A Stochastic Model for Particle Deposition and Bounceoff

A new model for particle deposition and bounceoff that combines current knowledge of turbulent bursts with the stochastic properties of turbulent fluctuations is presented. The model predictions for deposition velocities agree with experimental results in the literature for dimensionless particle relaxation time τ_p ⁺ > 2. For τ_p ⁺ > 10, most of the particles delivered to the edge of the viscous sublayer are able to deposit onto the surface due to their inertia; the deposition velocity approaches an asymptotic value because the process becomes limited by the rate of turbulent delivery to the viscous sublayer. Because of the penetration of turbulent fluctuations into the viscous sublayer, the minimum values of vertical velocities needed for particles to deposit onto the surface are smaller than those predicted by the free flight model. Most of the deposition occurs from those turbulent fluctuations at the upper tail of the distribution of the vertical component of air velocity.

In addition to the deposition velocity, the model is able to provide the distribution of particle velocities on reaching the surface which is used to compute the fraction of particle bounceoff. The model predictions for the fractions of rebound agree reasonably with the measured results from a wind tunnel experiment for τ_p ⁺ > 2. However, both the deposition velocity and the fraction of rebound are underestimated by the model for τ_p ⁺ < 2. Other mechanisms such as Brownian diffusion must be included in further revisions to this model in order to obtain satisfactory predictions for smaller values of τ_p ⁺.     

Ultrafine Particle Sampling with the UNC Passive Aerosol Sampler

A model is presented to describe the collection of ultrafine particles by the UNC passive aerosol sampler. In this model, particle deposition velocity is calculated as a function of particle size, shape and other properties, as well as a function of sampler geometry. To validate the model, deposition velocities were measured for ultrafine particles between 15 and 90 nm in diameter. Passive aerosol samplers were placed in a 1 m ³ test chamber and exposed to an ultrafine aerosol of ammonium fluorescein. SEM images of particles collected by the samplers were taken at 125 kX magnification. Experimental values of deposition velocity were then determined using data from these images and from concurrent measurements of particle concentration and size distribution taken with an SMPS. Deposition velocities from the model and from the experiments were compared and found to agree well. These results suggest that the deposition velocity model presented here can be used to extend the use of the UNC passive aerosol sampler into the ultrafine particle size region.     

Fluxes of Fine Particles Over a Semi-Arid Pine Forest: Possible Effects of a Complex Terrain

Semi-arid forests are of growing importance due to expected ecosystem transformations following climatic changes. Dry deposition of atmospheric aerosols was measured for the first time in such an ecosystem, the Yatir forest in southern Israel. Size-segregated flux measurements for particles ranging between 0.25 μm and 0.65 μm were taken with an optical particle counter (OPC) using eddy covariance methodology. The averaged deposition velocity (V_d ) at this site was 3.8 ± 4.5 mm s^?1 for 0.25–0.28 μm particles, which is in agreement with deposition velocities measured in mid and northern latitude coniferous forests, and is most heavily influenced by the atmospheric stability and turbulence conditions, and to a lesser degree by the particle size. Both downward and upward fluxes were observed. Upward fluxes were not associated with a local particle source. The flux direction correlated strongly with wind direction, suggesting topographical effects. We hypothesize that a complex terrain and a patchy fetch affected the expected dependence of V_d on particle size and caused the observed upward fluxes of particles. The effect of topography on the deposition velocity grows greater as particle size increases, as has been shown in modeling and laboratory studies but had not been demonstrated yet in field studies. This hypothesis is consistent with the observed relationship between V_d and the friction velocity, the topography in the area of the flux tower, and the observed correlation of flux direction with wind direction.

[Supplementary materials are available for this article. Go to the publisher's online edition of Aerosol Science and Technology to view the free supplementary files.]

