WALL DEPOSITION OF SMALL SUSPENDED PARTICLES IN A TURBULENT CHANNEL FLOW

The diffusion of small suspended particles in a turbulent channel flow is studied by solving the transport advection-diffusion equation. The mean flowfield in the channel is simulated using a two-equation k-ε turbulence model. Deposition velocity is evaluated at different sections in the channel for different particle sizes and flow Reynolds numbers. The effects of turbulence dispersion and Brownian diffusion on particle deposition velocity are discussed. The variation of particle deposition velocity with particle diameter, density and flow Reynolds number are analyzed. The wall deposition velocities for different size particles are compared with those obtained by other models.     

Study of the growth of rhodium particles on different substrates

We have investigated the growth of small supported rhodium particles on different substrates (mica, Al₂O₃, NaCl). The particles were deposited in a vacuum from a special source permitting a low evaporation rate. The particle size, density and crystallographic structure dependencies on mean deposit thickness, deposition rate and substrate temperature during the deposition were studied by transmission electron microscopy and diffraction (TEM and TED). The results showed that it is possible to prepare a model Rh catalyst with a well-defined particle population by vacuum vapour deposition. These catalysts form relatively stable systems with respect to the thermal treatment. It was observed that the particle density, the mean size and the size dispersion of Rh particles are controlled by either atom diffusion or by particle migration on the substrate. The diffusion of atoms and clusters increases with the substrate temperature and the growth takes place also by particle coalescence.     

PENETRATION OF POLYDISPERSE AEROSOLS THROUGH SCREEN DIFFUSION BATTERY

As an alternative data reduction scheme for diffusion battery measurements, penetration of polydisperse aerosol particles in a screen type diffusion battery has been calculated employing Brownian diffusion and interception as the applicable deposition mechanisms. The influences of the mean particle size and the geometric standard deviation of the aerosol on penetrations of the total particle number, radius, surface area, and the total particle volume have been examined. It is quantitatively shown that depending upon the type of aerosol instrument in use as a particle counting means and depending upon the size distribution of the measured aerosols, penetration characteristics can become markedly different. For a highly dispersed aerosol having a small mean particle size, the total radius, the surface area and the total volume of aerosol particles are shown to penetrate a diffusion battery more slowly in that order than the total number of particles. However, when the mean size of the aerosol increases, such a monotomic increase in penetration becomes no longer valid due to increasing importance of the interceptional deposition. Experimental measurements have been performed to demonstrate applications of the calculated results.     

Particle deposition on ideal collectors from dilute flowing suspensions: Mathematical formulation,numerical solution,and simulations

This paper presents the quantitative formulation of the convective diffusion equation for particle deposition in ideal deposition systems. Collectors considered include the rotating disk, stagnation-point flow, parallel-plate channel, isolated sphere, and a porous medium composed of uniform spheres. For each collector, the complete particle transport equation, proper boundary conditions, and expressions for the particle deposition rate are formulated. Also presented are numerical procedures for solving the convective diffusion equation. Simulations for the effect of various physical and chemical-colloidal variables on the rate of particle deposition are presented and discussed. The theories presented apply to particle deposition from dilute suspensions in which interparticle interactions are negligible.     

EULERIAN AND LAGRANGIAN SIMULATIONS OF PARTICLE DEPOSITION FROM A POINT SOURCE IN A TURBULENT CHANNEL FLOW

Results comparing Eulerian and Lagrangian simulations of particle deposition from a point source in a channel are presented. The mean turbulent flow field is simulated using a two-equation k-ε turbulence model. In the first, approach, diffusion of aerosol particles is studied by solving the corresponding advection-diffusion equation. Deposition of particles in the intermediate size range are analyzed by considering both the turbulent eddy diffusion and the eddy impaction processes, as well as the Brownian diffusion effects. In the second approach, the turbulence fluctuating velocity field are numerically simulated as a Gaussian random process. The Lagrangian trajectories of aerosol particles in the channel are then evaluated by solving the corresponding particle equation of motion. Effects of Brownian diffusion on particle motions are also included. A series of digital simulations for particles of various sizes which are released at different locations across the channel are carried out. Depositions of different size particles on the wall under a variety of conditions are analyzed. The relative significance of turbulence and Brownian effects are also discussed.     

