Calculation of aerosol collection in fluidized filter beds

A method is proposed for calculating aerosol collection in fluidized filter beds. The method employs the bubble assembly model of fluidization and considers the bed to be a series of compartments, each of which comprises two or three phases. Aerosol collection is assumed to occur in these phases in accordance with existing theories of particle deposition. The validity of the method is tested against available experimental data.     

Drinking water denitrification in membrane bioreactor/membrane contactor systems

The results of an experimental study, developed on a membrane bioreactor/membrane contactor pilot plant, aimed at drinking water denitrification are presented and discussed. In the adopted configuration the water, contaminated by nitrates, flows inside the fibres of a membrane unit. Due to the existing concentration gradient, nitrates migrate through the membrane and are reduced to nitrogen gas by the autotrophic biomass attached on the exterior of the fibres, and fed with an external source of organic carbon. Data obtained varying influent flow values and nitrate influent concentrations, confirm the potentiality of the system and show the possibility of full-scale applications. A new mathematical model, useful for both simulation and design of the system is also presented. The model is based on simple mass balances in the flow direction, and through the membrane. Each fibre is considered a plug-flow reactor, and nitrate concentration outside the fibres is assumed to be always zero. To obtain an explicit expression useful for simulation and design of membrane bioreactors/membrane contactors, steady-state conditions are supposed. Experimental data are in good agreement with the model's results, and confirm its applicability.     

Simulation of Particle Size-Selective Air Samplers Placed in a Polydisperse Aerosol

The results of a numerical simulation of several air sampling instruments are presented. They are assumed to sample the same aerosol, with a log-normal particle-size distribution. Four instruments were studied: the 10-mm nylon cyclone, the MRE 113A gravimetric sampler, the CPM 3, and the CIP 10. The experimental data of particle collection efficiency were reduced by a model for each instrument. The model used combines two cumulative log-normal distribution functions, in order to have a good degree of flexibility necessary for representing the data of some devices that exhibit a maximum in efficiency (CPM 3, CIP 10). The concentrations “measured” by several air samplers were compared with each other; the differences were analyzed as functions of the aerosol parameters: mass median aerodynamic diameter and σ_g. The results that were obtained and those calculated from standard collection efficiencies, defining the conventional alveolar fraction of the aerosol, were also taken into account. This simulation method can be extended to any type of instrument and aerosol, and enables the prediction of the maximal deviations that could be observed between different instruments, or between one instrument and some reference standards.     

Contribution of synchrotron X-ray holotomography to the understanding of liquid distribution in a medium during liquid aerosol filtration

The three-dimensional structure of a fibrous filter determines its behaviour during filtration, such as the obtained pressure drop, the fractional efficiency and the filter lifetime. Therefore, suitable parameters describing the inner structure (the local packing density) are key inputs for modelling filter performance accurately. The synchrotron X-ray holotomography, carried out at the European Synchrotron Radiation Facility, was performed in this study to provide information on the three-dimensional structure of a fibrous filter. Moreover, this non-invasive technique was used to determine the liquid distribution in a filter clogged with a liquid aerosol of di-ethyl-hexyl-sebacate. These samples were imaged at a voxel size of 0.7 μm, which allows the quantification of the different phases within the filter (liquid, fibres and void space). The results complete the two-dimensional studies obtained by scanning electron microscopic and highlight the formation of liquid menisci not only on the filter surface but also in the filter depth. Image analyses of synchrotron X-ray holotomography radiographs also highlight a heterogeneous liquid distribution along the thickness of the clogged filter.     

An analysis of various nucleation mechanisms for sulfate particles in the stratosphere

A theoretical analysis of particle formation mechanisms under stratospheric conditions was carried out using a fully interactive one-dimensional model of aerosol formation and evolution. The formation mechanisms considered are homogeneous, ion and heterogeneous heteromolecular nucleation of H₂SO₄---H₂O systems, the clustering of sulfate radicals, and heterogeneous nucleation onto stable neutral ion—ion recombination complexes. We develop theoretical expressions for the nucleation rates, describe the manner in which the nucleation mechanisms are incorporated into the model, and present the results of model calculations. We find that although the different nucleation processes lead to greatly different rates of particle formation, the observed characteristics of the aerosol are hardly affected by the assumed particle formation mechanism. Consequently, it will be difficult to devise measurements to evaluate the relative importance of the various formation mechanisms. Our results show that the homogeneous and ion nucleation rates in the stratosphere are negligible. Heterogeneous nucleation onto stable ion—ion recombination products and the clustering of sulfate radicals are two processes which could lead to the generation of large numbers of particles in the stratosphere. Using presently available experimental techniques it is not possible to determine unambiguously which formation mechanism is responsible for the production of the stratospheric particles.     