Copyright 2013 American Association for Aerosol Research     

Effect of air flowrate on particle velocity profile in a circulating fluidized bed

The research was conducted in a cold flow circulating fluidized bed (CFB). The diameter and height of riser are 5 and 200 cm, respectively. The objective is to study effect of gas velocity on hydrodynamic of glass beads having mean diameter of 547 micron and density of 2,400 kg/m³. The measurement of particle velocity profile was achieved by using a high-speed camera and an image processing software. A probe of 0.5 cm in diameter was inserted into the riser at the height of 110 cm from gas distributor and was set at 3 positions along the radius of the riser; 0, 0.6, and 1.8 cm from center. Transport velocity (U _tr ), core-annulus velocity (V _CA ) and minimum pneumatic velocity (V _mp ) were employed in determining solid flow pattern in the riser. It was observed that the flow regimes changed from fast fluidization to core-annulus and to homogeneous dilute bed when the gas velocities increased from 7, 8 and 9 m/s, respectively. The results from high-speed camera showed that glass beads velocity existed a maximum value at the center of the riser and gradually decreased toward the wall for all three gas velocities. It was also found that most of solid traveled upward in the core of the riser, however, solid traveled downward was identified at the wall layer.     

A numerical study of particle wall-deposition in a turbulent square duct flow

The deposition of dense solid particles in a downward, fully developed turbulent square duct flow at Re_τ = 360, based on the mean friction velocity and the duct width, is studied using large eddy simulations of the fluid flow. The fluid and the particulate phases are treated using Eulerian and Lagrangian approaches, respectively. A finite-volume based, second-order accurate fractional step scheme is used to integrate the incompressible form of the unsteady, three-dimensional, filtered Navier-Stokes equations on an 80 × 80 × 128 grid. A dynamic subgrid kinetic energy model is used to account for the unresolved scales. The Lagrangian particle equation of motion includes the drag, lift, and gravity forces and is integrated using the fourth-order accurate Runge-Kutta scheme. Two values of particle to fluid density ratio (ρ_p/ρ_f = 1000 and 8900) and five values of dimensionless particle diameter (d_p/δ × 10⁶ = 100, 250, 500, 1000 and 2000, δ is the duct width) are studied. Two particle number densities, consisting of 10⁵ and 1.5 × 10⁶ particles initially in the domain, are examined.Variations in the probability distribution function (PDF) of the particle deposition location with dimensionless particle response time, i.e. Stokes number, are presented. The deposition is seen to occur with greater probability near the center of the duct walls, than at the corners. The average streamwise and wall-normal deposition velocities of the particles increase with Stokes number, with their maxima occurring near the center of the duct wall. The computed deposition rates are compared to previously reported results for a circular pipe flow. It is observed that the deposition rates in a square duct are greater than those in a pipe flow, especially for the low Stokes number particles. Also, wall-deposition of the low Stokes number particles increases significantly by including the subgrid velocity fluctuations in computing the fluid forces on the particles. Two-way coupling and, to a greater extent, four-way coupling are seen to increase the deposition rates.     

A consideration of circulating bed electrodes for the recovery of metal from dilute solutions

A comparison is made of three types of circulating particulate electrodes: spouted (circulating) bed (SBE), vortex bed (VBE) and moving bed (MBE). In applications such as metal recovery, all electrodes perform similarly in terms of current efficiency. On the basis of scale-up, it appears that the spouted bed electrode is the preferred system.Nomenclature I cell current (A) - F Faraday constant (94487 C mol^–1) - C dimensionless concentration - C _F friction factor - C ₀ Initial concentration (mol m^–3) - D pipe equivalent diameter (m) - e _b bed voidage - e _c voidage of conveying section - L bed length (m) - S _b cross section area of bed (m²) - S _T cross section area of conveying section (m²) - T dimensionless time=It/nFVC ₀ - U _f superficial liquid velocity in conveying (m s^–1) - U _i particle terminal velocity corrected for wall effects (m s^–1) - U _s particle velocity in transport (m s^–1) - U _SL slip velocity (m s^–1) - t time (s) - V electrolyte volume (m³) - V _f liquid velocity in the bed (m s^–1) - V _mf minimum fluidization velocity (m s^–1) - V _s particle velocity in the bed (m s^–1) - P pressure drop (NM^–2) - fluid density (kg m^–3) - _s particle density (kg m^–3) - Re Reynolds number     

