Behavior of Compact Nonspherical Particles in the TSI Aerodynamic Particle Sizer Model APS33B: Ultra-Stokesian Drag Forces

The aerodynamic behavior of aggregates consisting of uniform polystyrene latex (PSL) spheres and unaggregated cuboidal Natrojarosite particles in a TSI aerodynamic particle sizer (Model APS33B) has been studied. In initial tests, monodisperse PSL micro-spheres ranging from 0.3 to 7 μm in geometric diameter were generated from aqueous suspensions using a Lovelace nebulizer. APS33B responses for these uniform-sized particles showed multiple peaks. The major (primary) peak, which resulted from the smallest particle, corresponded to the unaggregated single spheres (singlets); the second, third, and fourth peaks were identified as doublets, triangular triplets, and tetrahedral quadruplets, respectively. Both doublets and triplets moved with their long axes in perpendicular (maximum drag) orientation to the flow direction in the APS33B. In contrast, the tetrahedral particles were isometric and had the same dynamic shape factor (drag resistance) for all three primary orientations. The particle Reynolds numbers (Re _p) for these particles were calculated and ranged from 0.2 to 30 in the sensing volume of the APS33B detector (i.e., ultra-Stokesian conditions). Ultra-Stokesian drag forces for all three types of aggregates were, therefore, estimated and expressed as a function of an empirical factor (1 + aRe ^b _p) to the Stokesian drag force. The ultra-Stokesian drag of a Natrojarosite particle was measured in the range 20 Re _p < 50 and could be described with a similar expression. This approach facilitates the study of the dynamic behavior of nonspherical particles and yields new information about the characteristics of drag forces in the ultra-Stokesian regime     

Evaluating the Mobility of Nanorods in Electric Fields

The mobility of a nonspherical particle is a function of both particle shape and orientation. In turn, the higher magnitude of electric field causes nonspherical particles to align more along the field direction, increasing their mobility or decreasing their mobility diameter. In previous works, Li et al. developed a general theory for the orientation-averaged mobility and the dynamic shape factor applicable to any axially symmetric particles in an electric field, and applied it to the specific cases of nanowires and doublets of spheres. In this work, the theory for a nanowire is compared with experimental results of gold nanorods with known shape determined by TEM images. We compare the experimental measured mobility sizes with the theoretical predicted mobility in the continuum, free molecular, and the transition regime. The mobility size shift trends in the electric fields based on our model, expressed both in the free molecular regime and in the transition regime, are in good agreement with the experimental results. For rods of dimension: width d_r = 17 nm and length L_r = 270 nm, where one length scale is smaller than the mean free path and one larger, the results clearly show that the flow regime of a slender rod is mostly controlled by the diameter of the rod (i.e., the smallest dimension). In this case, the free molecule transport properties best represented our nanorod. Combining both theory and experiment we show how, by evaluating the mobility as a function of applied electric field, we can extract both rod length and diameter.

Copyright 2013 American Association for Aerosol Research     

On the Effect of Particle Alignment in the DMA

The Differential Mobility Analyzer (DMA) is designed to measure particle mobility diameter, which for spherical particles is equal to particle volume equivalent diameter. In contrast, the mobility diameter of aspherical particles is a function of the particle shape and orientation. The magnitude of the DMA electric fields is such that it can cause aspherical particles to align preferentially in a specific orientation. The same electric field and the sheath flow rate ( q _sh ) define the particle mobility diameter. But, the fact that particle orientation depends on the electric field makes the dynamic shape factor and hence the mobility diameter depend on q _sh . Here, we describe an operating procedure that relies on a tandem DMA system, in which the second DMA is operated at a number of q _sh , to obtain information about particle shape by measuring the effect of particle alignment on the particle mobility diameter. We show how the relationship between the mobility diameter and q _sh can even be used to physically separate particles according to their shapes. In addition we explore the use of simultaneous measurements of particle alignment and particle vacuum aerodynamic diameters to gain further information on particle shape and account for particle alignment in the calculations of dynamic shape factor. We first test this approach on doublets and compact triplets of PSL spheres, for which the orientation dependent dynamic shape factors are known. We then investigate applications on a number of polydisperse particle systems of various shapes.     

