1017 0.63 1017 V 1.57 1017 d p
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(13)
Where V is the voltage applied in the corona charger in kV and dp is the particle diameter in m. 4.2. Filtration tests
The pressure drop and the particle penetration, the main parameters normally used to characterize the performance of a filter, were measured during each filtration test. The filtration tests were performed with three gas superficial velocities (0.05, 0.08, and 0.12 m/s) and three levels of particle charge, (0, -3, and -6 kV). Penetration was measured at the early stages of the filtration to avoid the effect of the deposited particles on the filter performance.
4.2.1. Experimental penetration as a function of particle charge
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ACCEPTED MANUSCRIPT Table 3 shows the experimental data of penetration as a function of particle size for three levels of filtration velocity (U = 0.05. 0.08 and 0.12 m/s) and three levels of particle charge (0. -3 and -6 kV). Fig. 7
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show that penetration decreased with the increase in the particle diameter, which was more evident for
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particles smaller than 3.5 µm. The filter removed particles larger than 3.5 µm with, at least 96% efficiency. In addition, as expected for inertially dominated filtration, the results showed that particle
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penetration decreased with the increase in the filtration superficial velocity.
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Table 3 Figure 7
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In all cases the results indicated that the global collection efficiency of the filter was very sensitive to the variation of the charge level of particles. When comparing the experimental results of penetration, it
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is evident that the effect of electrostatic capture mechanism on the performance of the filter is quite
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substantial: the penetration decreases substantially with the increase of the particle charge level, especially
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for particle diameter smaller than 3.5 µm and lower values of filtration velocities. These conditions favored the dipole-image forces of electrified particles on the collectors, which is the probable electrophorectic mechanism in action. As the particle-fiber interaction prevails in deep filtration, these results stress the importance of the electrophoretic capture mechanism. 4.2.2. Experimental versus theoretical penetration as a function of particle charge Besides the experimental data, Fig 8 shows the results of calculation (from Eq. 2) of
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Penetration (lines). In these conditions, the filter was considered clean, and the theoretical development of the individual collector efficiency was applied. The individual collector efficiency T (Eq 11) was estimated using Eqs. (3) to (6) for the mechanical mechanisms and Eq.(10) for the electrophoretic mechanism. The charge level of the particles was obtained from Eq. (13). The general trend of the experimental results agreed with the theoretical prediction: the penetration decreased with the increase in the particle diameter and with the increase in particle charge for all the 12
ACCEPTED MANUSCRIPT superficial velocities tested. The calculated values of penetration also correctly predicted that penetration decreased with the increase in the gas superficial velocity. However, Fig. 8 also shows that the theoretical
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prediction tended to overestimate the results. This discrepancy increased as particle size decreased. The
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conformity with the prediction is reasonable for particles above 4 m. In this region, the theoretical prediction could identify the predominant action of the inertial and direct interception mechanisms. On the
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other hand, the experimental results presented a weak correspondence with theoretical data for particles
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smaller than 4 m, in which the electrophoretic mechanism tend to be more effective.
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Figure 8
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4.2.3. The proposed correlation
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We have observed that the discrepancy between the experimental data and the predicted values is
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mainly due to the poor representation of electrostatic effects (Eq. 10). Thus, considering the strong dependency between particle charge and penetration, the correlation used to predict the electrophoretic mechanism will be examined further.
Like Eq. (10) (from Ludgren and Whitby [23]), Eq. (9) from Coury [11] also did not represent well the electrostatic effects. Thus, in this work we used our experimental data to fit a new correlation to represent the electrophoretic efficiency (ηE), using the same structure of Es. (9) and (10). The obtained equation was the following:
E 2.6(K M )1 / 2
(14)
Where 10-4 < KM < 2×10-3. These three equations (Eqs. 9, 10 and 14) were here used for predicting the electrophoretic efficiency ηE for the experimental conditions of these three works, i.e. the present work and the two 13
ACCEPTED MANUSCRIPT previous studies [11, 23]. Figure 9 compares the experimental results of these three works with the prediction by Eq. 9 (Fig. 9a), Eq. 10 (Fig. 9b) and Eq. 14 (Fig. 9c). It can be noticed that, although Eq.
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(14) fits better to the data set, each equation represents well only their own experimental data and fail in
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representing the whole set of available data.
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Figure 9
Each of these three studies used different filter media and different aerosol particles. The different
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filter media were accounted for in the parameter KM, which includes their dielectric constant. However, we consider here that the electric properties of the aerosol are relevant, and may be the reason for the
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discrepancies observed. These three works used particles with markedly different dielectric constants, as
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Table 4
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shown in Table 4.
The trends of the results depicted in Fig. 9 suggest that the values of the electrophoretic efficiency (ηE) are inversely proportional to dielectric constants (εp). Thus, to also represent the effect of electric properties of the aerosol on the ηE , we proposed a new correlation for the prediction of the electrophoretic efficiency ( Eq. 15):
E
14.84 (K M ) 1 / 2 p
(15)
Where 10-6 < KM < 10-2. Fig. 10 shows the comparison of the prediction of electrophoretic efficiency (ηE) by Eq (15) with the experimental results of the three selected works [11, 23 and the present study]. It can be seen that Eq. 14
ACCEPTED MANUSCRIPT (15) noticeably improves the representation of the complex phenomena of the electrophoretic collection of
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aerosols, as compared with Eqs. (9), (10) and (14) (Fig. 9).
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Figure 10
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4.2.4. Pressure drop
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We measured the increase in the pressure drop in the filter for approximately 90 min of filtration. To compare the results, considering the different gas velocities, we expressed the pressure drop as a
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function of the mass retained in the filter. Fig. 11 shows the pressure drop variation in the filter with the
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Figure 11
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the pressure drop in the clean filter.
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mass of the particles retained in the filter for three different gas superficial velocities. Eq. (12) represents
In addition to the expected result of increasing pressure drop with the increase of the mass retained in the filter (MTR) and in the filtration velocity, it can be seen that, for the same pressure drop, higher MTR values were found in the tests without corona when compared to the tests with -3 and -6 kV. This trend strengthened as the filtration velocity increased. It also can be seen that the pressure drop in the filter was sensitive to the variation in the particle charge level: in all cases, the pressure drop variation increased when the charge level raised. The reasons for this behavior are not trivial. One of the possible causes may be related to the size of the collected particles: as the filtration efficiency of fine particles substantially increases with the electrophoretic mechanism, the structure of the deposited particles may differ for each charge level [36]. Therefore, the
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ACCEPTED MANUSCRIPT increase of the resistance to gas flow with the increase of charge level may be due to the deposits formed
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by finer particles.
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5. Conclusions
The effect of presence of electrostatic charges in particles on the performance of a fiber filter was
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investigated in this work, considering the collection efficiency and pressure drop. The correlations from
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the literature for particle collection failed to predict the filter performance. We proposed a new correlation for the electrophoretic collection mechanism. This new correlation represented well the experimental data
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of this work, as well as of other works of the literature.
filtration area (m2)
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Af
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Nomenclature
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Cd, Cd’ parameters in the diffusional efficiency Cr
parameter in the direct interception efficiency
dc
collector (fiber) diameter (m)
dp
particle diameter (m)
n1,n2
number of particles in the filter entrance and exit
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diffusivity coefficient (m2/s)
E
filter efficiency (-)
FS
Cunningham slip factor (-)
g
gravitational acceleration (m/s2)
H
filter thickness (m)
KB
Boltzmann constant [(kg m)/(s2 K)]
Ku
Kuwabara number (-) 16
ACCEPTED MANUSCRIPT image-dipole parameter (-)
KnC
collector Knudsen number (-)
NR
interception parameter
P
penetration (-)
Pe
Peclet number (-)
q
particle charge (C)
ReC
collector Reynolds number (-)
St
Stokes number (-)
T
absolute temperature (K)
U
gas superficial velocity (m/s)
V
voltage applied at the corona charger (kV)
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PT
KM
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Greek symbols P
pressure drop across the filter (kg/ms2)
P0
pressure drop across the filter for t = 0 (kg/m s2)
filter porosity (-)
permittivity of free space (C2s2/kg m3)
C
collector dielectric constant (-)
f
fluid dielectric constant (-)
particle dielectric constant (-)
gas mean free path (m)
gas viscosity (kg/ms)
g
gas density (kg/m3) 17
ACCEPTED MANUSCRIPT particle density (kg/m3)
C
corrected efficiency (-)
D
single collector diffusional efficiency (-)
DI
single collector direct interception efficiency (-)
E
single collector electrophoretic efficiency (-)
G
single collector gravitational efficiency (-)
I
single collector inertial efficiency (-)
T
total collection efficiency of an individual collector (-)
correction factor for the individual collector (-)
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PT
p
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Aknowledgments
References
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The authors are indebted to FAPEMIG and FAPESP for the financial support provided.
