Log-normal Particle Size Distribution Research Articles

A time-dependent Eulerian model of droplet diffusion in turbulent flow

Industrial sprays are common in many operations where liquid application to surfaces is required. Maximization of the spray process efficacy depends on accurate simulation of spray characteristics and surrounding flow conditions. Traditionally, droplet modeling has been performed using a Lagrangian approach which requires tracking a sufficient number of droplets to form statistical estimates of droplet deposition. Alternatively for this study, an Eulerian-based flow and droplet transport model using the Direct Quadrature Method of Moments (DQMOM) is applied to spray modeling and is coupled with the Reynolds Averaged Navier Stokes (RANS) equations and Shear Stress Transport (SST) turbulence model. A new turbulent diffusion model is developed for droplet transport which accounts for inertia and time-limit effects and covers a wide range of operational parameters associated with aerial spraying. The model is based on a full parametric study using Lagrangian particle tracking in a uniform, homogeneous and isotropic turbulent flow field and is subsequently implemented within the Eulerian DQMOM framework and compared to: 1) Lagrangian tracking predictions of a log-normal particle size distribution injected into a homogeneous, isotropic turbulent flow field, and 2) full-scale experimental wind tunnel measurements in the anisotropic, non-homogeneous wake of a hollow cone hydraulic nozzle.

Evaluating quantitative 3-D image analysis as a design tool for low enriched uranium fuel compacts for the transient reactor test facility: A preliminary study

3-D image analysis when combined with a non-destructive examination technique such as X-ray computed tomography (CT) provides a highly quantitative tool for the investigation of a material's structure. In this investigation 3-D image analysis and X-ray CT were combined to analyze the microstructure of a preliminary sub-sized fuel compact for the Transient Reactor Test Facility's low enriched uranium conversion program to assess the feasibility of the combined techniques for use in the optimization of the fuel block fabrication process.The quantitative image analysis focused on determining the size and spatial distribution of the surrogate fuel particles and the size, shape, and orientation of voids within the compact. Additionally, the maximum effect of microstructural features on heat transfer through the carbonaceous matrix of the preliminary compact was estimated.The surrogate fuel particles occupied 0.8% of the compact by volume with a log-normal distribution of particle sizes with a mean diameter of 39μm and a standard deviation of 16μm. Roughly 39% of the particles had a diameter greater than the specified maximum particle size of 44μm suggesting that the particles agglomerate during fabrication. The local volume fraction of particles also varies significantly within the compact, although uniformities appear to be evenly dispersed throughout the analysed volume. The voids produced during fabrication were on average plate-like in nature with their major axis oriented perpendicular to the compaction direction of the compact. Finally, the microstructure, mainly the large preferentially oriented voids, may cause a small degree of anisotropy in the thermal diffusivity within the compact. α∥/α⊥, the ratio of thermal diffusivities parallel to and perpendicular to the compaction direction are expected to be no less than 0.95 with an upper bound of 1.

Role of Dipolar Interactions and Volume Particle Size Distribution on the Nonmonotonic Magnetic Field Dependence of the Blocking Temperature in Magnetic Nanoparticles

The nonmonotonic behavior of the magnetic field dependence H of the superparamagnetic blocking temperature TB(H) (or Tmax(H)) of an assembly of magnetic nanoparticles NPs was studied both experimentally and theoretically. We have combined the measurements of zero-field cooling ZFC magnetization curves under H performed on samples with increasing concentration of Ni nanoparticles and Monte Carlo simulations. As a result, we have found that increasing the strength of the dipolar interaction between granules and the occurrence of a very narrow width of a log-normal volume particle size distribution of the NPs suppress the nonmonotonic behavior of Tmax(H).

Modeling and Understanding Combination pMDI Formulations with Both Dissolved and Suspended Drugs.