Determination of the Scalar Friction Factor for Nonspherical Particles and Aggregates Across the Entire Knudsen Number Range by Direct Simulation Monte Carlo (DSMC)

The friction factor of an aerosol particle depends upon the Knudsen number (Kn), as gas molecule–particle momentum transfer occurs in the transition regime. For spheres, the friction factor can be calculated using the Stokes–Millikan equation (with the slip correction factor). However, a suitable friction factor relationship remains sought-after for nonspherical particles. We use direct simulation Monte Carlo (DSMC) to evaluate an algebraic expression for the transition regime friction factor that is intended for application to arbitrarily shaped particles. The tested friction factor expression is derived from dimensional analysis and is analogous to Dahneke's adjusted sphere expression. In applying this expression to nonspherical objects, we argue for the use of two previously developed drag approximations in the continuum (Kn → 0) and free molecular (Kn → ∞) regimes: the Hubbard–Douglas approximation and the projected area (PA) approximation, respectively. These approximations lead to two calculable geometric parameters for any particle: the Smoluchowski radius, R _S, and the projected area, PA. Dimensional analysis reveals that Kn should be calculated with PA/πR _S as the normalizing length scale, and with Kn defined in this manner, traditional relationships for the slip correction factor should apply for arbitrarily shaped particles. Furthermore, with this expression, Kn-dependent parameters, such as the dynamic shape factor, are readily calculable for nonspherical objects. DSMC calculations of the orientationally averaged drag on spheres and test aggregates (dimers, and open and dense 20-mers) in the range Kn = 0.05–10 provide strong support for the proposed method for friction factor calculation in the transition regime. Experimental measurements of the drag on aggregates composed of 2–5 primary particles further agree well with DSMC results, with differences of less than 10% typically between theoretical predictions, numerical calculations, and experimental measurements.

Copyright 2012 American Association for Aerosol Research     

Effect of the surface roughness and construction material on wall slip in the flow of concentrated suspensions

Recent studies on polyethylene, elastomers, and thermoplastics have revealed that the construction material and surface roughness are two important factors affecting wall slip. In this study, to determine the true rheological behavior of model concentrated suspensions, a multiple‐gap separation method was used in a parallel disk rheometer. The model suspensions studied were poly (methyl methacrylate) particles with an average particle size of 121.2 μm in hydroxyl‐terminated polybutadiene. The aim of this study was to investigate the effect of disk R_a in the range of 0.49–1.51 μm and disk construction material on the wall slip and the true viscosity of the model concentrated suspensions. The wall slip velocity and the viscosity were found to be independent of R_a for particle size‐to‐disk R_a ratios of 80–247. Also, the true viscosity was found not to be affected by the rheometer surface construction material. Glass surfaces resulted in the highest slip velocity, whereas aluminum surfaces resulted in the lowest slip velocity. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3341–3347, 2007     

Silver Nanowire Penetration Through Screen Filter

Understanding the filtration characteristics of fibrous particles is important since those particles have caused health and environmental concerns. Due to the straight morphology of metal nanowires, unlike carbon nanotube (CNT) particles nanowires can be considered as appropriate test material to evaluate existing filtration theory for cylindrical particles. We measured the penetration of silver nanowires in the size range of d_m = 200 to 400 nm through screen mesh filter. By using Li et al. (2012)'s theory, we determined the orientation status of silver nanowires inside differential mobility analyzer (DMA) and calculated the dynamic shape factor of nanowires. Theoretical penetration was obtained by using single fiber theory with modified interception parameter including orientation angle between a filter wire and a particle. The orientation angle obtained by fitting experimental data into single fiber theory for the 1 layer of screen mesh filter is found to be close to 40° indicating random orientation of nanowires near filter. However, in the experiments with multi-layers of screen mesh, any tendency related to the orientation angle was not found. We performed numerical simulations for the filtration processes such as impaction, diffusion, interception, and interception of diffusing particles by introducing modified slip correction factor. Overall, when interception of diffusing particles is considered in addition to diffusion and interception, numerically simulation results and theoretical prediction agree better with experimental data regarding the penetration of silver nanowires through the 1 layer of screen mesh filter.

