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At least 811 records · Page 45

Performance Assessment of Portable Optical Particle Spectrometer (POPS)

Accurate representation of atmospheric aerosol properties is a long-standing problem in atmospheric research. Modern pilotless aerial systems provide a new platform for atmospheric in situ measurement. However, small airborne platforms require miniaturized instrumentation due to apparent size, power, and weight limitations. A Portable Optical Particle Spectrometer (POPS) is an emerged instrument to measure ambient aerosol size distribution with high time and size resolution, designed for deployment on a small unmanned aerial system (UAS) or tethered balloon system (TBS) platforms. This study evaluates the performance of a POPS with an upgraded laser heater and additional temperature sensors in the aerosol pathway. POPS maintains its performance under different environmental conditions as long as the laser temperature remains above 25 °C and the aerosol flow temperature inside the optical chamber is 15 °C higher than the ambient temperature. The comparison between POPS and an Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) suggests that the coincidence error is less than 25% when the number concentration is less than 4000 cm –3 . The size distributions measured by both of them remained unaffected up to 15,000 cm –3 . While both instruments’ sizing accuracy is affected by the aerosol chemical composition and morphology, the influence is more profound on the POPS.

47 OTHER INSTRUMENTATION↗

The Significance of Multi-Size Carbon Fibers on the Mechanical and Fracture Characteristics of Fiber Reinforced Cement Composites

One of the main challenges of using a high fiber volume content in a cement composite is the narrow margin of fiber volume content beyond which fibers can cause an adverse effect on the mechanical properties. In this paper, the significance of fiber size distribution and fiber volume content of different proportions of chopped and milled carbon microfibers are investigated. The mixes’ flowability showed improvement with altering the fiber size distribution despite having a high fiber content. Uniaxial compression cylinders and unnotched and notched beams were cast and then tested at 7 and 28 days of age. It was found that the compressive strength is significantly affected by fiber size distribution more than fiber volume content. On the other hand, the modulus of rupture and fracture toughness are proportional to the fiber volume content with little effect of fiber size distribution. Finally, neither high fiber volume content nor altered fiber size distribution significantly affected the elastic modulus of the fiber cement composites.

Abdellatef, Mohammed↗

Rainbow Fourier Transform

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Alexandrov, Mikhail D.↗

A Diethylene Glycol Condensation Particle Counter for Rapid Sizing of sub-3 nm Atmospheric Clusters

AbstractThis paper describes the modification of a laminar flow, thermally diffusive universal-fluid condensation particle counter (standard operation: 50% detection efficiency at 5 nm) to rapidly measure the size distribution of sub 3 nm aerosol. Sub 3 nm detection was achieved by using diethylene glycol as the working fluid, which enabled high instrument super-saturations while minimizing homogenous nucleation of the working fluid; a detection efficiency of 50% was achieved at 1.6 nm with laboratory-generated ammonium sulfate aerosol. Rapid aerosol sizing beneath 3 nm was achieved by inverting the measured grown droplet size distribution (1 second sampling) to recover the sampled aerosol size distribution. The developed inversion algorithm utilizes analytical kernel functions determined from the instrument response to pseudo-monodisperse ammonium sulfate aerosol from 1.5 nm to 20 nm, generated by a high resolution DMA and a nano DMA. The inversion algorithm was tested numerically with assumed, idealized aerosol size distributions consistent with observed new particle formation events, yielding reasonable agreement between inverted and assumed aerosol size distributions below 3 nm. Furthermore, this technique provides a measure of the aerosol size assuming an aerosol composition identical to that of the aerosol used to generate the experimentally determined kernel function.