[1] A. Jaworek, A. Krupa, T. Czech. Modern Electrostatic Devices and Methods for Exhaust Gascleaning: A Brief Review. J. Electrostatics 65 (2007) 133-155.
[2] S. Huang, C. Chen, C. Chang, C. Lai, C. Chen. Penetration of 4.5 nm to 10 μm aerosol particles through fibrous filters. J. Aer. Sci. 38 (2007) 719-727.
[3] J. Steffens, J.R. Coury. Collection efficiency of fiber filters operating on the removal of nano-sized aerosol particles: I-Homogeneous fibers. Sep. Purif. Technol. 58 (2007) 99-105. 18
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[4] J. Steffens, J.R. Coury. Collection Efficiency of Fiber Filters Operating on the Removal of Nano-Sized
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PT
Aerosol Particles. II- Heterogeneous Fibers Sep. Purif. Technol. 58 (2007) 106-112.
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[5] O.B. Duarte Filho., W.D. Marra Jr., G.C. Kachan, J.R. Coury. Filtration of Electrified Solid Particles.
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Ind. Eng. Chem. Res. 39 (2000) 3884-3895.
[6] J.R. Coury, K.V. Thambimuthu, R. Clift. Capture and rebound of dust in granular bed filters. Powder
MA
Technol. 50 (1987) 253-265.
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[7] N.L. Freitas, J.A.S. Gonçalves, M.D.M. Innocentini, J.R. Coury. Development of a Double-Layered Ceramic Filter for Aerosol Filtration at High-Temperatures: The Filter Collection Efficiency. J. Haz. Mat.
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136 (2006) 747-756.
[8] O. Hanne, N. Timo, K. Hannu. Increase the utilisation of fly ash with electrostatic precipitation Minerals Eng. 19 (2006) 1596-1602.
[9] V.G. Guerra, A.P.R.A. Ribeiro, J.A.S. Gonçalves, J.R. Coury. Effect of Operational Parameters in the Droplet Size of a Venturi Scrubber with Multi-Orifice Injection. Mat. Sci. Forum. 530 (2006) 370-375.
[10] M.J. Matteson, Filtration: Principles and Practices, second ed., Marcel Dekker Inc., New York 1987.
19
ACCEPTED MANUSCRIPT [11] J.R. Coury, Electrostatic Effects in Granular Bed Filtration of Gases. University of Cambridge
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(1983), Ph.D. Thesis.
[12] G.I. Tardos, R. Pfeffer, Z.M. Zhao, The influence of dust loading on the performance of
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electrostatically enhanced fibrous filters. In: 21st Meeting of the Fine Particle Society, Abstracts, San
NU
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Diego (1990) E.U.A.
[13] D.C. Walsh, J.I.T. Stenhouse. Clogging of an electrically active fibrous fillter material: Experimental
MA
results and two-dimensional simulations. Powder Technol. 93 (2007) 63-75.
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[14] J.R. Coury, D. Guang, J.A. Raper, R. Clift. Measurement of electrostatic charge on gas-borne
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particles and the effect of charges on fabric filtration, Process Safety and Environmental Protection.
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TransI ChemE, 69 (1991) 97-106.
[15] Y. Mori, T. Shiomi, N. Katada, H. Minamide, K. Iinoya. Effects of corona precharger on performance of fabric filter. J. Chem. Eng. of Japan, 15 (1982) 211-216.
[16] M. He, S. Dhaniyala, M. Wagner. Aerosol filtration with mobility-classified particles: role of multiply charged particles in skewing penetration measurements. Aerosol Sci. Technol., 49 (2015) 705– 716.
[17] A. L. Sanchez, J. A. Hubbard, J. G. Dellinger, B. L. Servantes. Experimental study of electrostatic aerosol filtration at moderate filter face velocity. Aerosol Sci. Technol., 47 (2013) 606–615.
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ACCEPTED MANUSCRIPT [18] T.S. Zaripov, W.Holländer, S. K. Zaripov, E.A. Kosterina. Aerosol flow with charged particles in
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dense array of spheres. Phys. mathem., 157 (2015) 96–102
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[19] W.C. Hinds, Aerosol technology: properties, in: Behavior and Measurement of Airborne Particles,
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second ed., John Wiley & Sons, New York, 1999.
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[20] S. Payet, D. Boulaud, G. Madelaine, A. Renoux. Penetration and Pressure Drop of a HEPA Filter
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During Loading with Submicron Liquid Particles. J. Aer. Sci. 23 (1992) 723-735.
[21] B.Y.H. Liu, K.L. Rubow, Efficiency, pressure drop and figure of merit of high efficiency fibrous and
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112-116.
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membrane filter media. Proceedings of the 5th World Filtration Congress, Nice 5-8 jun, France, (1990)
[22] R. Gougeon, D. Boulaud, H. Fissan, R. Lange, A. Renoux. Theoretical and experimental study of fibrous filters loading with liquid aerosols in the inertial regime. J. Aerosol Sci. 25 (1994) 189-190.
[23] D.A. Lundgren, K.T. Whitby. Effect of particle electrostatic charge on filtration by fibrous filter. Ind. Eng. Chem. Process Design Development, 4 (1965) 345-349.
[24] C.B. Song, H.S. Park, K.W. Lee. Experimental study of filter clogging with monodisperse PSL particles. Powder Technol. 163 (2006) 152-159.
[25] W.D. Marra Jr., J.R. Coury. Measurement of the electrostatic charge in airborne particles: I development of the equipment and preliminary results. Braz. J. Chem. Eng. 17 (2000) 39-50. 21
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[26] M.V. Rodrigues, W.D. Marra Jr, R.G. Almeida, J.R. Coury. Measurement of the electrostatic
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charge in airborne particles: II – Particle charge distribution of different aerosols. Braz. J. Chem. Eng. 23
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(2006) 125-133.
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[27] R.C. Flagan. History of electrical aerosol measurements. Aer. Sci. Tech. 28 (1998) 301-380.
[28] D.C. Oliveira, C.A.K. Almeida, L.G.M. Vieira, J.J.R. Damasceno, M.A.S. Barrozo. Influence of
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Braz. J. Chem. Eng., 26 (2009) 575-582
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geometric dimensions on the performance of a filtering hydrocyclone: an experimental and CFD study.
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[29] R.C. Weast, Handbook of Chemistry and Physics, 64th edition, CRC Press, Florida, 1983.
[30] M. L. Aguiar, J. R. Coury. Cake Formation in Fabric Filtration of Gases. Ind. Eng. Chem. Research, 35 (1996) 3673-3679.
[31] L.X. Ito, M.L. Aguiar. A study of the porosity of gas filtration cakes, in: Proceedings of the Filtech, vol. 2, Düsseldorf, October, (2003) 116-123.
[32] W. D. Marra Jr., M. V. Rodrigues, R.G.A. Miranda, M.A.S. Barrozo, J.R. Coury. The effect of the generation and handling in the acquired electrostatic charge in airborne particles. Powder Technol. 191 (2009) 299–308.
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ACCEPTED MANUSCRIPT [33] L.G.M. Vieira, J.J.R. Damasceno, M.A.S. Barrozo. Improvement of hydrocyclone separation
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performance by incorporating a conical filtering wall. Chem. Eng. Proc. 49 (2010) 460-467.