Copyright 2014 American Association for Aerosol Research     

Particle Morphology and Density Characterization by Combined Mobility and Aerodynamic Diameter Measurements. Part 2: Application to Combustion-Generated Soot Aerosols as a Function of Fuel Equivalence Ratio

Composition, shape factor, size, and fractal dimension of soot aerosol particles generated in a propane/O₂, flame were determined as a function of the fuel equivalence ratio (φ). Soot particles were first size-selected by a differential mobility analyzer (DMA) and then analyzed by an Aerodyne aerosol mass spectrometer (AMS). The DMA provides particles of known mobility diameter (d_m ). The AMS quantitatively measures the mass spectrum of the nonrefractory components of the particles and also provides the vacuum aerodynamic diam eter (d_va ) corresponding to the particles of known mobility diameter. The measured d_m, d_va , and nonrefractory composition are used in a system of equations based on the formulation presented in the companion article to estimate the particle dynamic shape factor, total mass, and black carbon (BC) content. Fractal dimension was estimated based on the mass-mobility relationship. Two types of soot particles were observed depending on the fuel equivalence ratio. Type 1: for φ < 4 (lower propane/O₂), d_va ; was nearly constant and independent of d_m . The value of d_va increased with increasing φ. Analysis of the governing equations showed that these particles were highly irregular (likely fractal aggregates), with a dynamic shape factor that increased with d_m and φ. The fractal dimension of these particles was approximately 1.7. These particles were composed mostly of BC, with the organic carbon content increasing as φ increased. At φ = 1.85, the particles were about 90% BC, 5% PAH, and 5% aliphatic hydrocarbon (particle density = 1.80 g/cm³). Type 2: for φ > 4 (high propane/O₂), d_va was linearly proportional to d_m . Analysis of the governing equations showed that these particles were nearly spherical (likely compact aggregates), with a dynamic shape factor of 1.1 (versus 1 for a sphere) and a fr actal dimension of 2.95 (3 for a sphere). These particles were composed of about 50% PAH, 45% BC, and 5% aliphatic hydrocarbons (particle density = 1.50 g/cm³). These results help interpret some measurement s obtained in recent field studies.     

Triaxial Crystalline Orientation of MgTi2O5 Achieved Using a Strong Magnetic Field and Geometric Effect

Tailoring the crystallographic orientation in ceramics is very useful for improving their properties. We reported that the colloidal processing in a strong magnetic field was able to control the crystallographic orientation even in diamagnetic ceramics. In this process, a strong magnetic field is applied to the particles in a stable suspension. The orientation of the crystal depends on the axis having easy magnetization and one‐dimensional orientation can be controlled. In this study, our concept is that control of multiaxial crystalline orientation in ceramics by using both anisometric particles and a magnetic field. The control of the triaxial orientation was achieved by tape casting of rod‐like MgTi₂O₅ particle in a magnetic field. The b‐axis was aligned by the magnetic field, and the a‐axis was aligned by the geometric effect and shear stress during tape casting.     

Electrophoresis in suspensions of charged porous spheres in salt-free media

Electrophoresis in either dilute or concentrated suspensions of charged porous spheres in salt-free media is investigated theoretically in this study. The Brinkman model and the Kuwabara’s unit cell model are adopted to simulate the porous structure and the suspensions, respectively.We found, among other things, that the polarization effect due to the convection flow within the porous sphere is a crucial factor in determining its electrophoretic behavior. An induced electric field opposite to the applied electric field is generated, which deters the particle motion significantly when the particle is highly permeable. Approximate analytical prediction for dilute suspensions neglecting convection flow can overestimate the mobility severely in this situation. The approximate analytical prediction is satisfactory when the permeability of particle is low, though. Counterion condensation happens at high fixed charge density which decreases the mobility drastically and the mobility approaches a constant value asymptotically. The mobility profile of the particles with increasing volume fraction can exhibit local minimum if the corresponding dimensionless parameter Q_fix/(λa)² is high, where Q_fix and λa are, respectively, the fixed charge density and the friction coefficient of the porous particles in dimensionless form. This is due to the overlapping of counterion clouds surrounding particles, which offsets the polarization effect, becomes significant as the suspension gets concentrated. No such phenomenon for low Q_fix/(λa)², where the mobility profile decreases monotonously with increasing volume fraction. Comparison with experimental data available in the literature for polyelectrolyte suspensions is excellent, indicating the reliability of this analysis, as well as the success of using charged porous sphere to model a polyelectrolyte system.     