54 ENVIRONMENTAL SCIENCES↗

Comparing Aircraft Observations of Snowfall to Forecasts Using Single or Two Moment Bulk Water Microphysics Schemes

High resolution weather forecast models with explicit prediction of hydrometeor type, size distribution, and fall speed may be useful in the development of precipitation retrievals, by providing representative characteristics of frozen hydrometeors. Several single or double-moment microphysics schemes are currently available within the Weather Research and Forecasting (WRF) model, allowing for the prediction of up to three ice species. Each scheme incorporates different assumptions regarding the characteristics of their ice classes, particularly in terms of size distribution, density, and fall speed. In addition to the prediction of hydrometeor content, these schemes must accurately represent the vertical profile of water vapor to account for possible attenuation, along with the size distribution, density, and shape characteristics of ice crystals that are relevant to microwave scattering. An evaluation of a particular scheme requires the availability of field campaign measurements. The Canadian CloudSat/CALIPSO Validation Project (C3VP) obtained measurements of ice crystal shapes, size distributions, fall speeds, and precipitation during several intensive observation periods. In this study, C3VP observations obtained during the 22 January 2007 synoptic-scale snowfall event are compared against WRF model output, based upon forecasts using four single-moment and two double-moment schemes available as of version 3.1. Schemes are compared against aircraft observations by examining differences in size distribution, density, and content. In addition to direct measurements from aircraft probes, simulated precipitation can also be converted to equivalent, remotely sensed characteristics through the use of the NASA Goddard Satellite Data Simulator Unit. Outputs from high resolution forecasts are compared against radar and satellite observations emphasizing differences in assumed crystal shape and size distribution characteristics.

Molthan, Andrew L.↗

Size and time-resolved growth rate measurements of 1 to 5 nm freshly formed atmospheric nuclei

This study presents measurements of size and time-resolved particle diameter growth rates for freshly nucleated particles down to 1 nm geometric diameter. Novel data analysis methods were developed, de-coupling for the first time the size and time-dependence of particle growth rates by fitting the aerosol general dynamic equation to size distributions obtained at an instant in time. Size distributions of freshly nucleated total aerosol (neutral and charged) were measured during two intensive measurement campaigns in different environments (Atlanta, GA and Boulder, CO) using a recently developed electrical mobility spectrometer with a diethylene glycol-based ultrafine condensation particle counter as the particle detector. One new particle formation (NPF) event from each campaign was analyzed in detail. At a given instant in time during the NPF event, size-resolved growth rates were obtained directly from measured size distributions and were found to increase approximately linearly with particle size from {approx}1 to 3 nm geometric diameter, increasing from 5.5 {+-} 0.8 to 7.6 {+-} 0.6 nm h{sup -1} in Atlanta (13:00) and from 5.6 {+-} 2 to 27 {+-} 5 nm h{sup -1} in Boulder (13:00). The resulting growth rate enhancement {Lambda}, defined as the ratio of the observed growth rate to the growth rate due to the condensation of sulfuric acid only, was found to increase approximately linearly with size from {approx}1 to 3 nm geometric diameter. For the presented NPF events, values for {Lambda} had lower limits that approached {approx}1 at 1.2 nm geometric diameter in Atlanta and {approx}3 at 0.8 nm geometric diameter in Boulder, and had upper limits that reached 8.3 at 4.1 nm geometric diameter in Atlanta and 25 at 2.7 nm geometric diameter in Boulder. Nucleated particle survival probability calculations comparing the effects of constant and size-dependent growth indicate that neglecting the strong dependence of growth rate on size from 1 to 3 nm observed in this study could lead to a significant overestimation of CCN survival probability.

54 ENVIRONMENTAL SCIENCES↗

Endogenic craters on basaltic lava flows - Size frequency distributions

Circular crater forms, termed collapse depressions, which occur on many basalt flows on the earth have also been detected on the moon and Mars and possibly on Mercury and Io. The admixture of collapse craters with impact craters would affect age determinations of planetary surface units based on impact crater statistics by making them appear anomalously old. In the work described in the present paper, the techniques conventionally used in planetary crater counting were applied to the determination of the size range and size frequency distribution of collapse craters on lava flows in Idaho, California, and New Mexico. Collapse depressions range in size from 3 to 80 m in diameter; their cumulative size distributions are similar to those of small impact craters on the moon.