EULERIAN AND LAGRANGIAN SIMULATIONS OF PARTICLE DEPOSITION FROM A POINT SOURCE IN A TURBULENT CHANNEL FLOW

ABSTRACT

Results comparing Eulerian and Lagrangian simulations of particle deposition from a point source in a channel are presented. The mean turbulent flow field is simulated using a two-equation k-? turbulence model. In the first, approach, diffusion of aerosol particles is studied by solving the corresponding advection-diffusion equation. Deposition of particles in the intermediate size range are analyzed by considering both the turbulent eddy diffusion and the eddy impaction processes, as well as the Brownian diffusion effects. In the second approach, the turbulence fluctuating velocity field are numerically simulated as a Gaussian random process. The Lagrangian trajectories of aerosol particles in the channel are then evaluated by solving the corresponding particle equation of motion. Effects of Brownian diffusion on particle motions are also included. A series of digital simulations for particles of various sizes which are released at different locations across the channel are carried out. Depositions of different size particles on the wall under a variety of conditions are analyzed. The relative significance of turbulence and Brownian effects are also discussed.     

Thermophoretic deposition of particles from a boundary layer flow onto a continuously moving wavy surface

Summary A theoretical model for the coupled transport mechanisms of diffusion, convection and thermophoresis was developed to describe the particle deposition onto a continuously moving wavy surface. The numerical results reveal that the mean deposition effect of the wavy plate is greater than of a flat plate and more significant with the wavy amplitude increasing, and that the increasing rate is nearly equal to the value obtained by dividing the additional surface area of the wavy plate compared to the flat plate by 2.4 times the flat plate area.     

An analytical solution of the population balance equation for simultaneous Brownian and shear coagulation in the continuum regime

Brownian coagulation of aerosol particles can take place in both laminar and turbulent flows. Thus, the simultaneous Brownian and shear coagulation will always occur in practical applications. This study presents an analytical solution to describe the size evolution of polydisperse particles undergoing simultaneous Brownian and shear coagulation. The analytical solution is derived using the log-normal method of moments (LNMOM) with some approximations. Then, the analytical solution is validated by comparing with previous analytical solutions derived for limiting cases. The results show that the present analytical solution is consistent with previous analytical solutions for these limiting cases. Further, the time trajectories of the total particle number concentration, the geometric standard deviation and the geometric number mean particle volume predicted by the present analytical solution are compared with those of a numerical LNMOM model. The results show that the present analytical solution gives good predictions of the total particle number concentration but less accurate predictions of the geometric standard deviation and the geometric number mean particle volume. A dimensionless analysis shows that the coagulation rate ratio and the initial polydispersity are two important factors for characterizing the size evolution of simultaneous Brownian and shear coagulation.     

DEPOSITION OF SUBMICRON AEROSOL PARTICLES DURING INTEGRATED CIRCUIT MANUFACTURING: THEORY

ABSTRACT

Submicron (≤1μm) particle contamination can produce unacceptably low yields in the manufacture of integrated circuits. Calculations were made to predict deposition velocities of 0·01-lOμm particles, incorporating gravitational, dlffusional, and electrostatic effects. The results were summarized in equations that correlate non-dimensional deposition (Sherwood number) with convective-diffusion (Peclet number) and with electrostatics (Boltzmann and Fuchs charge distributions). These equations were used In conjunction with particle size distributions to predict particle deposition. In a companion paper |25| the predictions were shown to compare well with limited experimental data. To reduce deposition product surfaces should not be electrically charged and, where possible, these surfaces should be at higher temperatures than the ambient gas. For quality control purposes, the deposition flux predictions could serve to link the specifications of gas cleanliness with the specifications of surface cleanliness.     

Radon progeny size distributions and enhanced deposition effects from high radon concentrations in an enclosed chamber

Prior work studying radon progeny in a small enclosed chamber found that at high (222)Rn concentrations an enhanced surface deposition was observed. Subsequent measurements for unfiltered air showed minimal charged particle mobility influence. Progeny particle size measurements reported here, performed at the US Department of Energy Environmental Measurement Laboratory (now with Home Security Department), using the EML graded screen array (GSA) system show in unfiltered air that the high (222)Rn levels causes a reduction in the attached (218)Po progeny airborne particulates and formation of additional normal sized unattached ( approximately 0.80 nm) and also even smaller (218)Po below 0.50 nm. At a (222)Rn level of 51 kBq m(-3), 73% of all (218)Po are of a mean particle diameter of about 0.40 +/- 0.02 nm. At this (222)Rn level, the ratio of (218)Po to (222)Rn airborne concentrations is reduced significantly from the concentration ratio at low (222)Rn levels. Similar reductions and size reformations were observed for the (214)Pb and (214)Bi/Po progeny. The particle size changes are further confirmed using the plateout rates and corresponding deposition velocities. The Crump and Seinfeld deposition theory provides the corresponding particle diffusion coefficients. With the diffusion coefficient to ultrafine clustered particle diameter correlation of Ramamurthi and Hopke, good agreement is obtained between EML GSA and deposition velocity data down to 0.40 nm. Strong evidence is presented that the progeny size reduction is due to, as a result of air ionization, the increased neutralization rate (primarily from electron scavenging of OH molecules) of the initially charged progeny. This is shown to increase with the (1/2) power of (222)Rn concentration and relative humidity as well as increased air change rate in the chamber. These results imply that at (222)Rn levels above 50 kBq m(-3), at relative humidity of 52%, a considerable reduction in lung dose could occur from preferential deposition of the progeny in the nasal and oral passages.     