Slip velocity and slip layer thickness in flow of concentrated suspensions

The rheological characterization of highly filled suspensions consisting of a Newtonian matrix (hydroxyl-terminated polybutadiene), mixed with two different sizes of aluminum powder (30% and above by volume) and two different sizes of glass beads (50% and above by volume), was performed using a parallel disk rheometer with emphasis on the wall slip phenomenon. The effects of the solid content, particle size, type of solid particle material, and temperature on slip velocity and slip layer thickness were investigated. Suspensions of small particles of aluminum (mean diameter of 5.03 μm) did not show slip at any concentration up to the maximum packing fraction. However, suspensions of the other particles exhibited slip at the wall, at concentrations close to their maximum packing fraction. In these suspensions, the slip velocity increased linearly with the shear stress, and at constant shear stress, the slip velocity increased with increasing temperature. The slip layer thickness increased proportionally with increasing size of the particles for the glass beads. Up to a certain value of (filler content/maximum packing fraction), ϕ/ϕ_m, the slip layer thickness divided by the particle diameter, δ/D_P, was 0, but it suddenly increased and reached a value that was independent of ϕ/ϕ_m and the temperature. On average, the ratio of δ/D_P was 0.071 for aluminum and 0.037 for glass beads. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 515–522, 1998     

Diffusion of ellipsoidal granular particles in shear flow

The diffusion of nonspherical particles has not been well understood due to the complexity of their contact mechanics and self-organization of their orientations. We perform discrete element method simulations of monodisperse ellipsoids in a shear flow with Lees-Edwards boundary conditions to quantify the relation between the diffusion coefficient and the flow parameters. The results indicate that the particle aspect ratio strongly affects the diffusion coefficient by influencing the particle orientation and alignment. We develop a scaling law for the diffusion coefficient perpendicular to the flow direction, D_yy, which combines the influences of the shear rate , the solids fraction f, the effective particle diameter d_eff and the particle aspect ratio Z. We show that , where k_d is a dimensionless pre-factor, and a fit is obtained for the functional form of χ(f, Z). This scaling law will be useful in developing continuum transport models for applications.     

High Precision Density Measurements of Single Particles: The Density of Metastable Phases

We describe a system designed to measure the size, composition, and density of individual spherical particles in real time. It uses a Differential Mobility Analyzer (DMA) to select a monodisperse particle population and the single particle mass spectrometer to measure individual particle aerodynamic diameter. Together the mobility and aerodynamic diameters yield particle density. The mass spectrometer aerodynamic sizing resolution d _{ν a} /Δ d _{ν a} is ～ 50 and > 100 for 200 nm and 800 nm particles respectively and together with the DMA the overall system resolution is 20. We demonstrate that the line shape of the aerodynamic size distribution can be used to identify asphericity. We present results from two operational schemes: one suitable for most applications, yielding particle density with a precision of ± 2.5%, and a high precision variant, that uses an internal calibrant to remove any of the systematic errors and significantly improves the measurement quality. The high precision scheme is most suitable for laboratory studies, making it possible to follow slight changes in particle density. An application of the system to measure the density of hygroscopic particles in deep metastable phases near zero relative humidity is presented. The density data presented here are consistent with conclusions reached in a number of other studies, namely, that some particle systems, once deliquesced, persist as droplets down to near zero relative humidity.     

On the influence of particle shape and process conditions in the pressure drop and hydrodynamics in a wall-effect fixed bed

A low tube-to-particle diameter ratio (d_t/d_e,p) fixed bed, packed with spherical and nonspherical catalyst supports, was used to investigate pressure drop at varying temperature (298–673?K) and inlet pressure (245–294?kPa). The d_t/d_e,p ranged from 3 to 6, namely, a large wall-effect fixed bed, with an average void fraction between 0.38 and 0.61. These conditions pertain to multitubular fixed-bed reactors used for exothermic reactions. The pressure drop was notably influenced by the particle size and morphology as well as temperature. The use of particles with d_t/d_e,p?0.55) appeared suitable for pressure drop control. The fluid velocity profiles were calculated by applying the Navier–Stokes–Darcy–Forchheimer equation computing the respective permeability parameters with refitted state-of-the-art pressure drop correlations. The fluid flow exhibited different velocity zones across the fixed bed, the highest velocity zone being located near the reactor wall. The axial velocity component was influenced by the catalyst morphology, as well as temperature and inlet pressure.     