Radial gas mixing characteristics in a downer reactor

In a downer reactor (0.1 m-I.D.x3.5 m-high), the effects of gas velocity (1.6-4.5 m/s), solids circulation rate (0–40kg/m²s) and particle size (84, 164 Μm) on the gas mixing coefficient have been determined. The radial dispersion coefficient(D _r ) decreases and the radial Peclet number (Pe_r) increases as gas velocity increases. At lower gas velocities, D_r in the bed of particles is lower than that of gas flow only, but the reverse trend is observed at higher gas velocities. Gas mixing in the reactor of smaller particle size varies significantly with gas velocity, whereas gas mixing varies smoothly in the reactor of larger particle size. At lower gas velocities, D_r increases with increasing solids circulation rate (G_s), however, D_r decreases with increasing G_s at higher gas velocities. Based on the obtained D_r values, the downer reactor is found to be a good gas-solids contacting reactor having good radial gas mixing.     

Eulerian Model for Prediction of Particle Transport and Deposition in Turbulent Duct Flows with Thermophoresis

The Reynolds-averaged equations for turbulent particle population/transport in an Eulerian framework must be closed by specifying models for several terms: a turbophoretic force; a turbulent thermophoretic force; and a turbulent particle-diffusion term. In this article, new models are proposed for the turbophoretic term, as a particle-size dependent extrapolation of the corresponding turbulent fluid-velocity correlation, and for the turbulent thermophoretic term as an eddy-viscosity-scaled multiple of the corresponding mean thermophoretic term, appropriate for small low-inertia particles with τ⁺_p < 10. When the turbophoresis model is incorporated in a system of equations that describes particle motion within the surrounding fluid, it predicts particle deposition velocities that are in good agreement with experimental data over a range of particle sizes. When this equation system is included in a computational model to predict particle transport in turbulent pipe flows, the efficiency of particle deposition in pipes with upstream heating and downstream cooling is found to be in fair agreement with experimental measurements at two different Reynolds numbers, and over a range of particle sizes and temperature differences.

Copyright 2015 American Association for Aerosol Research     

Treatment of settled piggery waste by a down‐flow anaerobic fixed bed reactor

A study of the effect of organic volumetric loading rate (B_V) on the performance of a down‐flow anaerobic fixed bed reactor (DFAFBR) treating settled piggery waste was carried out at a range of between 1.1 and 6.8 g COD dm^?3 d^?1. The reactor operated at good removal efficiencies and stability under the operational conditions studied. Logarithmic empirical equations described adequately the removal efficiency for different parameters studied (COD, SCOD, BOD, TS, VS, TSS, VSS and phosphorous). Although process stability was affected by the increase of B_V, process failure was not observed. A logarithmic relationship was found to describe the influence of B_V on the TVFA/alkalinity ratio (p). A linear correlation was found between the effluent substrate concentration and the values of p and between p and the CO₂/CH₄ ratio in the biogas. The effect of the hydraulic volumetric loading rate (H_V) on the flow pattern of the reactor was evaluated. Dispersion number (D_n) was in the range of 0.17–0.37 for the maximum and minimum values of H_V studied, respectively. The ratio between the real and theoretical HRT increased as the H_V decreased. These results demonstrate that axial dispersion increased as the H_V and the Reynolds number decreased. Due to the hydraulic behaviour of the reactor, the kinetic model developed by Lawrence and McCarty was used for describing the experimental results obtained. Maximum specific substrate removal rate (K), specific organic loading rate constant (K_L), microbial decay coefficient (K_d), microbial yield coefficient (Y), maximum microbial growth rate (U_M) and saturation constant (K_S) were found to be: 3.1 (g COD g VSS^?1 d^?1), 3.0 (g COD g VSS^?1 d^?1), 0.062 (d^?1), 0.15 (g VSS g COD removed^?1), 0.39 (d^?1) and 2.6 (g SCOD dm^?3), respectively. Copyright © 2004 Society of Chemical Industry     