DEPOSITION OF SUBMICRON AEROSOL PARTICLES DURING INTEGRATED CIRCUIT MANUFACTURING: THEORY

Submicron (≤1μm) particle contamination can produce unacceptably low yields in the manufacture of integrated circuits. Calculations were made to predict deposition velocities of 0·01-lOμm particles, incorporating gravitational, dlffusional, and electrostatic effects. The results were summarized in equations that correlate non-dimensional deposition (Sherwood number) with convective-diffusion (Peclet number) and with electrostatics (Boltzmann and Fuchs charge distributions). These equations were used In conjunction with particle size distributions to predict particle deposition. In a companion paper |25| the predictions were shown to compare well with limited experimental data. To reduce deposition product surfaces should not be electrically charged and, where possible, these surfaces should be at higher temperatures than the ambient gas. For quality control purposes, the deposition flux predictions could serve to link the specifications of gas cleanliness with the specifications of surface cleanliness.     

Numerical study to predict the particle deposition under the influence of operating forces on a tilted surface in the turbulent flow

This study uses a v2-f turbulence model with a two-phase Eulerian approach. The v2-f model can accurately calculate the near wall fluctuations in y-direction, which mainly represent the anisotropic nature of turbulent flow. The model performance is examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The effects of lift, turbophoretic, electrostatic and Brownian forces together with turbulent diffusion are examined on the particle deposition rate. The influence of the tilt angle and surface roughness on the particle deposition rate were investigated. The results show that, using the v2-f model predicts the rate of deposition with reasonable accuracy. It is observed that in high relaxation time the effect of lift force on the particle deposition is very important. It is also indicated that decreasing the tilt angle from 90° to 0° enhances the deposition rate especially for large size particles. Furthermore, the results show that increasing the Reynolds number at a specific tilt angle decreases the rate of particle deposition and the tilt angle has insignificant impact on the particle deposition rate in high shear velocity or high Reynolds number.     

Predicting the Particle Deposition Characteristics Using a Modified Eulerian Method on a Tilted Surface in the Turbulent Flow

This study uses a v2-f turbulence model with a two phase Eulerian approach. The v2-f model can accurately calculate the near wall fluctuationsm which mainly represent the nonisotropic nature of turbulent flow near the walls. The Eulerian method was modified based on considering the most important mechanisms in the particle deposition rate when compared to the experimental data. The model performance is examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The model takes into account the effects of lift, turbophoretic, electrostatic, gravitational, and Brownian forces together with turbulent diffusion on the particle deposition rate. Electrostatic forces due to mirror charging and due to charged particles under the influence of an electric field were considered. The influence of the tilt angle on the particle deposition rate was investigated. The results show that, using the modified model with v2-f model predicts the rate of deposition with reasonable accuracy. It is shown that considering the turbophoretic force as the only inertia force and neglecting the lift force, leads to reasonable accuracy in predicting particle deposition rate. It is also observed that when the mirror charging and electric field are present, the electrostatic force has the dominant effect in a wider range of particles’ size. Furthermore, the results show that increasing the Reynolds number at a given tilt angle decreases the rate of particle deposition and the tilt angle has insignificant impact on the particle deposition rate in high shear velocity or high Reynolds number.     

Stochastic model of ultrafine particle deposition and clearance in the human respiratory tract

Deposition and clearance of insoluble ultrafine particles, ranging from 1 to 100 nm, were simulated by stochastic models using Monte Carlo methods. Brownian motion is the dominant mode of deposition in human airways. The additional effects of convective diffusion in bifurcations and axial diffusion (convective mixing) primarily affect particle transport and deposition of particles in the 1-10 nm range. Regarding total deposition, the effects of both convective mechanisms are practically compensated by the concomitant effect of molecular radial diffusion (Brownian motion). During the first hours following inhalation, 1 nm particles are predicted to be cleared much faster than particles in the size range from 10 to 100 nm, with a retained fraction of about 80% after 24 h. For 1-10 nm particles, extracellular transfer to blood is the most likely mode of clearance, while uptake and subsequent accumulation in epithelial cells are assumed to be the preferential mechanisms for 10-100 nm particles.     