A simulation model has been established to predict the residual aerodynamic particle size distribution (APSD) of dual-component pressurized metered dose inhalers (pMDIs). More specifically, this model estimates the APSD of pMDI formulations containing dissolved and suspended compounds for various formulations, and has been verified experimentally. Simulated and experimental data illustrate that APSDs of the dissolved and suspended components of the pMDI are influenced by concentrations of the dissolved and micronized suspended drugs, along with suspended drug size. Atomized droplets from such combination formulations may contain varying number of suspended drug particles and a representative concentration of dissolved drug. These sub-populations of atomized droplets may explain the residual APSDs. The suspended drug follows a monomodal, lognormal distribution and is more greatly impacted by the size and concentration of the suspended drug in comparison to the concentration of dissolved drug. On the other hand, dissolved drug illustrates a bimodal, lognormal residual particle size distribution both theoretically and experimentally. The smaller mode consists of residual particles made of dissolved drug only, while the larger mode consists of residual particles that contain both dissolved and suspended drugs. The model effectively predicted the size distributions of both the dissolved and suspended components of combination formulations (r(2) value of 0.914 for the comparison of simulated versus experimental MMAD values for the formulations examined). The results demonstrate that this model is a useful tool that may be able to expedite the development of combination pMDI formulation.

Uncertainty in two-channel infrared remote sensing retrievals of a well-characterised volcanic ash cloud

This work provides a sensitivity study of a two-channel passive infrared remote sensing retrieval of effective radius and optical depth using the Spinning Enhanced Visible and Infrared Imager with channels centred at 10.8 and 12.0 μm and a look-up table approach to calculate mass column loading. The retrieval is applied to images of two ash clouds from the 2010 Eyjafjallajokull eruption on 6 and 13 May 2010. The 2010 eruption of Eyjafjallajokull is well characterised, especially in terms of the airborne volcanic ash, which allows the relative uncertainties to be investigated within the realms of observation and reasonable approximation. The parameters investigated are as follows: refractive index, surface temperature, cloud top temperature, ash bulk density and, in particular, the uncertainties related to the spread of the ash particle size distribution—in terms of the geometric standard deviation of a lognormal particle size distribution. The lack of constraint on particle size distribution is shown to cause the largest uncertainty in retrieved mass column loading for the 6 May and 13 May ash cloud. A review of measured in situ size distributions of airborne particles is presented with justification for the choice of a lognormal size distribution for the 2010 Eyjafjallajokull eruption.

Big grains go far: understanding the discrepancy between tephrochronology and satellite infrared measurements of volcanic ash

Abstract. There is a large discrepancy between the size of volcanic ash particles measured on the ground at least 500 km from their source volcano (known as cryptotephra) and those reported by satellite remote sensing (effective radius of 0.5–9 μm; 95% of particles < 17 μm diameter). Here we present new results from the fields of tephrochronology (a dating technique based on volcanic ash layers), dispersion modelling and satellite remote sensing in an attempt to understand why. A literature review and measurements of prehistoric and recent eruptions were used to characterise the size range of cryptotephra grains. Icelandic cryptotephra deposited in NW Europe has lognormal particle size distributions (PSDs) with median lengths of 20–70 μm (geometric standard deviation: 1.40–1.66; 95th percentile length: 42–126 μm). Grain-size range estimates from the literature are similar. We modelled the settling of volcanic ash using measured fall velocities of ash particles, a release height typical of moderate Icelandic eruptions (10 km), and a wind speed typical for NW Europe (10 m s−1), to show that an ash cloud can transport particles up to 80 μm diameter up to 850 km in 24 h. Thus, even moderately sized Icelandic eruptions can be expected to deposit cryptotephra on mainland Europe. Using simulated satellite infrared data for dispersion-model-derived ash clouds, we demonstrate a systematic bias towards small grain sizes in retrievals of volcanic ash clouds that contain large proportions of cryptotephra-sized grains. As the median radius of the simulated PSD increases, fewer ash-containing pixels are correctly identified. Where retrievals are made of simulated clouds with mass median radii larger than ~ 10 μm, the mean retrieved reff plateaus at around 9 μm. Assuming Mie scattering by dense spheres when interpreting satellite infrared brightness temperature difference (BTD) data puts an upper limit on retrieved particle sizes. If larger, irregularly shaped ash grains can also produce a BTD effect, this will result in further underestimation of grain size, e.g. in coarse ash clouds close to a volcano.