Deposition of Particles by a Confined Impinging Jet onto a Flat Surface at Re = 10 4

An axisymmetric turbulent air jet flow (with vertical and downward orientation) laden with fluorescent solid particles was impinged normally onto a flat surface. The particle deposition efficiency and distribution on the flat surface were measured experimentally using fluorometry and imaging techniques. The fluorescent particles (5.0 μm diameter) were dispersed by a nebulizer and injected in a stream of compressed air, resulting in a steady flow (Q = 111 L/min). A round nozzle was used to generate a jet characterized by a Reynolds number of Re = 10 ⁴ , based on the nozzle diameter (D = 15.0 mm) and nozzle exit velocity (u = 10.5 m/s). Three dimensionless distances from the nozzle's exit to the impaction surface, L/D = 2, 4, and 6, were investigated. It was observed that although having similar total deposition efficiencies (16.5–17.8%), shorter nozzle to surface distances (L/D = 2 and 4) show a more pronounced ring-like radial deposition pattern around the stagnation point. These shorter distances also exhibit significantly lower particle deposition near the stagnation point when compared to the longer distance (L/D = 6). Indeed, in moving through L/D = 2, 4, and 6, peak deposition density values of 254, 347, and 685 particles/mm ² shift through radii of 2.1 D, 0.8 D, and 0.1 D, respectively. In addition to the experiments, numerical simulation was also performed, which showed that the particle deposition was dominated by a turbulent dispersion mechanism for L/D = 2, with inertial impaction becoming more important for the L/D = 4 and 6 cases.     

Effects of air temperature and humidity on particle deposition

Particle deposition in a fully developed turbulent duct flow was studied. The random walk model of Lagrangian approach was used to predict the trajectories of 3000 particles with a density of 900 kg/m³. The effects of thermophoretic force and air humidity were also considered. The results were compared with the previous studies with a particle size range of 0.01–50 μm and air flow velocity of 5 m/s. The profile of dimensionless deposition velocity with relaxation time presents a V-shaped curve and the results are in good agreement with the previous studies.The effects of air temperature and humidity on particle deposition with a particle size of 1 μm were also investigated. The results show that thermophoretic force accelerates particle deposition onto the duct walls with increasing temperature difference between air flow and the duct wall surface. Meanwhile, it was found that particle deposition velocity increases with air humidity.     

Energy dissipation rate and pressure fluctuations in a three phase fluidized bed with a large column diameter

The effects of liquid (0.02-0.10 m/s) and gas (0.0-0.10 m/s) velocities and particle size (1.0, 2.3, 3.0 mm) on the pressure fluctuations and energy dissipation rate in three phase fluidized beds were determined in a large column (0.376 m-I.D.× 2.1 m high). The standard deviation of pressure fluctuations and energy dissipation rate increase with gas and liquid velocities but, decrease in the radial direction of three phase fluidized beds. The energy dissipation rate was well correlated with dimensionless groups as: E_d=16.788Fr ₁ ^0.183 Fr _g ^0.139 (1-ψ)^0.442+1.265Fr _g ^0.143 Re^0.181.     

Numerical analysis of particle mixing in a rotating fluidized bed

This paper describes the numerical analysis of particle mixing in a rotating fluidized bed (RFB). A two-dimensional discrete element method (DEM) and computational fluid dynamics (CFD) coupling model were proposed to analyze the radial particle mixing in the RFB. Spherical polyethylene particles (Geldart group B particles) were used as model particles under the assumptions that they were cohesionless and mono-disperse with their diameter of 0.5 mm.The validity of the proposed model was confirmed by the comparison between the calculated degree of particle mixing and the experimental one, which was obtained by measuring the lightness of the recorded image taken by a high-speed video camera. Effects of the operating parameters (gas velocity, centrifugal acceleration, particle bed height, and vessel radius) on the radial particle mixing rate were numerically analyzed. The radial particle mixing rate was found to be strongly affected by the bubble characteristics, especially by the bubble size. The mathematical model for the rate coefficient of particle mixing as functions of operating parameters was empirically proposed. The radial particle mixing rate in a RFB could be well correlated by the three dimensionless numbers: dimensionless acceleration (Ac), bubble Froude number (Fr_b), and dimensionless radius on the surface of particle bed (β_s).     