Greeley, R.↗

Breakups are complicated: an efficient representation of collisional breakup in the superdroplet method

Abstract. A key constraint of particle-based methods for modeling cloud microphysics is the conservation of total particle number, which is required for computational tractability. The process of collisional breakup poses a particular challenge to this framework, as breakup events often produce many droplet fragments of varying sizes, which would require creating new particles in the system. This work introduces a representation of collisional breakup in the so-called “superdroplet” method which conserves the total number of superdroplets in the system. This representation extends an existing stochastic collisional-coalescence scheme and samples from a fragment size distribution in an additional Monte Carlo step. This method is demonstrated in a set of idealized box model and single-column warm-rain simulations. We further discuss the effects of the breakup dynamic and fragment size distribution on the particle size distribution, hydrometeor population, and microphysical process rates. Box model experiments serve to characterize the impacts of properties such as coalescence efficiency and fragmentation function on the relative roles of collisional breakup and coalescence. The results demonstrate that this representation of collisional breakup can produce a stationary particle size distribution, in which breakup and coalescence rates are approximately equal, and that it recovers expected behavior such as a reduction in precipitate-sized particles in the column model. The breakup algorithm presented here contributes to an open-source pythonic implementation of the superdroplet method, PySDM, which will facilitate future research using particle-based microphysics.

de Jong, Emily (ORCID:0000000253104554)↗

Simulation of radioactive plume transport in the atmosphere including dynamics of particle aggregation and breakup

Accurate prediction of the atmospheric transport of debris particles relies heavily on our knowledge of the size distribution of the particles within a debris cloud. Assuming a fixed particle size during simulations is not always viable since the size distribution of the debris can change during transport. Various microphysical processes, such as aggregation and breakup, influence debris particles and dictate any changes to the size distribution. To track those changes that can occur, a population balance model can be adopted and instituted within a model framework. Nonetheless, many of the models that simulate the transport of radioactive debris following a device-driven fission incident have historically neglected to consider these processes. As such, this work describes our effort to develop a modeling framework capable of simulating the transport and deposition of a radioactive plume generated from a fission incident with a dynamic population balance including particle aggregation and breakup. Herein the impact of aggregation and breakup, individually and collectively, on the particle size distribution is explored using the developed framework. When simulating aggregation, for example, six mechanisms, including Brownian coagulation, the convective enhancement to Brownian coagulation, van der Waals-viscous force correction for Brownian coagulation, gravitational collection, turbulent inertial motion, and turbulent shear, are considered. Brownian coagulation and its corrections have, as one would expect, a large impact on relatively small aggregates. Aggregates with a diameter that is less than or equal to 1.0 μm, for instance, comprise 50.6 vol % of all aggregates in the absence of aggregation and 31.2 vol % when Brownian coagulation and its corrections are considered. Gravitational collection and, to a much lesser extent, turbulent shear and turbulent inertial motion are, conversely, of great importance to relatively large aggregates (i.e., diameter greater than 3.0 μm). Additionally, the individual effects of atmospheric and particle parameters, such as wind speed and particle density, are examined. Of the parameters examined, turbulent energy dissipation and aggregate fractal dimension (i.e., aggregate shape with lower values representing more irregular particles) were of substantial importance since both terms directly impact aggregate stability and, by extension, the breakup rate. Large-scale transport and deposition simulations in a dry atmosphere are also presented and discussed as a proof of concept.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Liquid Water Cloud Properties During the Polarimeter Definition Experiment (PODEX)

We present retrievals of water cloud properties from the measurements made by the Research Scanning Polarimeter (RSP) during the Polarimeter Definition Experiment (PODEX) held between January 14 and February 6, 2013. The RSP was onboard the high-altitude NASA ER-2 aircraft based at NASA Dryden Aircraft Operation Facility in Palmdale, California. The retrieved cloud characteristics include cloud optical thickness, effective radius and variance of cloud droplet size distribution derived using a parameter-fitting technique, as well as the complete droplet size distribution function obtained by means of Rainbow Fourier Transform. Multi-modal size distributions are decomposed into several modes and the respective effective radii and variances are computed. The methodology used to produce the retrieval dataset is illustrated on the examples of a marine stratocumulus deck off California coast and stratus/fog over California's Central Valley. In the latter case the observed bimodal droplet size distributions were attributed to two-layer cloud structure. All retrieval data are available online from NASA GISS website.