Impact of continuous particle size distribution width and particle sphericity on minimum pickup velocity in gas–solid pneumatic conveying

The minimum pickup velocity (Upu) for pneumatic conveying is analogous to the minimum fluidization velocity (Umf) in fluidization systems in that both dictate the minimum gas velocity required and have important implications in gas–solid flows. However, Upu is not as well-understood as Umf. In this work, the impact of the width of lognormal particle size distributions (PSDs) and particle sphericity (φ) on Upu was determined by the modified weight loss method. Three Geldart Group B materials (namely, glass, aluminum oxide and plastic), with various PSD widths and different particle sphericities (φ), were investigated. Two observations are worth highlighting: (i) as PSD width increases, Upu surprisingly exhibits a non-monotonic behavior (namely, decreases then increases), and (ii) the lower the particle sphericity (φ) is, the greater the extent of the non-monotonic behavior becomes. The discrepancy between the Upu values of the experimental data here and values predicted by available correlations underscores the non-negligible impact of PSD width and particle sphericity, which thereby warrants more understanding and the incorporation of such effects to improve the predictive capability of gas–solid pneumatic conveying.

Comparing nadir and limb observations of polar mesospheric clouds: The effect of the assumed particle size distribution

Nadir viewing observations of Polar Mesospheric Clouds (PMCs) from the Cloud Imaging and Particle Size (CIPS) instrument on the Aeronomy of Ice in the Mesosphere (AIM) spacecraft are compared to Common Volume (CV), limb-viewing observations by the Solar Occultation For Ice Experiment (SOFIE) also on AIM. CIPS makes multiple observations of PMC-scattered UV sunlight from a given location at a variety of geometries and uses the variation of the radiance with scattering angle to determine a cloud albedo, particle size distribution, and Ice Water Content (IWC). SOFIE uses IR solar occultation in 16 channels (0.3–5μm) to obtain altitude profiles of ice properties including the particle size distribution and IWC in addition to temperature, water vapor abundance, and other environmental parameters. CIPS and SOFIE made CV observations from 2007 to 2009. In order to compare the CV observations from the two instruments, SOFIE observations are used to predict the mean PMC properties observed by CIPS. Initial agreement is poor with SOFIE predicting particle size distributions with systematically smaller mean radii and a factor of two more albedo and IWC than observed by CIPS. We show that significantly improved agreement is obtained if the PMC ice is assumed to contain 0.5% meteoric smoke by mass, in agreement with previous studies. We show that the comparison is further improved if an adjustment is made in the CIPS data processing regarding the removal of Rayleigh scattered sunlight below the clouds. This change has an effect on the CV PMC, but is negligible for most of the observed clouds outside the CV. Finally, we examine the role of the assumed shape of the ice particle size distribution. Both experiments nominally assume the shape is Gaussian with a width parameter roughly half of the mean radius. We analyze modeled ice particle distributions and show that, for the column integrated ice distribution, Log-normal and Exponential distributions better represent the range of masses that contribute to the IWC. We further show that agreement between SOFIE and CIPS is further improved with the assumption of either Log-normal or Exponential ice particle size distributions. This improvement suggests that the range of mass bearing particle radii is larger, but not significantly shifted from what is obtained by assuming a Gaussian distribution. The assumption of an Exponential particle size distribution, as shown to be justifiable here, has the attractive benefits of being characterized with a single parameter, the mean radius, which greatly facilitates studies of the spatial and temporal variation of PMC particle size distributions as well as comparisons between observations and models. Overall, our results represent a validation of both the CIPS and SOFIE datasets.