Studies on thermo-acoustic parameters in the dilute solutions of poly(ethyleneglycol)

Ultrasonic velocities and densities have been measured for the dilute solutions of poly(ethylene glycol) of average molecular mass 400 g mol^?1 in benzene at different temperatures between 299 and 328 K. The experimental data have been used to compute the thermo-acoustical parameters namely isentropic compressibility (β), intermolecular free length (L _f), molar volume (V _m), Schoff’s available volume (V _a(s)), acoustic impedance (Z), molar sound velocity (R _a), and molar compressibility (W). Variation of these parameters with temperature of the sample and mole fraction of the solute in the solution, keeping one of the either constant has been discussed to collect the informations on molecular structure and intermolecular interactions.     

Particle Deposition in Museums: Comparison of Modeling and Measurement Results

Deposition of airborne particles may lead to soiling and /or chemical damage of objects kept indoors, including works of art in museums. Measurements recently were made of the deposition velocity of fine particles (diameter range: 0.05–2.1 μm) onto surfaces in five Southern California museums. In this paper, theoretical predictions of particle deposition velocities onto vertical surfaces are developed for comparison against the experimental results. Deposition velocities are calculated from data on surface-air temperature difference and near-wall air velocity using idealized representations of the air flow field near the wall. For the five sites studied, the wall-air temperature differences were generally in the range of a few tenths to a few degrees Kelvin. Average air velocities measured at 1 cm from the wall were in the range 0.08–0.19 m s^?1. Based on a combination of modeling predictions and measurement results, the best estimate values of deposition velocity for the wall studied at each site are obtained. These values are in the range (1.3–20) × 10^?6 m s^?1 for particles with 0.05–μm diameter and (0.1–3.3) × 10^?6 for particles with 1-μm diameter. The range of 15–30 in deposition velocity for a given particle size is due primarily to differences among sites in the near-wall air flow regime, with the low and high values associated with forced laminar flow and homogeneous turbulence in the core of the room, respectively.     

Dimensional Analysis of Crossflow Microfiltration Data

Abstract

A new approach to correlating crossflow microfiltration (CFMF) data based on dimensional analysis is presented. The steady state flux was assumed to be a function of the trans‐membrane pressure (ΔP), the crossflow velocity (u), the particle concentration (c), filtrate viscosity (μ), and membrane resistance (R _m). Correlations of the form J/u=K(ΔP/cu ²) ^a (ΔP/μuR _m) ^b were tested on three sets of published data: one for CFMF of dried yeast suspensions in a laminar flow hollow fiber module, one for dried yeast suspensions in a turbulent flow tubular module and one for suspensions of latex particles in a laminar flow flat sheet module. The R ² values for the fits of the correlations to the data were 0.98, 0.94, and 0.91 respectively.     

Seasonal Variation of Airborne Particle Deposition Efficiency in the Human Respiratory System

Particulate matter (PM) is associated with human health effects but the apparent toxicity of PM in epidemiological studies varies with season. PM toxicity may change due to seasonal shifts in composition or particle size distributions that in turn affect respiratory deposition efficiencies. In the current study, size-resolved PM composition was measured in the largest city (Fresno) in California's heavily polluted San Joaquin Valley during the summer (30 days) and winter (20 days) between 2006 and 2009 for 21 metals, organic carbon, elemental carbon, and 7 water-soluble ions. The Multiple-Path Particle Dosimetry model was applied to determine if seasonal variation in size-resolved composition influences respiratory deposition patterns. Mg, Al, S, V, Mn, Fe, Ni, Ba, SO₄ ^2-, Na⁺, and Ca²⁺ had larger total deposition efficiencies (p < 0.004) during the summer versus the winter in all three regions of the respiratory tract. This trend results from increased relative concentrations of the target analytes per μg m^?3 ambient PM_1.8 concentration and would be detected with routine PM_2.5 filter samples. V, Zn, Se, NO₃ ^-, SO₄ ^2-, and NH₄ ⁺ also experienced seasonal size distribution shifts that enhanced the specific deposition efficiency in the tracheobronchial and pulmonary regions during the summer months (p < 0.05). This enhanced deposition would not be detected by routine filter samples because all of the size distribution changes occur at particle diameters <2.5 μm. This study demonstrates that changes to the particle size distributions (<2.5 μm) can enhance respiratory deposition efficiencies for trace metals and/or water-soluble ions and this may contribute to seasonal shifts in PM toxicity.     