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[34] M.A. Santos, R.C. Santana, F. Capponi, C.H. Ataíde, M.A.S. Barrozo, Effect of ionic species on the
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performance of apatite flotation. Sep. Purif. Technol. 76 (2010) 15-20.
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[35] M.S. Oliveira, G.M. Queiroz, R.C. Guimarães, C.H. Ataíde, M.A.S. Barrozo. Selectivity in phosphate
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column flotation. Minerals Eng. 20 (2007) 197-199
[36] B. Huang, Q. Yao, S. Li, H. Zhao, Q. Song, C. You. Experimental investigation on the particle
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capture by a single fiber using microscopic image technique. Powder Technol., 163 (2006) 125-133.
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ACCEPTED MANUSCRIPT Table 1. Single fiber collection mechanisms
References
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Mechanical mechanisms 1/3
d 2pρ P g
I 0.0334 St 3/2
(direct intercep.) (5) (inertial) (6)
ln 1- ε 3 1- ε ; - + 1- ε 2 4 4
D=
K BTFS 3πμd p
;
NR
dp dc
; C r 1 1.996Kn c ; Kn c 2 / d c ;
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;
NR
24
[10]
[22] 1/3
εPe Cd = 1+ 0.388Kn c Ku
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Ud C D
Ku = -
D
2
Where:
[20]
[21]
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2 NR DI 0.6 Cr Ku 1 N R
Pe =
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(gravitational) (4)
18μU
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ηG =
(diffusional) (3)
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ε -2/3 ' ηD = 1.6 Pe Cd Cd Ku
;
Rec
1/3 ; ε -2/3 C'd = 1/ 1+1.6 Pe Cd Ku
Ug d c
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24.80
Al2O3
5.00
Fe2O3
2.44
F-
2.00
K2O
1.24
MgO
0.51
Na2O
0.13
Cl-
0.11
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P2O5
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28.10
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SiO2
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32.20
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CaO
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Mass (%)
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Main constituents
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Table 2. Chemical composition of the phosphate rock concentrate
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ACCEPTED MANUSCRIPT Table 3– Experimental penetration as a function of particle size for three levels of filtration velocity (U =
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0.05. 0.08 and 0.12 m/s) and three levels of particle charge (0. -3 and -6 kV).
Corona: -3 kV
Corona: -6 kV
5.5
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Corona: 0 kV
4.1
4.0
3.9
4.7
3.4
2.1
1.9
1.5
1.1
1.2
1.3
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1.0
0.8
0.8
0.8
0.9
1.0
0.6
0.4
0.7
0.6
0.6
0.4
0.3
0.2
0.4
0.4
0.3
0.05 m/s
0.08m/s
0.12m/s
2.31
22.0
18.9
11.8
2.69
6.4
5.7
4.1
3.26
3.9
3.7
3.1
3.98
3.1
2.5
0.7
5.95
1.8
1.2
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(10-6m)
0.12m/s
0.05 m/s 0.08m/s
0.12m/s
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0.6
0.05 m/s 0.08m/s
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dp
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Experimental penetration[%]
Table 4- Dielectric constant of the particles used in the present work and previous studies [11, 20]. Author
Particle dieletric constant, εp (-)
Lundgren e Whitby [20]
7.6
Coury [11]
2.6
This work
6.5
26
ACCEPTED MANUSCRIPT Figures Captions Fig. 1. Single collector efficiency as a function of particle diameter [11].
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Fig. 2. Scheme of the experimental apparatus
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Fig. 3. Scheme of filtration support (Dimensions in cm)
Fig. 4. The polypropylene fabric filter utilized in this work (1000x).
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Fig. 5. Corona charger device. Dimensions in cm.
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Fig. 6. Median charge and S.Dev. vs. particle diameter for three cases of particle charge evaluated (0, -3 kV and -6 kV)
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Fig. 7. Penetration as a function of particle size for three levels of filtration velocity (U = 0.05, 0.08 and
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0.12 m/s) and three levels of particle charge (0, -3 and -6 kV).
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Fig. 8. Experimental and calculated penetration as a function of particle size for three filtration velocities (U = 0.05, 0.08 and 0.12 m/s) and three levels of particle charge ( 0, -3 and -6 kV). Calculated penetration
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were obtained from Eq (2) and the equations in Table 1 (mechanical mechanisms) and Eq. (10) for the electrophoretic mechanism
Fig. 9. Comparison between the experimental results for ηE and the predictions by: (a) Eq. (9); (b) Eq. (10); and (c) Eq. (14).
Fig. 10. Comparison between the experimental results for ηE of three selected studies [11, 20 and the present work] with the predictions from Eq. (15).
Fig. 11. Increase in pressure drop the filter as a function of mass of dust collected (MTR) for three filtration velocities and three levels of corona voltage
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ACCEPTED MANUSCRIPT Figure 1
-1
10
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TOTAL electrophoretic
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gravitational -8
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inertial + dir. intercep 1x10
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Clean Air
high voltage source
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Rotating Plate
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corona charger
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Electrostatic Charge Classifier
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Particle Size Analyzer
Flowmeter pump
Computer
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U=0.05 m/s Experimental 0 kv Experimental -3 kv Experimental -6 kv Theoretical 0 kv Theoretical -3 kv Theoretical -6 kv
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U=0.08 m/s Experimental 0 kv Experimental -3 kv Experimental -6 kv Theoretical 0 kv Theoretical -3 kv Theoretical -6 kv
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(a)
This work ref. [11] ref. [20] 1E-3 1E-3
0,01
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1E-3 1E-3
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U = 0.05 m/s corona 0 kV corona -3 kV corona -6 kV eq. 12
P - P0 [Pa]
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This work ref. [11] ref. [20]
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ACCEPTED MANUSCRIPT Highlights
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The effect of particle charge level on the performance of a fiber filter during aerosol filtration was studied.
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A relationship between the charge of particles and their diameter was identified.
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Correlations from the literature did not adequately predict the experimental data behaviour.
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A new expression for the electrophoretic collection mechanism was proposed. The new correlation represented well the experimental data of this work, as well as of other works
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of the literature
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S0032-5910(17)30250-4 doi:10.1016/j.powtec.2017.03.033 PTEC 12438
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
16 November 2016 7 March 2017 12 March 2017
Please cite this article as: M.V. Rodrigues, M.A.S. Barrozo, J.A.S. Gon¸calves, J.R. Coury, Effect of particle electrostatic charge on aerosol filtration by a fibrous filter, Powder Technology (2017), doi:10.1016/j.powtec.2017.03.033
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ACCEPTED MANUSCRIPT Effect of particle electrostatic charge on aerosol filtration by a fibrous filter
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M.V. Rodrigues1, M.A.S. Barrozo2* J.A.S. Gonçalves3 and J.R. Coury3
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1 Institute of Science and Technology -Federal University of Alfenas-Campus of Poços de Caldas, MG, Brazil 2 Faculty of Chemical Engineering, Federal University of Uberlandia, Uberlandia, MG, Brazil
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3 Department of Chemical Engineering, Federal University of São Carlos, Sao Carlos, SP, Brazil
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Abstract
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This study aimed to investigate the influence of the particle charge level on collection efficiency
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and pressure drop during aerosol filtration in a fiber filter. An Electrostatic Charge Classifier (ECC)
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measured the charge level of aerosol as a function of the particle diameter. The filter was made of polypropylene; its mass per area was 600 g/m2, its diameter was 0.047 m, and its thickness was 0.0026 m. Phosphate rock was the test dust (density: 3030 kg/m3; average Stokes diameter: 3.25 m). The aerosol was dispersed in air by a TSI Venturi type generator, model SSPD 3433. The particle charging was achieved by a corona charger. A relationship between the charge of particles and their diameter was identified. From the filtration results, it was analyzed the effect of the electrostatic charges in the particles on the performance of the filter (collection efficiency and pressure drop). The correlations from the literature did not adequately predict the experimental data behaviour. Thus, we proposed a new expression for the electrophoretic collection mechanism, which was consistent with the experimental results found in this research, as well as of other studies in the literature. Keywords: filtration, solid-gas separation, fibrous filters.