Magnetic nanoparticles for biophysical applications synthesized by high-power physical dispersion

The low cost and high output methods of high-power physical dispersion: the electrical explosion of wire and the laser target evaporation were elaborated for the production of iron oxide magnetic nanoparticles (MNPs) with controlled dispersion parameters and highly reproducible functional properties. The synthesized MNPs were spherical in shape with mean diameter 10nm and lognormal particle size distribution. The phase composition, shape, particle size and functional properties of MNPs were cross-examined by a variety of contemporary experimental techniques. The phase structure of MNPs corresponds to the inverse spinel of magnetite. Meanwhile, due to the non-equilibrium conditions of the dispersion chemical composition of MNPs is close to maghemite—γ-Fe2O3. Their magnetic properties are reproducible and very close to the single domain superparamagnetic behavior. The stability of the suspensions of these MNPs and their applicability in the biophysical purposes such as magneto-induced heating have been demonstrated.

Exponential blocking-temperature distribution in ferritin extracted from magnetization measurements

We developed a direct method to extract the zero-field zero-temperature anisotropy energy barrier distribution of magnetic particles in the form of a blocking-temperature distribution. The key idea is to modify measurement procedures slightly to make nonequilibrium magnetization calculations (including the time evolution of magnetization) easier. We applied this method to the biomagnetic molecule ferritin and successfully reproduced field-cool magnetization by using the extracted distribution. We find that the resulting distribution is more like an exponential type and that the distribution cannot be correlated simply to the widely known log-normal particle-size distribution. The method also allows us to determine the values of the zero-temperature coercivity and Bloch coefficient, which are in good agreement with those determined from other techniques.

Microstructure and micromechanics of polydisperse granular materials: Effect of the shape of particle size distribution

The uniaxial compression of polydisperse spheres with continuous: normal, log-normal, arbitrary and discrete uniform particle size distribution was modelled with the discrete element method (DEM). The evolution of solid fraction, coordination number and fabric tensor with increasing compressive stress was investigated in granular packings of equal mean particle diameter and standard deviation of particle mean diameter. The study of the relationship between the shape of particle size distribution and the micromechanical properties of granular packings included the determination of the contact forces and the degree of mobilisation of friction in contacts between particles. Slight influence of the shape of continuous particle size distribution on the solid fraction and coordination number in polydisperse packings was observed. The discrete uniform distribution provided the number of contacts lower by 7% as compared to continuous distribution. Concerning the mobilisation of friction in contacts between spheres, the average ratio of the tangential: normal contact forces in packing with discrete distribution was 25% higher than the one calculated for normal particle size distribution.

Optimum size of nanorods for heating application

Magnetic nanoparticles (MNP׳s) have become increasingly important in heating applications such as hyperthermia treatment of cancer due to their ability to release heat when a remote external alternating magnetic field is applied. It has been shown that the heating capability of such particles varies significantly with the size of particles used. In this paper, we theoretically evaluate the heating capability of rod-shaped MNP׳s and identify conditions under which these particles display highest efficiency. For optimally sized monodisperse particles, the power generated by rod-shaped particles is found to be equal to that generated by spherical particles. However, for particles which are not mono dispersed, rod-shaped particles are found to be more effective in heating as a result of the greater spread in the power density distribution curve. Additionally, for rod-shaped particles, a dispersion in the radius of the particle contributes more to the reduction in loss power when compared to a dispersion in the length. We further identify the optimum size, i.e the radius and length of nanorods, given a bi-variate log-normal distribution of particle size in two dimensions.

Stratospheric aerosol particle size information in Odin-OSIRIS limb scatter spectra

Abstract. The Optical Spectrograph and InfraRed Imaging System (OSIRIS) onboard the Odin satellite has now taken over a decade of limb scatter measurements that have been used to retrieve the version 5 stratospheric aerosol extinction product. This product is retrieved using a representative particle size distribution to calculate scattering cross sections and scattering phase functions for the forward model calculations. In this work the information content of OSIRIS measurements with respect to stratospheric aerosol is systematically examined for the purpose of retrieving particle size information along with the extinction coefficient. The benefit of using measurements at different wavelengths and scattering angles in the retrieval is studied, and it is found that incorporation of the 1530 nm radiance measurement is key for a robust retrieval of particle size information. It is also found that using OSIRIS measurements at the different solar geometries available on the Odin orbit simultaneously provides little additional benefit. Based on these results, an improved aerosol retrieval algorithm is developed that couples the retrieval of aerosol extinction and mode radius of a log-normal particle size distribution. Comparison of these results with coincident measurements from SAGE III shows agreement in retrieved extinction to within approximately 10% over the bulk of the aerosol layer, which is comparable to version 5. The retrieved particle size, when converted to Ångström coefficient, shows good qualitative agreement with SAGE II measurements made at somewhat shorter wavelengths.