Electromagnetic scattering↗

Evaluation of TiO{sub 2} and TiO{sub 2}/Au nanoparticles as a Potential Radiosensitizers by Decomposition of Methylene Blue

Nanomaterials are constantly used in several applications of science and engineering. Nanoparticles are currently utilized in computer circuits, clothes, luminescent devices, catalysis, medicine, among many others uses. In the clinical field nanomaterials have become an innovative alternative for early diagnosis and treatment of a significant number of medical conditions. Nanoparticles can be utilized in applications ranging from contrast agents for imaging purposes to carriers for drug delivery in cancerous tumors. The use of nanoparticles made of high atomic number elements as noble metals, is becoming an attractive approach for enhancing the radiation dose delivered to a tissue during radiation therapy. The enhancement effect that makes the cells more sensitive to radiation is known as radiosensitization. Materials such as gold (Au) and titanium dioxide (TiO{sub 2}) at the nanoscale have become promising radiosensitizers. When TiO{sub 2} is irradiated with high energy photons, electron-holes are created within the material. This species interacts with surrounding medium generating reactive oxygen species (ROS). ROS create a toxic environment for cancerous cells, ultimately causing their death. On the other hand gold has a different interaction with ionizing radiation. Upon radiation, gold releases a spray of secondary products such as photoelectrons, auger electrons, and characteristic X-rays. The energy created by the escaping electrons leads to DNA strands breaks in the cells causing their death. Therefore, if these nanoparticles are initially accumulated in the tissue to be treated, the dose delivered during radiation therapy is amplified. This represents a synergistic approach to enhance radiation therapy while substantially reducing side effects. Radiosensitization by nanoparticles often depends on their particle size, morphology and synthesis route. The most commonly used methods to synthesize metallic nanoparticles such as gold involves chemical reduction of a metal precursor. In this case, reducing agents are used in order to transform the metallic ions to metal atoms that will subsequently coalesce and grow to form the nanoparticles . Nevertheless there are alternative methods that do not require a chemical reducing agent. Radiation synthesis is one of those processes. The interaction of ionizing radiation with an aqueous solution containing a metal precursor, leads to a phenomena known as radiolysis of water. Radiolysis of water produces chemical species such as solvated electrons (e{sup -}{sub aq}), and hydrogen atoms (H{sup +}). These species are strong reducing agents that bring the metal ions existing in solution into stable metal atoms that will form nanoparticles. Radiation synthesis is a novel method that offers significant advantages over conventional approaches such as wet chemistry routes. In this approach, no further chemical reducing agents are needed, thus it does not generate byproducts that may affect the nanoparticles properties. This is particularly important in medical applications. Furthermore, this technique is designed to work at room temperature and under atmospheric pressures. Nonetheless the most outstanding feature of radiation synthesis is the possibility to control the particle size and size distribution. This route allows for narrow particle size distributions with size ranging from 2 to 30 nm. Furthermore, the availability of different ionizing radiation producing devices such as synchrotrons, X-ray irradiators, and gamma irradiators enables the possibility of manufacturing nanomaterials under various conditions. In this work, Au nanoparticles were deposited onto TiO{sub 2} using the radiation synthesis method. In addition, the radiosensitization characteristics of TiO{sub 2} and TiO{sub 2}/Au nanoparticles were evaluated through the decomposition of the organic dye Methylene Blue (MB). In order to analyze the degradation of the dye the TiO{sub 2} and TiO{sub 2}/Au nanoparticles were placed in an aqueous solution along with MB and subjected to X-ray irradiation. The samples were irradiated for 30 and 60 minutes. The degradation of the MB after irradiation in the presence and absence of the nanomaterials was measured by UV-Vis spectroscopy following the decrease in the absorbance of the dye at 664 nm. (authors)