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1. Introduction
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Scientific and technological efforts have been dedicating the development of techniques to remove
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particles from the air, especially those smaller than 2.5 m, which can cause serious health problems. Researches on particulate control technologies have tried to find new, improved, cheaper and energy-
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saving structural materials and methods to collect small particles [1].
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__________________________________
*Corresponding author at: FEQ/UFU, Av. João Naves de Avila 2121, 38408-100, Uberlândia-MG, Brazil.
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Tel.: +55 34 996776099; +55 34 3230 9400. E-mail address: [email protected] (M.A.S. Barrozo)
Nanometer, submicron and micron-sized particles could be removed from gas stream by a group of
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devices, includes fibrous [2, 3, 4]; granular [5, 6] and ceramic filters [7], electrostatic precipitators [8] and
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wet scrubbers [9].
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The basic problem of the filtration theory is to express both pressure drop (P) and filter efficiency (E) as a function of the relevant variables and to describe the properties of the particles dispersion, medium, and filters [10]. Particularly, the electrostatic charge in the particles significantly contributes to the filter performance by affecting the collection efficiency and the pressure drop [11]. However, this phenomenon has not been comprehensively studied and ought to be investigated [12]. Electrical forces from a charged particle can far exceed gravitational forces and, in some circumstances, can even exceed aerodynamic forces in a moving air stream. As controlled handling of particles is exceptionally difficult to achieve [13], electrostatic particle charging is an important phenomenon related to powder handling [14]. Duarte Filho et al. [5] studied the filtration of electrified solid particles in a fixed bed of sand. The particles were electrified by impact. They performed the filtration tests with three bed heights (0.01, 0.02, and 0.04 m), three gas superficial velocities (0.07, 0.11, and 0.15 m/s), and four levels of particle 2
ACCEPTED MANUSCRIPT charging. The authors obtained a nonlinear response of both particle penetration and pressure drop with the particle charge.
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Mori et al. [15] studied the effects of a positive corona precharger on the performance of fabric
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filters in the air with controlled humidity. When the corona precharger was switched on, the charge of the particles did not vary according to the air relative humidity. On the other hand, when the corona
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precharger was switched off, the particle charge decreased with the increase in the relative humidity.
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He et al. [16] used a differential mobility analyzer (DMA) to measure the filter penetration. The authors observed that the presence of these multiply charged particles critically affects filter penetration
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measurements. The fraction of multiply charged particles upstream and downstream of the filter depends on the aerosol size distribution entering the DMA and the filter penetration characteristics.
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The effects of electrostatic fiber charge were quantified by by Sanchez et al. [17], comparing filter
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efficiencies for charged and uncharged filter media. The effects of particle charge were also quantified by
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using NaCl test aerosols in two electrostatic charge configurations: aerosol in the Boltzmann equilibrium charge distribution and uncharged aerosol, where all charged particles were removed in an electrostatic precipitator. A substantial increase in overall collection efficiency was observed when electrostatically charged filter media were used.
The problem of aerosol flow with charged particles in a dense array of spheres was studied by Zaripov et al. [18]. Velocity field of the carrier phase flow was found by solving the Navier–Stokes equations using CFD code ANSYS Fluent. Particle trajectories were calculated taking into account aerodynamic drag, gravity force and electrostatic force for single charge. The deposition efficiency of charged particles was quantified. The present paper aimed to investigate the influence of the particle charge level on the collection efficiency and the pressure drop during the first stages of filtration. We evaluated electrostatic forces,
3
ACCEPTED MANUSCRIPT particularly image-dipole forces, between charged particles and uncharged fibers. Then, we proposed a
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model for total collection efficiency considering the dipole-image mechanism action.
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2. Filtration in fibrous filter and electrostatics effects
Filter performance is generally described in terms of total efficiency (E) and pressure drop (P).
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The total collection efficiency is the ratio of the number of particles collected by the filter to the number
n 2 - n1 n2
(1)
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E=
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of particles going to the medium:
Where n2 is the upstream concentration, and n1 is the downstream concentration of the filter.
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Penetration (P), defined by P 1 E , also characterizes the filter performance. Extensive studies
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on deep-bed filtration in granular and fabric filters have pointed out total efficiency as an exponential
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function of the filter thickness (H) composed of fiber collectors of diameters dc. The following equation [19] determines this variable:
4H(1 ) T P 1 E exp d C
(2)
Where is the filter porosity and T is the total collection efficiency of an individual collector. The total collector efficiency is the overall contribution of the efficiencies due to a number of collection mechanisms, which ideally represent the physical principles that promote the contact between the particle and the collector. Thus, the term T is normally considered as the sum of the individual efficiencies [5]. 2.1. Collection mechanisms
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ACCEPTED MANUSCRIPT The collection mechanisms responsible for most of particle collection in practical applications are mechanical or electrophoretic. Many equations describe the action of collection mechanisms in the
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literature. Table 1 summarizes the mechanical mechanisms: diffusional, gravitational, direct interception
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and inertial.
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Table 1
2.2. Electrophoretic mechanism
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Electrophoretic collection regards the presence of electrostatic charges in particles or in the collectors or in both. These charges can be generated by some phenomena inherent in the process (e.g.
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triboelectrification) or can be deliberately produced (by corona charging, for example). The attraction
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between particles and the collector occurs by several mechanisms [11]: (i) charged particle and an
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oppositely charged collector (Coulombic attraction); (ii) charged particle and an image dipole in a collector; (iii) charged collector and an image dipole in a particle; (iv) space charge repulsion; and (v) charged particle and a grounded collector. Kraemer and Johnstone [11] derived characteristic dimensionless groups for each of these mechanisms. For mechanism (ii), which is very relevant in this study, the image-dipole parameter KM was defined as: KM
c f FSq 2 2 c 2f 3 0d p dc2U
(7)
Where q is the particle charge, 0 is the permittivity of free space, and c and f are the collector and fluid dielectric constants, respectively.
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ACCEPTED MANUSCRIPT Nielsen and Hill [11] derived a relation between KM and the efficiency for individual collectors, for the case of inertialess particle of negligible size collected by isolated spheres. The correlation is given
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by: (8)
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E K M
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Coury [11] obtained experimental values for ηE as a function of KM in a granular bed filter operating to remove fly ash from air streams. The following correlation represented the best fitting for this
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author’s experimental data:
(9)
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E 8.246(K M )1 / 2 Where: 10-6 < KM < 10-4.
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Lundgren and Whitby [23] verified the influence of electrostatic charge on particle removal from
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gas by a fibrous filter. The authors used methylene blue as the test aerosol. They concluded that the image force can be the primary mechanism responsible for the removal of aerosol particles by a fibrous filter.
a cylinder:
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The authors proposed the following equation to fit the experimental data obtained for viscous flow around
E 1.5(K M )1 / 2
(10)
Where: 10-6 < KM < 10-2.
2.3. Combined filtration mechanism In the process of deposition on fibers, particles can be subject to the simultaneous effect of all deposition mechanisms, playing different roles under different filtration conditions [10]. Usually, only one or two deposition mechanisms play a dominant role. In general, researchers assume that the total collection efficiency of a fibrous filter is given by the sum of the individual efficiencies; however, in
6
ACCEPTED MANUSCRIPT reality, the effects can overlap each other. A general practice in this case is to add the predicted values for each individual mechanism using Eq. (11).
T D I DI G E
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(11)
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Fig. 1 presents the collection efficiency of an individual collector as a function of the particle
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diameter in a granular bed filtration. In this case, the filtration velocity was 0.11 m/s.
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Figure 1
2.4. Filter pressure drop
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The classical correlation proposed by Davies [24] is usually used for estimating the pressure drop evolution (P) of a clean fibrous filter with filtration velocity (U):
1 561 3
d C2
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3/ 2
(12)
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1 P 64U L
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Where L is a filter thickness, U is filtration superficial velocity, is gas viscosity, dC is the fiber diameter and is the filter porosity.