Multimodal particle size distributions of fine-grained sediments: mathematical modeling and field investigation

Multimodal particle size distributions (PSDs) of fine-grained cohesive sediments are common in marine and coastal environments. The curve-fitting software in this study decomposed such multimodal PSDs into subordinate log-normal PSDs. Four modal peaks, consisting of four-level ordered structures of primary particles, flocculi, microflocs, and macroflocs, were identified and found to alternately rise and sink in a flow-varying tidal cycle due to shear-dependent flocculation. The four modal PSD could be simplified further into two discrete size groups of flocculi and flocs. This allowed the development of a two-class population balance equation (TCPBE) model with flocculi and flocs to simulate flocculation involving multimodal PSDs. The one-dimensional vertical (1-DV) TCPBE model further incorporated the Navier-Stokes equation with the k-e turbulence closure and the sediment mass balance equations. Multimodal flocculation as well as turbulent flow and sediment transport in a flow-varying tidal cycle could be simulated well using the proposed model. The 1-DV TCPBE was concluded to be the simplest model that is capable of simulating multimodal flocculation in the turbulent flow field of marine and coastal zones.

Controlled synthesis of nickel ferrite nanocrystals with tunable properties using a novel induction thermal plasma method

Nickel ferrite spinel nanopowders were synthesised using a solution spray radio-frequency inductively coupled plasma reactor over a wide range of compositions (NixFe3-xO4, x ≤ 1), with metastable powders produced for x = 0, 0.25, and 0.5. X-ray fluorescence and X-ray diffraction coupled to Rietveld refinement show that this synthesis technique offers an excellent level of control over both the chemical and crystallographic composition of the nanopowder through the control of the input Fe/Ni ratio. The technique produces highly crystalline nanopowders without the need for post-synthesis annealing. A bulk Fe/Ni ratio ≥2 yields a pure spinel NixFe3-xO4 phase, whereas Fe/Ni ratio <2 results in the excess Ni partitioning to a secondary bunsenite (Nix,Fe1-x)O phase. Morphological analysis using transmission electron microscopy shows that two types of particles are produced in different parts of the reactor: a highly faceted powder with the truncated octahedron morphology and a smaller-sized random agglomerate. The faceted particles have a log-normal particle size distribution, with an average size of about 30 nm while the agglomerates have a characteristic length of ∼3–5 nm.

Sub-micrometer salt aerosol production intended for marine cloud brightening

This paper is largely concerned with research focused on, but not restricted to, aspects of Marine Cloud Brightening (MCB), one of several geo-engineering ideas for reducing the amount of sunlight arriving at the Earth's surface, thereby compensating for global warming resulting from fossil-fuel burning. Predominant attention is given to the development of techniques for generating sprays of sub-micrometer salt particles that can enter marine stratocumulus clouds and increase their albedo, thus producing a cooling. Generation of sub-micrometer salt particles by spraying salt solutions at supercritical conditions is described, along with a description of the apparatus used. Log-normal particle size distributions having median diameters of 32 to 286nm, with GSDs (Geometric Standard Deviations) around 2, were generated by two variations on the technique.