An approach for evaluating aerosol particle deposition from a natural convection flow onto a vertical flat plate.

An approach through numerical integration for evaluating aerosol particle deposition onto a vertical flat plate is proposed. The airflow was based on the assumption of a two-dimensional, incompressible and steady state laminar flow driven by a buoyancy force. The mechanisms of particle deposition were coupled from natural convection, Brownian diffusion, thermophoresis and electrophoresis due to constant electric strength. This approach demonstrated an easier method of prediction and produced a very good agreement with the thermophoresis exact solution. Results described the role of thermophoretic and electrophoretic forces on particle deposition. The thermophoresis effect was predicted to be particularly important for particles of d(p)>/=0.1 microm moving toward a cold surface or away from a hot surface at a given temperature gradient. The electrophoresis effect dominates the deposition of submicron particles.     

Numerical model of particle deposition on fin surface of heat exchanger

Dust particle deposition on fin surface has a significant influence on the performance of fin-and-tube heat exchangers, and the purpose of this study is to develop a numerical model for predicting the particle deposition rate on fin surface. In the model, the particle trajectories were calculated by the particle motion equation; the particle deposition on the fin surface was described based on the critical impact angle and the critical sticking velocity of incident particles; the particle deposition on the formed fouling layer was described based on the critical impact angle, the critical sticking velocity and the critical removal velocity of incident particles. The particle distributions on fin surface predicted by the model agree well with the images captured in the visualization experiment. The predicted particle deposition weight per unit area can describe 88% of the experimental data within a deviation of ±20% and the mean deviation is 12.8%.     

Brownian dynamics study of polymer-stabilized nanoparticles

A Brownian dynamics simulation was carried out for a spherical nanoparticle with polymer chains tethered to its surface. These simulations are relevant to understanding the transport properties of polymer-stabilized nanoparticles in environmental and other applications. Hydrodynamic interactions (HI) were taken into account to properly describe the diffusion properties of a stabilized particle. HI are important in this context because of the close proximity of the surface-tethered polymer chains. HI were implemented using a method introduced by Fixman (1986 Macromolecules 19 1204), which uses a Chebyshev polynomial expansion to calculate the square root of the diffusion tensor. Simulation predictions were compared to published experimental data for the hydrodynamic radius of a silica particle stabilized by polystyrene tethered chains, and good agreement was achieved. A relationship that allows polymer-stabilized particles with arbitrary polymer-chain densities to be modelled is developed.     

Gas Flow and Particle Transport and Deposition in a Pilot-Scale Furnace

The present work describes a computer simulation study of gas flow and particle transport and deposition in a pilot-scale furnace with cooling system. The Gambit code is used to generate the geometry and the computational grid. An unstructured mesh is generated for the pilot-scale boiler. The FLUENT code is used for evaluating the gas mean velocity, turbulence fluctuation energy, and mean pressure, as well as temperature fields and chemical species concentrations. The particle equation of motion includes the nonlinear drag, gravity, Brownian, lift, and thermophoretic forces. The gas velocity and thermal conditions in the furnace are studied. Ensembles of particle trajectories are generated and statistically analyzed. Particle deposition rates on different walls are evaluated, and the effect of particle size is studied.     

AC electric fields and particle deposition on a sphere

The National Radiological Protection Board's Independent Advisory Group on Non-ionising Radiation considered the possible effects on health of particle deposition in the vicinity of power lines and recommended, inter alia, that further studies were needed to reduce the uncertainties regarding the dependence of deposition on particle size and air flow. Empirical heat transfer data have been used to estimate the effects of thermophoresis on particle deposition on a sphere mimicking the human head. It is shown that these effects become significant for particle diameters >6 nm and skin temperature needs to be considered when modelling the deposition of larger particles. If one assumes that deposition takes place to smooth surfaces under isothermal conditions, the model predicts, in line with the calculations of Fews et al., that exposure to a power line electric field will enhance deposition (relative to that from diffusion) throughout the size range up to 10 mum. However, such models do not represent deposition on the skin because of the neglect of the effects of surface temperature and texture. Previous workers have measured the ratio of deposition with and without electric field exposure. It is suggested that this is a misleading parameter and data should be presented in terms of the collection efficiencies, which are proportional to the actual amount deposited.