3. Experimental methodology
3.1. Charge particles measurement
The particle charge distribution was measured using the Electrostatic Charge Classifier (ECC). This device has been extensively used to measure particle charge distribution [25, 26]. A full description of the apparatus and the techniques used to measure distribution, magnitude, and polarity of the charge carried by the airborne particles is given elsewhere [11, 14, 27].
3.2. Experimental apparatus and filtration rig
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ACCEPTED MANUSCRIPT Fig. 2 presents a schematic view of the experimental apparatus used in this study. The experimental apparatus included an aerosol generator, an aerosol charger, an aerosol charge meter (ECC),
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a filtration rig, the filter media, a flowmeter, valves, a vacuum pump, and a particle diameter analyzer
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(TSI APS 3320). In the present work we have used particles in the range of 0.5 to 20.5 m, with a Stokes
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mean diameter of 3.25 m.
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Figure 2
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A particle-free air stream, kept dry by passing through a silica gel column, was fed to a TSI Powder Disperser, model 3433, which disperses small quantities of powders from a rotary table by means
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of an aspirator in the form of a Venturi nozzle. Then, the loaded stream was directed to the particle
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charger and fed into the ECC, for charge measurement, or the filtration rig. Fig. 3 details the filtration rig,
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which presents a downward flux. The increase in the voltage of the corona charger gradually raised the charge level. A micromanometer (Furness FC012) monitored the pressure drop across the filter. We tested aerosol penetration by isokinetic sampling with an Aerodynamic Particle Sizer (APS 3320 by TSI), which counted the number of particles before and after filter within five ranges, from 0.5 to 20.5 µm. We conducted filtration tests with three gas superficial velocities (0.05, 0.08, and 0.12 m/s) and three levels of corona charging (0, -3, and -6 kV).
Figure 3
3.3. Filtering media The polypropylene filter [28] used in the experiments, supplied by Gino Cacciari Ltd., was 2.6 mm thick and had a weight per unit face area of 660 g/cm2. Its dielectric constant was 2.4 [29] and its porosity 8
ACCEPTED MANUSCRIPT was 0.752 0.07 (determined by Aguiar et al. [30, 31]). Fig. 4 displays a sample of the micrograph of the polypropylene filter surface. The micrographs were analyzed in the Image Pro-Plus 3.0 software, and the
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fiber diameters measured were 23.0 1.8 m.
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Figure 4
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3.4. Aerosol generator
The TSI Powder Disperser (3433) produced the poly-dispersed aerosol. It is an appropriate device
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to disperse small quantities of dry powder with diameters between 1 and 50 m using the Venturi aspiration technique [32]. We placed the powder over the surface of a rotating disc, and a brush spread it,
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forming a uniform layer, which was then aspirated by the Venturi through a capillary tube. The lower and
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upper sections of the capillary tube were very close to the surface of the rotating disc and to the narrow
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portion of the Venturi, respectively. The increase in the air velocity in the narrow portion of the Venturi created a low-pressure zone, and, consequently, the particles were aspired by the capillary tube.
3.5. Corona charger
Fig. 5 shows the corona charger used in the experiments. It consisted of a cylindrical PVC tube with tapered ends to facilitate the connection with the aerosol generator and the ECC. The main body had a grounded cylindrical copper electrode with an inner diameter of 4.8 cm and length of 10 cm. The space between wire and cylindrical electrode is 2.4 cm. The discharge electrode was located at the central portion of the charger (Fig. 5). It consisted of a 0.25-mm-diameter stainless steel wire. This wire was connected to a high voltage supply, Exactus model EAT 22 2012-B. This source can apply an electric potential ranging from 0 to -20 kV and a current from 0
9
ACCEPTED MANUSCRIPT to 10 mA. It produces positive corona currents, as well as negative ones. For the present study, the
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potential applied was -3 and -6 kV.
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Figure 5
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3.6. The test aerosol
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A phosphate rock concentrate [33-35], non-cohesive and non-hygroscopic powder, was the test material. Its density was 3030 kg/m3, its sphericity was 0.60, its dielectric constant was 6.5, and Stokes
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mean diameter was 3.25 m. Table 2 presents the chemical composition of the concentrate
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Table 2
4. Results and discussion
4.1. Particle charge measurements
All tests were performed under controlled laboratory conditions. The air humidity and temperature were kept at 443% and 232 oC, respectively. The Electrostatic Charge Classifier (ECC) measured the charge level of the aerosol as a function of the particle diameter. Three levels of charge were carried out: (a) the charges acquired by the particles naturally derived from the aerosol generation procedure without using any additional charging method (corona 0 kV); (b and c) the particle charging was achieved by a corona charger as a supplementary method (corona -3kV and corona -6 kV, respectively).
10
ACCEPTED MANUSCRIPT Fig. 6 shows the particle charge distribution of the phosphate rock concentrate (median charge and standard deviation) in the three conditions evaluated. All cases indicated a linear dependency between the
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particle charge and its diameter. The increase in the voltage of the corona charger (0, -3, -6 kV) gradually raised the charge level. The measurements indicated that the median charge of particles increased from -
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1.3×10-17C to -4.1×10-17C in case (a); from -2.2×10-17C to -8.4×10-17C in case (b), and from -3.4×10-17C to
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considerable amount of particles was positively charged.
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-12.5×10-17C in case (c). In addition, in all cases, although the median charges were negative, a
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Figure 6
The data were treated by multiple regression technique. Eq 13 shows the obtained relationship (r2 =
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0.88) between the particle charge (q), in Coulombs, the corona voltage (V), in kV, and particle diameter
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(dp) in m .
q 3.13 1017 0.63 1017 V 1.57 1017 d p
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(13)
Where V is the voltage applied in the corona charger in kV and dp is the particle diameter in m. 4.2. Filtration tests
The pressure drop and the particle penetration, the main parameters normally used to characterize the performance of a filter, were measured during each filtration test. The filtration tests were performed with three gas superficial velocities (0.05, 0.08, and 0.12 m/s) and three levels of particle charge, (0, -3, and -6 kV). Penetration was measured at the early stages of the filtration to avoid the effect of the deposited particles on the filter performance.
4.2.1. Experimental penetration as a function of particle charge
11
ACCEPTED MANUSCRIPT Table 3 shows the experimental data of penetration as a function of particle size for three levels of filtration velocity (U = 0.05. 0.08 and 0.12 m/s) and three levels of particle charge (0. -3 and -6 kV). Fig. 7
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show that penetration decreased with the increase in the particle diameter, which was more evident for
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particles smaller than 3.5 µm. The filter removed particles larger than 3.5 µm with, at least 96% efficiency. In addition, as expected for inertially dominated filtration, the results showed that particle
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penetration decreased with the increase in the filtration superficial velocity.
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Table 3 Figure 7
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In all cases the results indicated that the global collection efficiency of the filter was very sensitive to the variation of the charge level of particles. When comparing the experimental results of penetration, it
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is evident that the effect of electrostatic capture mechanism on the performance of the filter is quite
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substantial: the penetration decreases substantially with the increase of the particle charge level, especially
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for particle diameter smaller than 3.5 µm and lower values of filtration velocities. These conditions favored the dipole-image forces of electrified particles on the collectors, which is the probable electrophorectic mechanism in action. As the particle-fiber interaction prevails in deep filtration, these results stress the importance of the electrophoretic capture mechanism. 4.2.2. Experimental versus theoretical penetration as a function of particle charge Besides the experimental data, Fig 8 shows the results of calculation (from Eq. 2) of
the
Penetration (lines). In these conditions, the filter was considered clean, and the theoretical development of the individual collector efficiency was applied. The individual collector efficiency T (Eq 11) was estimated using Eqs. (3) to (6) for the mechanical mechanisms and Eq.(10) for the electrophoretic mechanism. The charge level of the particles was obtained from Eq. (13). The general trend of the experimental results agreed with the theoretical prediction: the penetration decreased with the increase in the particle diameter and with the increase in particle charge for all the 12
ACCEPTED MANUSCRIPT superficial velocities tested. The calculated values of penetration also correctly predicted that penetration decreased with the increase in the gas superficial velocity. However, Fig. 8 also shows that the theoretical
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prediction tended to overestimate the results. This discrepancy increased as particle size decreased. The
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conformity with the prediction is reasonable for particles above 4 m. In this region, the theoretical prediction could identify the predominant action of the inertial and direct interception mechanisms. On the
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other hand, the experimental results presented a weak correspondence with theoretical data for particles
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smaller than 4 m, in which the electrophoretic mechanism tend to be more effective.