36 MATERIALS SCIENCE↗

Architected mesoporous crystalline magnesium silicates with ordered pore structures

Novel approaches to harness earth abundant silicates as building blocks for carbon dioxide removal, capture, utilization, and storage are gaining increasing attention in the context of sustainable and low carbon energy and resource recovery. Advancing a calibrated understanding of these fluid-silicate interactions is essential for developing scalable processes. One of the challenges in developing predictive controls over these interactions is the compositional and morphological heterogeneity of naturally occurring, heterogeneous magnesium silicate minerals. To address this challenge, the synthesis of architected mesoporous crystalline magnesium silicate (Mg 2 SiO 4 ) is proposed. While synthesis routes for producing amorphous mesoporous magnesium silicates have been developed via sol-gel methods, approaches to synthesize crystalline magnesium silicates with well-controlled pore size distributions have not been explored. The conventional approaches of converting matter that is amorphous to crystalline states at elevated temperatures results in a heterogeneous pore size distribution. To develop controls on pore size distribution, amorphous mesoporous magnesium silicates are coated with carbon. This approach preserves the pore size distributions during the amorphous to crystalline transformations of Mg-silicates at elevated temperatures. The carbon coating is removed on heating. Magnesium silicate particles produced using this approach have highly ordered pores around 2.58 nm and a specific surface area of 124.25 m 2 /g. In this study, we report the chemical compositions, morphologies, phase transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. The transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. Furthermore, the synthesis routes discussed in this study can be applied translationally to produce metal silicates with ordered mesoporous structures.

36 MATERIALS SCIENCE↗

Extreme value statistics analysis of fracture strengths of a sintered silicon nitride failing from pores

Statistical analysis and correlation between pore-size distribution and fracture strength distribution using the theory of extreme-value statistics is presented for a sintered silicon nitride. The pore-size distribution on a polished surface of this material was characterized, using an automatic optical image analyzer. The distribution measured on the two-dimensional plane surface was transformed to a population (volume) distribution, using the Schwartz-Saltykov diameter method. The population pore-size distribution and the distribution of the pore size at the fracture origin were correllated by extreme-value statistics. Fracture strength distribution was then predicted from the extreme-value pore-size distribution, usin a linear elastic fracture mechanics model of annular crack around pore and the fracture toughness of the ceramic. The predicted strength distribution was in good agreement with strength measurements in bending. In particular, the extreme-value statistics analysis explained the nonlinear trend in the linearized Weibull plot of measured strengths without postulating a lower-bound strength.

Chao, Luen-Yuan↗

Desert Dust Layers Over Polluted Marine Boundary Layers: ACE-2 Measurements and ACE-Asia Plans

Aerosols in ACE-Asia are expected to have some commonalties with those in ACE-2, along with important differences. Among the commonalities are occurrences of desert dust layers over polluted marine boundary layers. Differences include the nature of the dust (yellowish in the East Asia desert outflow, vs. reddish-brown in the Sahara Outflow measured in ACE-2) and the composition of boundary-layer aerosols (e.g., more absorbing, soot and organic aerosol in-the Asian plume, caused by coal and biomass burning, with limited controls). In this paper we present ACE-2 measurements and analyses as a guide to our plans for ACE-2 Asia. The measurements include: (1) Vertical profiles of aerosol optical depth and extinction (380-1558 nm), and of water vapor column and concentration, from the surface through the elevated desert dust, measured by the 14-channel Ames Airborne Tracking Sunphotometer (AATS-14); (2) Comparisons of airborne and shipborne sunphotometer optical depths to satellite-retrieved values, with and without desert dust; (3) Comparisons between airborne Sunphotometer optical depth and extinction spectra and those derived from coincident airborne in situ measurements of aerosol size distribution, scattering and absorption; (4) Comparisons between size distributions measured in situ and retrieved from sunphotometer optical depth spectra; (5) Comparisons between aerosol single scattering albedo values obtained by several techniques, using various combinations of measurements of backscatter, extinction, size distribution, scattering, absorption, and radiative flux. We show how analyses of these data can be used to address questions important to ACE-Asia, such as: (1) How do dust and other absorbing aerosols affect the accuracy of satellite optical depth retrievals? How important are asphericity effects? (2) How important are supermicron dust and seasalt aerosols to overall aerosol optical depth and radiative forcing? How well are these aerosols sampled by aircraft inlets and instruments? (3) How consistent are suborbital in situ and remote measurements of aerosols, among themselves and with satellite retrievals? What are the main reasons for observed inconsistencies?