Measurements of Morphology Changes of Fractal Soot Particles using Coating and Denuding Experiments: Implications for Optical Absorption and Atmospheric Lifetime

Mobility-selected fractal and non-fractal soot particles (mobility diameters d _m = 135 to 310 nm) were produced at three controlled fuel equivalence ratios (φ = 2.1, 3.5, and 4.5) by an ethylene/oxygen flame. Oleic acid (liquid) and anthracene (solid) coatings were alternately applied to the particles and removed. Simultaneous measurements with an Aerodyne aerosol mass spectrometer and a scanning mobility particle sizer yielded the particle mass, volume, density, composition, dynamic shape factor, fractal dimension, surface area, and the size and number of the primary spherules forming the fractal aggregate. For a given φ, the diameters of the primary spherules are approximately the same, independent of d _m (15 nm, 35 nm, and 55 nm for φ = 2.1, 3.5, and 4.5, respectively). As the coating thickness on a particle increases, the dynamic shape factor decreases but d _m remains constant until the particle reaches a spherical (for oleic acid) or non-fractal but irregular (for anthracene) shape. Under some conditions, liquid oleic acid coating causes the internal BC framework to rearrange into a more compact configuration. The surface area of fractal particles is up to 2.4 times greater than that of a sphere with the same d _m . Using the surface area determinations, the time for a fractal particle to obtain a monolayer of coating material is compared to that of spheres. If it is assumed that the fractal particle is a sphere with the same d _m as the fractal particle, the monolayer coating time is underestimated by a factor of up to 1.7.     

Comparison of Gravitational SPLITT Fractionation with Gravitational Settling for Separating Micron Size Particles

Abstract

The performance of gravitational Split‐flow thin‐channel (GrSPLITT) fractionation has been compared with conventional gravitational settling (GrSettling) method. Two modes of GrSPLITT (full‐feed depletion (FFD) mode and transport (TS) mode) were employed. Silica and natural river particles were used to test these techniques. The particles were fractionated at the following cutoff diameters (d _c ) 2, 4, 6, 10, 14, and 20 µm. The fractions with diameter <d _c were analyzed for their particle size distribution by both optical or scanning electron microscopy and image analysis. Several parameters were used to objectively compare the efficiency of the methods. Almost all of the tests showed that TS‐GrSPLITT had the highest separation efficiency. The ranking of FFD‐GrSPLITT and GrSettling were considered to be of equal ranking as the order varied for the different parameters and samples used.     

Particle capture efficiency of elliptic cylinder matrices for high-gradient magnetic separation

High-gradient magnetic separation (HGMS) is an effective method to recover fine weakly magnetic minerals or remove ferromagnetic and paramagnetic particles from aqueous solution. The most commonly used matrices are circular cylinders of high magnetic permeability. However, special cross-section matrices may present better magnetic characteristics and improve the separation efficiency. In this paper, the magnetic field and flow field characteristics of elliptic cross-section matrix were studied in the elliptic coordinate system. The particle capture of the elliptic matrix in the longitudinal configuration of HGMS was modelled and the motion equations of the magnetic particles were derived. The particle capture radius and efficiency were calculated and were compared with those of the circular matrix. Two circumstances were considered to investigate the particle capture of elliptic matrix: the short axis of the elliptic matrix is equal to the diameter of the circular matrix and the cross-section area of the elliptic matrix is equal to that of the circular matrix. The influence of λ (ratio of long axis to short axis) of the elliptic matrix on the capture efficiency of micron-sized paramagnetic particles in the two circumstances was also studied. The results showed that for all the conditions considered, there exists an optimum λ at which the particle capture efficiency reaches the maximum. With the matrices of the optimum λ and suitable d values, the capture efficiency of the 10 μm and 2 μm haematite particles can be improved by 6 ~ 22% and 1 ~ 3% compared with the circular matrices, respectively. Both approaches can be adopted to utilize elliptic matrices in HGMS to improve the particle capture efficiency. The results reveal the higher particle capture efficiency of the elliptic matrix and its application possibility in HGMS.     