The Dyeing of Synthetic-polymer Fibres with Aerosols of Disperse Dyes

A method is described for the determination of the rates of diffusion of 1,4-diaminoanthraquinone in polyester, nylon and cellulose triacetate fibres under anhydrous conditions below 150°C. As the results of the measurements of diffusion were favourable, the dyeing of synthetic-polymer fibres, particularly polyester fibres, by application of solid disperse dye in the form of an aerosol was studied. Batch dyeing of loose polyester fibres, utilising a fluidised-bed principle, was investigated, as was continuous dyeing by filtration of an aerosol through a moving layer of fibres. The latter method appears to be suitable for bulk dyeing.     

Zur frage der Abscheidung von Aerosolteilchen durch Diffundierende Gase

A simple model for the diffusiophoresis in the lung was tested. It consists essentially of two channels, which have been divided by a membrane filter. In both channels aerosol was flowing with a different carrying gas. Gas exchange through the membrane filter occurred and caused different deposition rates on each side of the filter. For equimolar counterdiffusion the deposition on the side of the heavier gas predominated. For model experiments with a “respiratory quotient” of 0·85 (volume-ratio of exhaled CO₂ to inhaled O₂) more particles have been deposited on the side of the lighter gas, but the deposition rate was much lower than in the case of equimolar counterdiffusion. The experimental results are supported by theoretical calculations. The effect of diffusiophoresis is small compared to other deposition mechanisms in the lung.     

Nondestructive Analysis of Total Nonvolatile Carbon by Forward Alpha Scattering Technique (FAST)

The oldest method of nuclear analysis, Rutherford scattering of alpha particles, is the basis of a technique we have developed that is capable of the quantitative nondestructive determination of carbon and all other elements lighter than sodium on an aerosol filter. Samples are collected on thin-stretched teflon filters, which are then placed in the 30-MeV alpha-particle beam of the Crocker Nuclear Laboratory's 193-cm cyclotron. Scattered alpha-particles are detected at the forward angles of 62 and 74 degrees, and the method has become known as FAST, for forward alpha scattering technique. The fluorine content of the air particles is assumed to be much less than the carbon content, and the filter blank carbon is subtracted from the known CF₂ ratio of teflon. Sensitivities for carbon are limited by the need to subtract the 70 μg/cm² of carbon in the filter, which can be done to ±5%, or ±3.5 μg/cm². This amounts to ±0.15 μg/m³ for the National Park Service aerosol samples. Since the FAST analysis is done in vacuum, only nonvolatile species are measured. This technique provides an alternative way to measure carbon without using artifact-prone quartz filters.     

A mathematical model for unsteady-state oxygen transfer in an external-loop airlift reactor

A mathematical model for simulation of unsteady-state oxygen transfer in an external-loop airlift reactor was developed. The airlift reactor was represented by a number of interconnected tanks, each of which was assumed to be well mixed. The effect of gas circulation rate on the oxygen transfer was considered. The model can be used for the determination of mass transfer performance of the airlift reactor in which the whole liquid phase cannot be assumed to be fully backmixed. The simulation results showed a good agreement with experimental results.     

A SIMPLIFIED METHOD OF CALCULATING AEROSOL FILTRATION IN FLUIDIZED FILTERS

A simplified model of calculating aerosol filtration in fluidized filters is proposed. Unlike earlier methods (Peters et al., 1982; Ushiki and Tien, 1984) which require compartment-to-compartment calculations, this method assumed that parameters which characterize fluidized bed structure, such as the volume fractions of the dense and bubble phases and the bubble diameter can be considered constant for the entire bed. Analytical solutions of effluent concentration and the total collection efficiency were obtained which correspond to two limiting situations regarding gas mixing in the dense phase. Comparisons between the analytical solutions and experimental data as well as results from more exact compartment-to-compartment calculations indicate that the simplified method gives results of reasonably good accuracy and is adequate for preliminary design calculations.     