Russell, Philip B.↗

Improving the Representation of Snow Crystal Properties with a Single-Moment Mircophysics Scheme

Single-moment microphysics schemes are utilized in an increasing number of applications and are widely available within numerical modeling packages, often executed in near real-time to aid in the issuance of weather forecasts and advisories. In order to simulate cloud microphysical and precipitation processes, a number of assumptions are made within these schemes. Snow crystals are often assumed to be spherical and of uniform density, and their size distribution intercept may be fixed to simplify calculation of the remaining parameters. Recently, the Canadian CloudSat/CALIPSO Validation Project (C3VP) provided aircraft observations of snow crystal size distributions and environmental state variables, sampling widespread snowfall associated with a passing extratropical cyclone on 22 January 2007. Aircraft instrumentation was supplemented by comparable surface estimations and sampling by two radars: the C-band, dual-polarimetric radar in King City, Ontario and the NASA CloudSat 94 GHz Cloud Profiling Radar. As radar systems respond to both hydrometeor mass and size distribution, they provide value when assessing the accuracy of cloud characteristics as simulated by a forecast model. However, simulation of the 94 GHz radar signal requires special attention, as radar backscatter is sensitive to the assumed crystal shape. Observations obtained during the 22 January 2007 event are used to validate assumptions of density and size distribution within the NASA Goddard six-class single-moment microphysics scheme. Two high resolution forecasts are performed on a 9-3-1 km grid, with C3VP-based alternative parameterizations incorporated and examined for improvement. In order to apply the CloudSat 94 GHz radar to model validation, the single scattering characteristics of various crystal types are used and demonstrate that the assumption of Mie spheres is insufficient for representing CloudSat reflectivity derived from winter precipitation. Furthermore, snow density and size distribution characteristics are allowed to vary with height, based upon direct aircraft estimates obtained from C3VP data. These combinations improve the representation of modeled clouds versus their radar-observed counterparts, based on profiles and vertical distributions of reflectivity. These meteorological events are commonplace within the mid-latitude cold season and present a challenge to operational forecasters. This study focuses on one event, likely representative of others during the winter season, and aims to improve the representation of snow for use in future operational forecasts.

Molthan, Andrew L.↗

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or “quakes”. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects “tuned critical” behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stressdependent cutoff function. In conclusion, the results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

58 GEOSCIENCES↗

Particle Tracking Methods for Battery Precipitation Reactions

Precipitation and deposition reactions at solid–liquid interfaces play a key role in a number of battery chemistries, including Li-ion, so-called “anode free” batteries, zinc-based battery chemistries, and lithium–sulfur, among others. Although models with heterogeneous nucleation and growth phenomena are present in the literature, papers have not to date provided much detail on the numerical algorithms used to track the temporal evolution of the particle size distribution of deposits on electrode surfaces. In this paper we examine several approaches to discretize and track the particle size distribution, demonstrating that common approaches lead to anomalous flattening of the particle size distribution. We conclude by presenting an algorithm that preserves the appropriate particle size distribution during particle growth.

Algorithms↗