Particle Deposition in Wakes: Inertial and Coulombic Effects on Capture By Single and Multiple Spheres in Line

Ten-micrometer dioctylphthalate droplets tagged with sodium fluorescein were collected on six metal spheres, 0.6 cm in diameter and arranged in a line parallel to the axis of flow. The particles carried negative charge in the range 0.9–1.7 × 10^?5 stC while the collectors were charged positively in the range 8.0–23.0 stC. The carrier stream velocities used were 600, 1200, 1500, 1800, and 2400 cm/s and spacings between targets of two through six diameters center-to-center were tested. Collection efficiencies for each target were determined by measuring the number of deposited particles, and the particle concentration in the air stream using fluorometric techniques.

An effective Coulombic attraction parameter K _Eeff , was defined to take into account non-Stokesian drag during particle collection at high velocities. This term was combined with an effective Stokes number to provide the empirical relation, for single spherical targets: η= 1.4[Stk _eff + (2K _Eeff )^1/2]. A model is presented to describe the concentration distribution of particles in the wakes of multiple spherical targets, in-line. This model is based on the lateral turbulent transport of particles into the wake between targets. A correlation between the particle deposition of any trailing target, normalized to that of the leading target, and the modified Graetz number, (n - l)^1/3(Gz)^?1, where n is the rank of the target in the series and Gz = 4(z/D)/Pe, enables one to predict deposition on trailing targets.     

The surface renewal model of wall turbulence for boundary layer flow with transpiration

The object of this paper is to develop and evaluate the basic surface renewal modeling approach for transpired turbulent boundary layer flows. Using a simple form of the surface renewal model in conjunction with the standard mixing length representation of the turbulent core, calculations are established for the dimensionless burst frequency s⁺, and distributions in velocity u⁺ within the inner region as a function of transpiration rate v⁺ and pressure gradient P⁺.     

Particle fluctuations and dispersion in three-phase fluidized beds with viscous and low surface tension media

Particle fluctuations and dispersion were investigated in a three-phase (gas–liquid–solid) fluidized bed with an inside diameter of 0.102 m and height of 2.5 m. Effects of gas and liquid velocities, particle size (0.5–3.0 mm), viscosity (1.0–38×10⁻³ Pa s) and surface tension (52–72×10⁻³ N/m) of continuous liquid media on the fluctuating frequency and dispersion coefficient of fluidized particles were examined, by adopting the relaxation method base on the stochastic model. The fluctuations and dispersion of fluidized solid particles were successfully analyzed by means of the pressure drop variation with time, which was chosen as a state variable, based on the stochastic model. The fluctuating frequency and dispersion coefficient of particles increased with increasing gas velocity, due to the increase of bubbling phenomena and bed porosity in which particles could move, fluctuate and travel. The frequency and dispersion coefficient of particles showed local maximum values with a variation of liquid velocity. The two values of fluctuating frequency and dispersion coefficient of particles increased with increase in particle size, but decreased with increase in liquid viscosity due to the restricted movement and motion of particles in the viscous liquid medium. Both fluctuating frequency and dispersion coefficient of particles increased with decrease in surface tension of liquid phase, due to the increase of bubbling phenomena with decrease in σ_L. The values of obtained particle dispersion coefficient were well correlated in terms of dimensionless groups as well as operating variables.