Electric charge distribution and capacitance of agglomerates of spherical particles: Theory and experimental simulation

Brown, Richard C. D.; Hemingway, M.A.

doi:10.1016/0021-8502(95)00524-2

Cited by 21 publications

(23 citation statements)

References 8 publications

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“…For the same volume diameter one can say that agglomerate particles have larger geometric surface area than spherical particles not depending on particle size. For the capacitance of particles, it is known that electrical capacitance of doublet particle is higher than that of singlet sphere (Brown & Hemingway, 1995). There is no exact analytical solution for the capacitance for agglomerates consisting of more than 2 spheres.…”

Section: Introductionmentioning

confidence: 99%

“…There is no exact analytical solution for the capacitance for agglomerates consisting of more than 2 spheres. For the electrical capacitance of loose agglomerate particle consisting of many primary spheres, Brown and Hemingway's (1995) approach using a variational method can be used. The variational calculation gives a better answer than any of the other approximate theories.…”

Section: Introductionmentioning

confidence: 99%

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The effect of particle morphology on unipolar diffusion charging of nanoparticle agglomerates in the transition regime

Shin

Wang

Mertler

et al. 2010

Journal of Aerosol Science

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of particle morphology on unipolar diffusion charging of nanoparticle agglomerates in the transition regime

Shin

Wang

Mertler

et al. 2010

Journal of Aerosol Science

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“…76 -84 Later studies have shown that unipolar and bipolar diffusion charging processes are affected by particle morphology and to a much lesser extent, composition. 57,[85][86][87][88][89][90][91][92] In summary, these studies have shown that…”

Section: Knmentioning

confidence: 86%

Alternatives to the Gravimetric Method for Quantification of Diesel Particulate Matter near the Lower Level of Detection

Swanson

Kittelson

Pui

et al. 2010

Journal of the Air & Waste Management Association

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This paper is part of the Journal of the Air & Waste Management Association's 2010 special issue on combustion aerosol measurements. The issue is a combination of papers that synthesize and evaluate ideas and perspectives that were presented by experts at a series of workshops sponsored by the Coordinating Research Council that aimed to evaluate the current and future status of diesel particulate matter (DPM) measurement. Measurement of DPM is a complex issue with many stakeholders, including air quality management and enforcement agencies, engine manufacturers, health experts, and climatologists. Adoption of the U.S. Environmental Protection Agency 2007 heavy-duty engine DPM standards posed a unique challenge to engine manufacturers. The new standards reduced DPM emissions to the point that improvements to the gravimetric method were required to increase the accuracy and the sensitivity of the measurement. Despite these improvements, the method still has shortcomings. The objectives of this paper are to review the physical and chemical properties of DPM that make gravimetric measurement difficult at very low concentrations and to review alternative metrics and methods that are potentially more accurate, sensitive, and specific. Particle volatility, size, surface area, and number metrics are considered, as well as methods to quantify them. Although the authors believe that an alternative method is required to meet the needs of engine manufacturers, the methods reviewed in the paper are applicable to other areas where the gravimetric method detection limit is approached and greater accuracy and sensitivity are required. The paper concludes by suggesting a method to measure active surface area, combined with a method to separate semi-volatile and solid fractions to further increase the specificity of the measurement, has potential for reducing the lower detection limit of DPM and enabling engine manufacturers to reduce DPM emissions in the future.

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“…We have shown earlier that agglomerate restructuring associated with temperature increase leads to a more compact cluster. Brown and Hemingway (1995) proved that a loose agglomerate has larger capacitance than a close-packed cluster comprising equal number of primary spheres. Following their approach Shin, Wang et al (2010) calculated the capacitance of agglomerates with different configurations and showed that this conclusion is valid for comparison based on the same mobility diameter too.…”

Section: Online Characterization Of Agglomerate Structure and Effectsmentioning

confidence: 99%

“…Shin, Wang et al (2010) calculated the particle electrical capacitance, which is directly proportional to the average charge per particle (Chang 1981), for loose agglomerates with different primary particle arrangements using the variational approach described by Brown and Hemingway (1995). Based on their results, an expression was suggested by Wang et al (2010) for the scaling factor N e :…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Measurement of Metal Nanoparticle Agglomerates Generated by Spark Discharge Using the Universal Nanoparticle Analyzer (UNPA)

Liu

Kim

Wang

et al. 2012

Aerosol Science and Technology

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Nanoparticle agglomerates play an essential role in the manufacturing of many nanomaterials and are commonly found in combustion products. Conventional aerosol instruments based on equivalent spheres are not directly applicable to the measurement of nanoparticle agglomerates. The increasing interest in real-time assessment of the structure of engineered nanoparticle agglomerates and the mass concentration of potentially hazardous agglomerates (e.g., diesel soot, welding fume) makes an instrument devoted to online structure and mass measurements for nanoparticle agglomerates highly desirable. A recently developed instrument, universal nanoparticle analyzer (UNPA), utilizes the close relation between agglomerate structure and unipolar charging properties and infers agglomerate structure from measurement of the average charge per agglomerate. It was used in this study to characterize in situ the structure of metal nanoparticle agglomerates generated by spark discharge, to study the effects of sintering on the structure of these agglomerates, and to make realtime assessment of their airborne mass concentration. The primary particles sizes measured by UNPA for the gold (Au), silver (Ag), and nickel (Ni) agglomerates are in reasonable agreement with the TEM (transmission electron microscopy) sizing results, d p = 7.9 ± 1.5, 11.8 ± 3.2, and 6.6 ± 1.0 nm, respectively. In addition, findings from the study of agglomerate structural change during sintering using the UNPA sensitivity coincide with results from TEM and mobility analyses. With regard to the mass concentration of silver agglomerates at room temperature, good agreement was found un- Address correspondence to David Y. H. Pui, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA. E-mail: dyhpui@umn.edu der our experimental conditions between results given by UNPA, the effective density, and the gravimetric measurement.

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Electric charge distribution and capacitance of agglomerates of spherical particles: Theory and experimental simulation

Cited by 21 publications

References 8 publications

The effect of particle morphology on unipolar diffusion charging of nanoparticle agglomerates in the transition regime

The effect of particle morphology on unipolar diffusion charging of nanoparticle agglomerates in the transition regime

Alternatives to the Gravimetric Method for Quantification of Diesel Particulate Matter near the Lower Level of Detection

Measurement of Metal Nanoparticle Agglomerates Generated by Spark Discharge Using the Universal Nanoparticle Analyzer (UNPA)

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