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Figure 8
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4.2.3. The proposed correlation
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We have observed that the discrepancy between the experimental data and the predicted values is
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mainly due to the poor representation of electrostatic effects (Eq. 10). Thus, considering the strong dependency between particle charge and penetration, the correlation used to predict the electrophoretic mechanism will be examined further.
Like Eq. (10) (from Ludgren and Whitby [23]), Eq. (9) from Coury [11] also did not represent well the electrostatic effects. Thus, in this work we used our experimental data to fit a new correlation to represent the electrophoretic efficiency (ηE), using the same structure of Es. (9) and (10). The obtained equation was the following:
E 2.6(K M )1 / 2
(14)
Where 10-4 < KM < 2×10-3. These three equations (Eqs. 9, 10 and 14) were here used for predicting the electrophoretic efficiency ηE for the experimental conditions of these three works, i.e. the present work and the two 13
ACCEPTED MANUSCRIPT previous studies [11, 23]. Figure 9 compares the experimental results of these three works with the prediction by Eq. 9 (Fig. 9a), Eq. 10 (Fig. 9b) and Eq. 14 (Fig. 9c). It can be noticed that, although Eq.
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(14) fits better to the data set, each equation represents well only their own experimental data and fail in
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representing the whole set of available data.
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Figure 9
Each of these three studies used different filter media and different aerosol particles. The different
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filter media were accounted for in the parameter KM, which includes their dielectric constant. However, we consider here that the electric properties of the aerosol are relevant, and may be the reason for the
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discrepancies observed. These three works used particles with markedly different dielectric constants, as
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Table 4
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shown in Table 4.
The trends of the results depicted in Fig. 9 suggest that the values of the electrophoretic efficiency (ηE) are inversely proportional to dielectric constants (εp). Thus, to also represent the effect of electric properties of the aerosol on the ηE , we proposed a new correlation for the prediction of the electrophoretic efficiency ( Eq. 15):
E
14.84 (K M ) 1 / 2 p
(15)
Where 10-6 < KM < 10-2. Fig. 10 shows the comparison of the prediction of electrophoretic efficiency (ηE) by Eq (15) with the experimental results of the three selected works [11, 23 and the present study]. It can be seen that Eq. 14
ACCEPTED MANUSCRIPT (15) noticeably improves the representation of the complex phenomena of the electrophoretic collection of
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aerosols, as compared with Eqs. (9), (10) and (14) (Fig. 9).
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Figure 10
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4.2.4. Pressure drop
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We measured the increase in the pressure drop in the filter for approximately 90 min of filtration. To compare the results, considering the different gas velocities, we expressed the pressure drop as a
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function of the mass retained in the filter. Fig. 11 shows the pressure drop variation in the filter with the
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Figure 11
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the pressure drop in the clean filter.
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mass of the particles retained in the filter for three different gas superficial velocities. Eq. (12) represents
In addition to the expected result of increasing pressure drop with the increase of the mass retained in the filter (MTR) and in the filtration velocity, it can be seen that, for the same pressure drop, higher MTR values were found in the tests without corona when compared to the tests with -3 and -6 kV. This trend strengthened as the filtration velocity increased. It also can be seen that the pressure drop in the filter was sensitive to the variation in the particle charge level: in all cases, the pressure drop variation increased when the charge level raised. The reasons for this behavior are not trivial. One of the possible causes may be related to the size of the collected particles: as the filtration efficiency of fine particles substantially increases with the electrophoretic mechanism, the structure of the deposited particles may differ for each charge level [36]. Therefore, the
15
ACCEPTED MANUSCRIPT increase of the resistance to gas flow with the increase of charge level may be due to the deposits formed
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by finer particles.
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5. Conclusions
The effect of presence of electrostatic charges in particles on the performance of a fiber filter was
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investigated in this work, considering the collection efficiency and pressure drop. The correlations from
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the literature for particle collection failed to predict the filter performance. We proposed a new correlation for the electrophoretic collection mechanism. This new correlation represented well the experimental data
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of this work, as well as of other works of the literature.
filtration area (m2)
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Af
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Nomenclature
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Cd, Cd’ parameters in the diffusional efficiency Cr
parameter in the direct interception efficiency
dc
collector (fiber) diameter (m)
dp
particle diameter (m)
n1,n2
number of particles in the filter entrance and exit
D
diffusivity coefficient (m2/s)
E
filter efficiency (-)
FS
Cunningham slip factor (-)
g
gravitational acceleration (m/s2)
H
filter thickness (m)
KB
Boltzmann constant [(kg m)/(s2 K)]
Ku
Kuwabara number (-) 16
ACCEPTED MANUSCRIPT image-dipole parameter (-)
KnC
collector Knudsen number (-)
NR
interception parameter
P
penetration (-)
Pe
Peclet number (-)
q
particle charge (C)
ReC
collector Reynolds number (-)
St
Stokes number (-)
T
absolute temperature (K)
U
gas superficial velocity (m/s)
V
voltage applied at the corona charger (kV)
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D
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KM
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Greek symbols P
pressure drop across the filter (kg/ms2)
P0
pressure drop across the filter for t = 0 (kg/m s2)
filter porosity (-)
permittivity of free space (C2s2/kg m3)
C
collector dielectric constant (-)
f
fluid dielectric constant (-)
particle dielectric constant (-)
gas mean free path (m)
gas viscosity (kg/ms)
g
gas density (kg/m3) 17
ACCEPTED MANUSCRIPT particle density (kg/m3)
C
corrected efficiency (-)
D
single collector diffusional efficiency (-)
DI
single collector direct interception efficiency (-)
E
single collector electrophoretic efficiency (-)
G
single collector gravitational efficiency (-)
I
single collector inertial efficiency (-)
T
total collection efficiency of an individual collector (-)
correction factor for the individual collector (-)
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p
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Aknowledgments
References
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The authors are indebted to FAPEMIG and FAPESP for the financial support provided.
[1] A. Jaworek, A. Krupa, T. Czech. Modern Electrostatic Devices and Methods for Exhaust Gascleaning: A Brief Review. J. Electrostatics 65 (2007) 133-155.
[2] S. Huang, C. Chen, C. Chang, C. Lai, C. Chen. Penetration of 4.5 nm to 10 μm aerosol particles through fibrous filters. J. Aer. Sci. 38 (2007) 719-727.
[3] J. Steffens, J.R. Coury. Collection efficiency of fiber filters operating on the removal of nano-sized aerosol particles: I-Homogeneous fibers. Sep. Purif. Technol. 58 (2007) 99-105. 18
ACCEPTED MANUSCRIPT
[4] J. Steffens, J.R. Coury. Collection Efficiency of Fiber Filters Operating on the Removal of Nano-Sized
RI
PT
Aerosol Particles. II- Heterogeneous Fibers Sep. Purif. Technol. 58 (2007) 106-112.
SC
[5] O.B. Duarte Filho., W.D. Marra Jr., G.C. Kachan, J.R. Coury. Filtration of Electrified Solid Particles.
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Ind. Eng. Chem. Res. 39 (2000) 3884-3895.
[6] J.R. Coury, K.V. Thambimuthu, R. Clift. Capture and rebound of dust in granular bed filters. Powder
MA
Technol. 50 (1987) 253-265.