Spin Polarization and Quantum Spins in Au Nanoparticles

The present study focuses on investigating the magnetic properties and the critical particle size for developing sizable spontaneous magnetic moment of bare Au nanoparticles. Seven sets of bare Au nanoparticle assemblies, with diameters from 3.5 to 17.5 nm, were fabricated with the gas condensation method. Line profiles of the X-ray diffraction peaks were used to determine the mean particle diameters and size distributions of the nanoparticle assemblies. The magnetization curves M(H_a) reveal Langevin field profiles. Magnetic hysteresis was clearly revealed in the low field regime even at 300 K. Contributions to the magnetization from different size particles in the nanoparticle assemblies were considered when analyzing the M(H_a) curves. The results show that the maximum particle moment will appear in 2.4 nm Au particles. A similar result of the maximum saturation magnetization appearing in 2.3 nm Au particles is also concluded through analysis of the dependency of the saturation magnetization M_P on particle size. The M_P(d) curve departs significantly from the 1/d dependence, but can be described by a log-normal function. Magnetization can be barely detected for Au particles larger than 27 nm. Magnetic field induced Zeeman magnetization from the quantum confined Kubo gap opening appears in Au nanoparticles smaller than 9.5 nm in diameter.     

Measurement of size-dependent dynamic shape factors of quartz particles in two flow regimes

Understanding and modeling the behavior of quartz dust particles, commonly found in the atmosphere, requires knowledge of many relevant particle properties, including particle shape. This study uses a single particle mass spectrometer, a differential mobility analyzer, and an aerosol particle mass analyzer to measure quartz aerosol particles mobility (d_m), vacuum aerodynamic, and volume equivalent diameters, mass, composition, effective density, and dynamic shape factor as a function of particle size, in both the free molecular and transition flow regimes. The results clearly demonstrate that dynamic shape factors can vary significantly as a function of particle size. For the quartz samples studied here, the dynamic shape factors increase with size, indicating that larger particles are significantly more aspherical than smaller particles. In addition, dynamic shape factors measured in the free-molecular (χ_v) and transition (χ_t) flow regimes can be significantly different, and these differences vary with the size of the quartz particles. For quartz, χ_v of small (d_m < 200 nm) particles is 1.25, while χ_v of larger particles (d_m ～ 440 nm) is 1.6, with a continuously increasing trend with particle size. In contrast, χ_t of small particles starts at 1.1 increasing slowly to 1.34 for 550 nm diameter particles. The multidimensional particle characterization approach used here goes beyond determination of average properties for each size, to provide additional information about how the particle dynamic shape factor may vary even for particles with the same mass and volume equivalent diameter.

© 2016 American Association for Aerosol Research     

Modification and laboratory evaluation of a TSI ultrafine condensation particle counter (Model 3776) for airborne measurements

A butanol-type ultrafine condensation particle counter (UCPC, Model 3776, TSI, Inc., Shoreview, MN, USA), which can achieve a 50% detection efficiency diameter (d₅₀) of 2.5 nm using a capillary-sheath structure, was modified and tested in the laboratory for airborne measurements. The aerosol flow rate through the capillary is a key factor affecting the quantification of aerosol particle number concentrations. A pressure-dependent correction factor for the aerosol flow rate was determined using a newly added mass flow meter for the sheath flow and the external calibration system. The effect of particle coincidence in the optical sensing volume was evaluated using an aerosol electrometer (AE, Model 3068B, TSI, Inc.) as a reference. An additional correction factor for the coincidence effect was derived to improve the quantification accuracy at higher concentrations. The particle detection efficiency relative to the AE was measured for mobility diameters of 3.1–50 nm and inlet absolute pressures of 101–40 kPa. The pressure dependence of the d₅₀ value, asymptotic detection efficiency, and shape of the particle detection efficiency curve is discussed, along with simple theoretical calculations for the diffusion loss of particles and the butanol saturation ratio in the condenser.

© 2017 American Association for Aerosol Science