Analytic solutions for filtration of polydisperse aerosols in fibrous filter

In this study, analytical solutions for penetration efficiency of a polydisperse aerosol in fibrous filter were derived employing Brownian diffusion and inertial impaction as removal mechanisms. Size distribution of aerosol particles was assumed to be represented by a log-normal function during the filtration. Derived solutions were compared with the exact solution, which is not based on the log-normal assumption, showing good agreement. Error resulting from the log-normal assumption was shown to be greater in the impaction-dominant regime than in the diffusion-dominant regime due to higher size dependency of collision kernel which destructed log-normal shape of size distribution. The penetration efficiency of the analytic solution initially decreases faster and then decreases slower than that of the exact solution in the diffusion-and intermediate dominant size regimes due to its polydispersity of particle distribution, while it overpredicted the particle removal in the impaction size range because of neglect of polidispersity effect. A new solution for the most penetrating particle diameter was also provided showing the dependence on filtration velocity, fiber volume fraction, and fiber size.     

A SIMPLIFIED METHOD OF CALCULATING AEROSOL FILTRATION IN FLUIDIZED FILTERS

A simplified model of calculating aerosol filtration in fluidized filters is proposed. Unlike earlier methods (Peters et al., 1982; Ushiki and Tien, 1984) which require compartment-to-compartment calculations, this method assumed that parameters which characterize fluidized bed structure, such as the volume fractions of the dense and bubble phases and the bubble diameter can be considered constant for the entire bed. Analytical solutions of effluent concentration and the total collection efficiency were obtained which correspond to two limiting situations regarding gas mixing in the dense phase. Comparisons between the analytical solutions and experimental data as well as results from more exact compartment-to-compartment calculations indicate that the simplified method gives results of reasonably good accuracy and is adequate for preliminary design calculations.     

A multiple state stochastic model for deep-bed filtration

A one-parameter stochastic model has been developed for the prediction of dynamic pressure drop in a deep-bed filter. The model is based on a finite-state and discrete-time Markov chain method whereby the pressure drop in a deep-bed filter can be estimated at discrete time intervals. The proposed model is simpler than the stochastic birth and death models available in literature. The bed is assumed to pass through different states of porosity during the filtration and it is spatially lumped in each state. For pressure drop calculation, the Carman-Kozeny equation is used in conjunction with the Payatakes-Tien-Turian model. Model equations are simple and can be easily solved on a personal computer. The theoretical results agree well with the plant data as well as with the available experimental data.     

Experimental filtration efficiencies for large pore nuclepore filters

Experimental filtration data were collected in an effort to validate an impaction model previously developed and presented. Using a sampler with a 9.5 μm pore diameter Nuclepore filter, collection efficiencies were measured for both liquid and solid aerosols over a size range of 2–9 μm. Data for the liquid aerosol showed good agreement with the impaction model; however, data for the solid aerosol indicated an appreciably lower collection efficiency than predicted by the model. The liquid aerosol data validate the impaction model. The solid aerosol data indicate particle bounce or reintrainment subsequent to impact and underscore particle capture as a problem to be dealt with if the Nuclepore surface is to be used as a size selective filter.     

Characterization of An Open-Pored Nickel Foam with Respect to Aerosol Filtration Efficiency by Means of Measurement and Simulation

The deposition of micron and submicron particles in metallic, ceramic, or synthetic open-pored foams is a special field of aerosol filtration in porous media. This is due to the more complicated pore structure than, for example, fibrous filter media. Therefore, the measurement as well as the simulation of aerosol filtration in open-pored foams involves certain custom-built techniques.

The filter efficiency for micron and submicron particles can be measured by differential electrical mobility analyser systems (DEMAS) or optical particle counters (OPC). Empirical formulas are available in literature for open-pored polyurethane foams to determine their aerosol filtration efficiency and pressure drop. An additional method for characterization is direct numerical simulation (DNS) by means of a three-dimensional (3D) model of the pore structure. These models can be obtained either by tomography or by mathematical generation.

In this work, the filter efficiency of an open-pored nickel foam with a cell diameter of 450 μm is determined by the methods previously mentioned. The experimental results are in good agreement with the results of the 3D simulation and a semi-empirical approach for polyurethane foams is adapted for a nickel foam.