TE
D
[7] N.L. Freitas, J.A.S. Gonçalves, M.D.M. Innocentini, J.R. Coury. Development of a Double-Layered Ceramic Filter for Aerosol Filtration at High-Temperatures: The Filter Collection Efficiency. J. Haz. Mat.
AC CE P
136 (2006) 747-756.
[8] O. Hanne, N. Timo, K. Hannu. Increase the utilisation of fly ash with electrostatic precipitation Minerals Eng. 19 (2006) 1596-1602.
[9] V.G. Guerra, A.P.R.A. Ribeiro, J.A.S. Gonçalves, J.R. Coury. Effect of Operational Parameters in the Droplet Size of a Venturi Scrubber with Multi-Orifice Injection. Mat. Sci. Forum. 530 (2006) 370-375.
[10] M.J. Matteson, Filtration: Principles and Practices, second ed., Marcel Dekker Inc., New York 1987.
19
ACCEPTED MANUSCRIPT [11] J.R. Coury, Electrostatic Effects in Granular Bed Filtration of Gases. University of Cambridge
PT
(1983), Ph.D. Thesis.
[12] G.I. Tardos, R. Pfeffer, Z.M. Zhao, The influence of dust loading on the performance of
RI
electrostatically enhanced fibrous filters. In: 21st Meeting of the Fine Particle Society, Abstracts, San
NU
SC
Diego (1990) E.U.A.
[13] D.C. Walsh, J.I.T. Stenhouse. Clogging of an electrically active fibrous fillter material: Experimental
MA
results and two-dimensional simulations. Powder Technol. 93 (2007) 63-75.
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[14] J.R. Coury, D. Guang, J.A. Raper, R. Clift. Measurement of electrostatic charge on gas-borne
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particles and the effect of charges on fabric filtration, Process Safety and Environmental Protection.
AC CE P
TransI ChemE, 69 (1991) 97-106.
[15] Y. Mori, T. Shiomi, N. Katada, H. Minamide, K. Iinoya. Effects of corona precharger on performance of fabric filter. J. Chem. Eng. of Japan, 15 (1982) 211-216.
[16] M. He, S. Dhaniyala, M. Wagner. Aerosol filtration with mobility-classified particles: role of multiply charged particles in skewing penetration measurements. Aerosol Sci. Technol., 49 (2015) 705– 716.
[17] A. L. Sanchez, J. A. Hubbard, J. G. Dellinger, B. L. Servantes. Experimental study of electrostatic aerosol filtration at moderate filter face velocity. Aerosol Sci. Technol., 47 (2013) 606–615.
20
ACCEPTED MANUSCRIPT [18] T.S. Zaripov, W.Holländer, S. K. Zaripov, E.A. Kosterina. Aerosol flow with charged particles in
PT
dense array of spheres. Phys. mathem., 157 (2015) 96–102
RI
[19] W.C. Hinds, Aerosol technology: properties, in: Behavior and Measurement of Airborne Particles,
SC
second ed., John Wiley & Sons, New York, 1999.
NU
[20] S. Payet, D. Boulaud, G. Madelaine, A. Renoux. Penetration and Pressure Drop of a HEPA Filter
MA
During Loading with Submicron Liquid Particles. J. Aer. Sci. 23 (1992) 723-735.
[21] B.Y.H. Liu, K.L. Rubow, Efficiency, pressure drop and figure of merit of high efficiency fibrous and
TE AC CE P
112-116.
D
membrane filter media. Proceedings of the 5th World Filtration Congress, Nice 5-8 jun, France, (1990)
[22] R. Gougeon, D. Boulaud, H. Fissan, R. Lange, A. Renoux. Theoretical and experimental study of fibrous filters loading with liquid aerosols in the inertial regime. J. Aerosol Sci. 25 (1994) 189-190.
[23] D.A. Lundgren, K.T. Whitby. Effect of particle electrostatic charge on filtration by fibrous filter. Ind. Eng. Chem. Process Design Development, 4 (1965) 345-349.
[24] C.B. Song, H.S. Park, K.W. Lee. Experimental study of filter clogging with monodisperse PSL particles. Powder Technol. 163 (2006) 152-159.
[25] W.D. Marra Jr., J.R. Coury. Measurement of the electrostatic charge in airborne particles: I development of the equipment and preliminary results. Braz. J. Chem. Eng. 17 (2000) 39-50. 21
ACCEPTED MANUSCRIPT
[26] M.V. Rodrigues, W.D. Marra Jr, R.G. Almeida, J.R. Coury. Measurement of the electrostatic
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charge in airborne particles: II – Particle charge distribution of different aerosols. Braz. J. Chem. Eng. 23
RI
(2006) 125-133.
NU
SC
[27] R.C. Flagan. History of electrical aerosol measurements. Aer. Sci. Tech. 28 (1998) 301-380.
[28] D.C. Oliveira, C.A.K. Almeida, L.G.M. Vieira, J.J.R. Damasceno, M.A.S. Barrozo. Influence of
D
Braz. J. Chem. Eng., 26 (2009) 575-582
MA
geometric dimensions on the performance of a filtering hydrocyclone: an experimental and CFD study.
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[29] R.C. Weast, Handbook of Chemistry and Physics, 64th edition, CRC Press, Florida, 1983.
[30] M. L. Aguiar, J. R. Coury. Cake Formation in Fabric Filtration of Gases. Ind. Eng. Chem. Research, 35 (1996) 3673-3679.
[31] L.X. Ito, M.L. Aguiar. A study of the porosity of gas filtration cakes, in: Proceedings of the Filtech, vol. 2, Düsseldorf, October, (2003) 116-123.
[32] W. D. Marra Jr., M. V. Rodrigues, R.G.A. Miranda, M.A.S. Barrozo, J.R. Coury. The effect of the generation and handling in the acquired electrostatic charge in airborne particles. Powder Technol. 191 (2009) 299–308.
22
ACCEPTED MANUSCRIPT [33] L.G.M. Vieira, J.J.R. Damasceno, M.A.S. Barrozo. Improvement of hydrocyclone separation
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performance by incorporating a conical filtering wall. Chem. Eng. Proc. 49 (2010) 460-467.
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[34] M.A. Santos, R.C. Santana, F. Capponi, C.H. Ataíde, M.A.S. Barrozo, Effect of ionic species on the
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performance of apatite flotation. Sep. Purif. Technol. 76 (2010) 15-20.
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[35] M.S. Oliveira, G.M. Queiroz, R.C. Guimarães, C.H. Ataíde, M.A.S. Barrozo. Selectivity in phosphate
MA
column flotation. Minerals Eng. 20 (2007) 197-199
[36] B. Huang, Q. Yao, S. Li, H. Zhao, Q. Song, C. You. Experimental investigation on the particle
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capture by a single fiber using microscopic image technique. Powder Technol., 163 (2006) 125-133.
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ACCEPTED MANUSCRIPT Table 1. Single fiber collection mechanisms
References
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Mechanical mechanisms 1/3
d 2pρ P g
I 0.0334 St 3/2
(direct intercep.) (5) (inertial) (6)
ln 1- ε 3 1- ε ; - + 1- ε 2 4 4
D=
K BTFS 3πμd p
;
NR
dp dc
; C r 1 1.996Kn c ; Kn c 2 / d c ;
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;
NR
24
[10]
[22] 1/3
εPe Cd = 1+ 0.388Kn c Ku
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Ud C D
Ku = -
D
2
Where:
[20]
[21]
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2 NR DI 0.6 Cr Ku 1 N R
Pe =
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(gravitational) (4)
18μU
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ηG =
(diffusional) (3)
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ε -2/3 ' ηD = 1.6 Pe Cd Cd Ku
;
Rec
1/3 ; ε -2/3 C'd = 1/ 1+1.6 Pe Cd Ku
Ug d c
ACCEPTED MANUSCRIPT
24.80
Al2O3
5.00
Fe2O3
2.44
F-
2.00
K2O
1.24
MgO
0.51
Na2O
0.13
Cl-
0.11
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P2O5
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28.10
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SiO2
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32.20
D
CaO
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Mass (%)
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Main constituents
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Table 2. Chemical composition of the phosphate rock concentrate
25
ACCEPTED MANUSCRIPT Table 3– Experimental penetration as a function of particle size for three levels of filtration velocity (U =
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0.05. 0.08 and 0.12 m/s) and three levels of particle charge (0. -3 and -6 kV).