Size-resolved particle distribution and gaseous concentrations by real-world road tunnel measurement

Measurements of aerosol particle number (PN) size distributions (15–700 nm), CO and NOx were performed in a bus tunnel, Australia. Daily mean particle size distributions (PSDs) of mixed diesel/compressed natural gas (CNG) buses traffic flow were determined in four consecutive measurement days. Emission factors (EFs) of PSD of diesel buses and CNG buses were obtained by multiple linear regression (MLR) methods, particle distributions of diesel buses and CNG buses were observed as single accumulation mode and nuclei-mode separately. PSDs of mixed traffic flow were decomposed by two log-normal fitting curves for each 30-minutes interval mean scans, all the mix fleet PSD emission can be well fitted by the summation of two log-normal distribution curves, and these were composed of nuclei mode curve and accumulation curve, which were affirmed as the CNG buses and diesel buses PN emission curves, respectively. Finally, PSDs of diesel buses and CNG buses were quantified by statistical whisker-box charts. For log-normal PSD of diesel buses, accumulation mode diameters were 74.5−87.5 nm, geometric standard deviations were 1.89−1.98. As to log-normal PSD of CNG buses, nuclei-mode diameters were 21−24 nm, geometric standard deviations were 1.27−1.31.

Particle size dependence of respiratory tract uptake in a population cohort

Background. Sources and exposure levels of fine particles (PM2.5) are well known to vary over different microenvironments. Less investigated is the impact of particle size distribution on the respiratory tract uptake. However, the particle size, ranging from few nanometers to many micrometers, over more than three orders of magnitude, significantly affects the infiltration of ambient particles indoors and the uptake of the particles in the respiratory tract. Aim. The aim of the work is to use realistic spatial and particle size distributions in Helsinki to estimate the contribution of various sources and particle sizes to the human uptakes by respiratory tract regions. Methods. The current work uses the FINRISK-cohort with 5700 subjects in the Helsinki metropolitan area to estimate the exposure levels, infiltration and respiratory tract uptake of the particles. Particle concentrations were estimated for 2010 using CAR-FMI dispersion model. Emission source information was used to estimate lognormal source specific particle size distributions for the tailpipe, coarse and regional background concentrations. Size distributions observed at the Hyytiälä background station were used for the latter; the two other distributions were based on literature and thus contain larger uncertainties. Previously developed and evaluated model was used to estimate the changes in the particle size distributions by infiltration. ICRP 1994 model was then used to estimate the respiratory tract uptakes. Results. Particle mass uptake was dominated by accumulation mode particles in the alveolar region, followed by same particle size range in the bronchiole and then coarse (Dp 1-2.5 µm) particles in the alveolar region. Conclusions. When looking at particle mass, ultrafines do not dominate uptakes even in the alveolar region. Accumulation mode particles have an order of magnitude higher contribution to alveolar uptakes when ignoring times spent in traffic.

Effect of milling time and pH on the dispersibility of lead zirconate titanate in aqueous media for inkjet printing

Micrometre-sized Pb(Zr 0.53 Ti 0.47 )O 3 (PZT) powder was dispersed in water, stabilized with the ammonium polyacrylate (PAANH 4 ) and milled to reduce the particle size. The influence of the pH, the amount of PAANH 4 , and the milling time on the zeta potential, the PZT particle size and the particle size distribution was studied. The agglomeration took place regardless the milling time at pH 3. The suspension, containing 5 vol.% of PZT and 5 wt.% of PAANH 4 , milled at pH 10 for 240 min, was stable and contained particles with a narrow, log-normal particle size distribution with the median size of 160 nm. The dissociated carboxyl groups from the PAANH 4 interacted with the PZT particles as evidenced by Fourier transform infrared spectroscopy and electrosterically stabilized the particles in water at pH 10. The PZT particle size and the stability of the suspension fitted the requirements for the ink, suitable for ink-jet printing.

Demagnetization factor for a powder of randomly packed spherical particles

The demagnetization factors for randomly packed spherical particle powders with different porosities, sample aspect ratios, and monodisperse, normal, and log-normal particle size distributions have been calculated using a numerical model. For a relative permeability of 2, comparable to room temperature Gd, the calculated demagnetization factor is close to the theoretical value. The normalized standard deviation of the magnetization in the powder was 6.0%–6.7%. The demagnetization factor decreased significantly, while the standard deviation of the magnetization increased, for increasing relative permeability.