Copyright 2015 American Association for Aerosol Research     

An Instrument for the Classification of Aerosols by Particle Relaxation Time: Theoretical Models of the Aerodynamic Aerosol Classifier

A new aerosol particle classifier, the aerodynamic aerosol classifier (AAC), is presented and its classifying characteristics are determined theoretically. The AAC consists of two rotating coaxial cylinders rotating at the same angular velocity. The aerosol to be classified enters through a gap in the inner cylinder and is carried axially by particle-free sheath flow. The centrifugal force causes the particles between the rotating cylinders to move in the radial direction and particles of a narrow range of particle relaxation times exit the classifier through a gap in the outer cylinder with the sample flow. Particles with larger relaxation times impact and adhere to the outer cylinder and particles with smaller relaxation times exit the classifier with the exhaust flow. Thus, the aerosol is classified by particle relaxation time from which the aerodynamic equivalent diameter can easily be found. Four theoretical models of the instrument transfer function are developed. Analytical particle streamline models (with and without the effects of particle diffusion), like those often used for mobility classifiers, are developed for the case when the centrifugal acceleration field is assumed to be uniform in the radial direction. More accurate models are developed when this assumption is not made. These models are the analytical limiting trajectory model which neglects the effects of diffusion and a numerical convective diffusion model that does not. It is shown that these models agree quite well when the gap between the cylinders is small compared to the radii of the cylinders. The models show that, theoretically, the AAC has a relatively wide classification range and high resolution.

Copyright 2013 American Association for Aerosol Research     

Thermophoresis of Liquid Airborne Particles in Gravity at Continuum Regime

An analytical study is presented for the thermophoretic motion of an aerosol droplet in a prescribed temperature gradient under the influence of gravity. The Peclet and Reynolds numbers are assumed small, so that the temperature distributions are governed by the Laplace equation and the flow fields are governed by the Stokes equation. The temperature discontinuity, thermal creep, and hydrodynamic slip features that occurred at the droplet surface are considered. The slow motion of a liquid aerosol sphere subject to the combination of thermophoresis and sedimentation is obtained by superposition of the individual solutions for pure thermophoresis and pure body-force-driven motion, since both the governing equations and boundary conditions in this problem are linear. The stream functions of the internal and external flows, which are displayed in both the laboratory frame and a reference frame moving with the droplet, as well as the migrating velocity of a droplet, are formulated generally. The flow structures manifest more remarkable topologies than do those of common intuition developed from sedimentation. Our results can be simplified to the corresponding motion for solid aerosol particles.     

Analysis and design of a centrifugal filter geometry for entrained particle separation

A method is developed for the analysis of centrifugal filters that are applied to the removal of small particles from a carrier fluid. The particular application considered is the removal of entrained microscopic oil droplets from “blow-by” escaping from the crankcase of an internal combustion engine. The analysis is general for the type of filter geometry considered, and is applied to two particular vane shapes, one of which is circular, and the other of which maintains a constant angle between the vane blade and the outgoing radius; the analysis results in expressions for transverse distances travelled by the particles between the vanes within their residence time within the filter. It is shown that an optimum radius of curvature or blade angle exists in each case. These expressions are used to predict filter efficiency in 3 models: a direct deterministic model, a model that incorporates the statistical nature of particle movement, and a model that includes a measure of particles susceptibility to be maintained in suspension due to turbulent fluctuations within the flow. Experimental results are given for a range of particle sizes and filter rotation speeds. It is shown that the deterministic model estimates the speed at around 95% efficiency well, but that the statistically based model gives better prediction over a broad range of particle sizes and spin speeds. The inclusion of a term to measure the particles susceptibility to turbulence is shown to give much better prediction for sub-micron particle sizes.     

RADIATIVE DRYING MODEL OF POROUS MATERIALS

A transient one dimensional first principles model is developed for the drying of a porous material (paper) that includes both heat and mass transfer. All three modes of heat transfer are considered; conduction, convection and radiation. The conduction is assumed to be in one dimension, through the porous material. The convection is assumed to exist only at the surface as a boundary condition. The radiation is assumed to be a volumetric phenomenon, so that the material internally absorbs, emits, and scatters energy. The absorption and scattering coefficients are spectrally dependent. Furthermore, the material is considered to have a non-unity refractive index with diffuse surfaces. In the mass transfer it is assumed that water exists in three phases: bound, free and vapor. The results provide profiles within the material for each moisture phase, temperature, and pressure and the effect of radiation on these distributions.     

The effect of the flow field recalculation on fibrous filter loading: a numerical simulation

We present a simple model for the loading process of aerosol particles on fibrous filters with the aim to show the influence that the flow recalculation around a single fibre has on the complete loading process, up to the final clogging of the filter. At each loading stage (i.e., at any given degree of particle deposition), the change of shape of the fibre is presented, and information on the flow field around a fibre and the filter efficiency are obtained. The effect of the flow recalculation on the filter efficiency is shown; the single fibre efficiency is proven to be overestimated when the effect of further deposition is neglected. To perform the study, we have developed a CFD code and we have combined it with particle trajectory simulations.