Corona: -3 kV
Corona: -6 kV
5.5
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Corona: 0 kV
4.1
4.0
3.9
4.7
3.4
2.1
1.9
1.5
1.1
1.2
1.3
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1.0
0.8
0.8
0.8
0.9
1.0
0.6
0.4
0.7
0.6
0.6
0.4
0.3
0.2
0.4
0.4
0.3
0.05 m/s
0.08m/s
0.12m/s
2.31
22.0
18.9
11.8
2.69
6.4
5.7
4.1
3.26
3.9
3.7
3.1
3.98
3.1
2.5
0.7
5.95
1.8
1.2
D
(10-6m)
0.12m/s
0.05 m/s 0.08m/s
0.12m/s
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0.6
0.05 m/s 0.08m/s
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dp
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Experimental penetration[%]
Table 4- Dielectric constant of the particles used in the present work and previous studies [11, 20]. Author
Particle dieletric constant, εp (-)
Lundgren e Whitby [20]
7.6
Coury [11]
2.6
This work
6.5
26
ACCEPTED MANUSCRIPT Figures Captions Fig. 1. Single collector efficiency as a function of particle diameter [11].
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Fig. 2. Scheme of the experimental apparatus
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Fig. 3. Scheme of filtration support (Dimensions in cm)
Fig. 4. The polypropylene fabric filter utilized in this work (1000x).
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Fig. 5. Corona charger device. Dimensions in cm.
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Fig. 6. Median charge and S.Dev. vs. particle diameter for three cases of particle charge evaluated (0, -3 kV and -6 kV)
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Fig. 7. Penetration as a function of particle size for three levels of filtration velocity (U = 0.05, 0.08 and
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0.12 m/s) and three levels of particle charge (0, -3 and -6 kV).
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Fig. 8. Experimental and calculated penetration as a function of particle size for three filtration velocities (U = 0.05, 0.08 and 0.12 m/s) and three levels of particle charge ( 0, -3 and -6 kV). Calculated penetration
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were obtained from Eq (2) and the equations in Table 1 (mechanical mechanisms) and Eq. (10) for the electrophoretic mechanism
Fig. 9. Comparison between the experimental results for ηE and the predictions by: (a) Eq. (9); (b) Eq. (10); and (c) Eq. (14).
Fig. 10. Comparison between the experimental results for ηE of three selected studies [11, 20 and the present work] with the predictions from Eq. (15).
Fig. 11. Increase in pressure drop the filter as a function of mass of dust collected (MTR) for three filtration velocities and three levels of corona voltage
27
ACCEPTED MANUSCRIPT Figure 1
-1
10
-2
TOTAL electrophoretic
10
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difusional
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10
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0
-3
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Collection efficiency of an individual collector
10
gravitational -8
1x10
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1x10
-7
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dP [m]
28
inertial + dir. intercep 1x10
-6
ACCEPTED MANUSCRIPT Figure 2
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Clean Air
high voltage source
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P
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Rotating Plate
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corona charger
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Electrostatic Charge Classifier
29
Particle Size Analyzer
Flowmeter pump
Computer
ACCEPTED MANUSCRIPT Figure 3
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3,2
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4
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Ø4,7
2
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3
22
1 5
2
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Legend: - filtering media; - isokinetic probe, - pressure drop; - aerosol inlet
30
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Figure 4
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Figure 5
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ACCEPTED MANUSCRIPT Figure 6 1,0x10
-16
-16
-3,0x10
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-2,0x10
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-16
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-1,0x10
corona 0 kV corona -3 kV corona -6 kV S. Dev
-16
2
3
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0,0
33
4 -6
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5
6
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5
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10
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0
0 5
6
2
NU
4 -6
dP [10 m]
MA
25
D
5
0
2
3
4
5 -6
dP [10 m]
34
5 -6
15
10
4
dP [10 m]
TE
Penetration [%]
20
3
U=0.12 m/s corona 0 kv corona -3 kv corona -6 kv
(c)
AC CE P
3
SC
10
PT
20
15
2
U=0.08 m/s corona 0 kv corona -3 kv corona -6 kv
(b) Penetration [%]
20
Penetration [%]
25
U=0.05 m/s corona 0 kv corona -3 kv corona -6 kv
(a)
6
6
ACCEPTED MANUSCRIPT Figure 8
U=0.05 m/s Experimental 0 kv Experimental -3 kv Experimental -6 kv Theoretical 0 kv Theoretical -3 kv Theoretical -6 kv
15
RI
20
U=0.08 m/s Experimental 0 kv Experimental -3 kv Experimental -6 kv Theoretical 0 kv Theoretical -3 kv Theoretical -6 kv
(b)
SC
15
10
NU
10
5
4
5
5
0
6
-6
dP [10 m]
2
3
D
U=0.12 m/s Experimental 0 kv Experimental -3 kv Experimental -6 kv Theoretical 0 kv Theoretical -3 kv Theoretical -6 kv
(c)
20
15
10
5
0
3
4
5 -6
dP [10 m]
35
5
dP [10 m]
25
2
4 -6
TE
3
Penetration [%]
2
MA
0
AC CE P
Penetration [%]
20
Penetration [%]
(a)
PT
25
25
6
6
ACCEPTED MANUSCRIPT
1
1
(a)
This work ref. [11] ref. [20] 1E-3 1E-3
0,01
0,1
1E-3 1E-3
This work ref. [11] ref. [20] 0,01
TE
(c)
E experim.
0,1
0,01
1E-3 1E-3
This work ref. [11] ref. [20] 0,01
0,1
E theor. eq. 14
36
0,1
E theor. eq. 10
D
1
1
MA
E theor. eq. 9
0,01
NU
0,01
SC
E experim.
0,1
AC CE P
E experim.
0,1
RI
(b)
PT
Figure 9
1
1
ACCEPTED MANUSCRIPT Figure 10 ..
PT
1
RI
This work ref. [11] ref. [20]
SC
0,01
NU
E experim
0,1
1E-3 1E-3
0,01
AC CE P
TE
D
MA
E theor. eq. 15
37
0,1
1
ACCEPTED MANUSCRIPT Figure 11
U = 0.05 m/s corona 0 kV corona -3 kV corona -6 kV eq. 12
P - P0 [Pa]
160
120 80
120 80
40
NU
40
0
0 1.0x10
-5
2.0x10
-5
3.0x10
0.0
-5
MA
MTR [Kg] 240
(c)
120
1.0x10
U = 0.12 m/s corona 0 kV corona -3 kV corona -6 kV eq. 12
80
40 0
0.0
1.0x10
-5
2.0x10
-5
MTR [Kg]
38
3.0x10
-5
-5
MTR [Kg]
TE
160
D
200
P - P0 [Pa]
0.0
AC CE P
P - P0 [Pa]
160
200
U = 0.08 m/s corona 0 kV corona -3 kV corona -6 kV eq. 12
RI
200
(b)
SC
(a)
PT
240
240
4.0x10
-5
2.0x10
-5
3.0x10
-5
ACCEPTED MANUSCRIPT Graphical Abstract
PT
1
This work ref. [11] ref. [20]
RI SC
1E-3 0,01
0,1
1
D
MA
E theor. eq. 15
TE
1E-3
NU
0,01
AC CE P
E experim
0,1
39
ACCEPTED MANUSCRIPT Highlights
PT
The effect of particle charge level on the performance of a fiber filter during aerosol filtration was studied.
RI
A relationship between the charge of particles and their diameter was identified.
SC
Correlations from the literature did not adequately predict the experimental data behaviour.
NU
A new expression for the electrophoretic collection mechanism was proposed. The new correlation represented well the experimental data of this work, as well as of other works
AC CE P
TE
D
MA
of the literature
40