The Bipolar Diffusion Charging of Nanoparticles: A Review and Development of Approaches for Non-Spherical Particles

Motion of nanoparticles suspended in fluids are dominated by Brownian diffusion-a physical property well understood following the work by Einstein in 1905. While theoretical derivation and experimental measurement of the diffusion coefficients for spherical particles are well developed, such information is lacking for non-spherical particles as the coupled rotational and translational motion hinders a clear description of the overall diffusive outcome. In this study, the Brownian diffusion of elongated nano-fibers is investigated numerically. Motion of the nano-fiber is resolved by solving the system of equations governing its coupled translational and rotational motion. To isolate the Brownian diffusion from other diffusive forces, test fibers are immersed in an unbounded quiescent fluid where only the hydrodynamic drag and Brownian forces are present. The study allows a close look at the Brownian diffusion of nano-fibers with respect to the translation, rotation, coupling, and how the rotation affects the particle's macroscopic diffusion properties. In this study, the Brownian diffusion of ellipsoidal particles are studied. The translational and the rotational Brownian motions and their coupling are included in the analysis. Particular attention was given to the rotational relaxation time in determining the non-spherical particle's isotropic and anisotropic diffusive properties. Theoretical and semi-empirical equations are developed to quantify the diffusion coefficients of nano-fibers. The predications are compared with available experimental data. The comparison to the analytic solution in the limiting case of a sphere is with excellent accuracy. The study opens up new approaches for studying fundamental diffusive processes of nonspherical elongated particles that are abundant in natural environment.

Section: Fiber Diffusion-equivalent Spheresmentioning

confidence: 99%

Brownian diffusion of fibers

Tian

Ahmadi

2016

“…Inaccuracies in the assumed charged fractions is one of the main contributors of the measurement uncertainties of such spectrometers (Liu and Deshler 2003) and can have a strong effect on the recovered number concentrations (Xiao et al 2012). Any progress in the understanding of charging mechanisms can help improve the quality of DMA size distribution measurements (Gopalakrishnan et al 2015), especially since experimental quantification of charging probabilities would be impractical in such applications.…”

Section: Introductionmentioning

confidence: 99%

Methodology to quantify the ratio of multiple-to single-charged fractions acquired in aerosol neutralizers

Mamakos

2016

A methodology for the quantification of the ratio of multiple-to single-charged fractions acquired in aerosol neutralizers is presented. These quantities are necessary for an accurate monodisperse calibration of aerosol instrumentation. A tandem Differential Mobility Analyzer (DMA) setup is required, with the second DMA scanning the electrical mobility spectra classified in the first DMA. In contrast to previous studies on the quantification of bipolar charge distribution utilizing tandem DMA schemes, the methodology targets at the direct determination of the multiple-to singlecharge fractions and does so through the analysis of the raw signal instead of the inverted size distributions, thus circumventing errors associated with the assumptions in the DMA data inversion. The proposed methodology is employed for the characterization of different types of aerosols commonly employed for instrument calibration. Spherical liquid particles (emery oil and dioctyl sebacate) were found to acquire lower multiple charge fractions than those suggested by the commonly employed regression fits of Wiedensohler, which was published in the year 1988 in the Journal of Aerosol Science (vol. 19,, but still within the range of values reported in the literature. Diffusion flame soot and spark generated graphite particles, produced by a miniCAST 6203C burner and a PALAS DNP 3000, respectively, exhibited higher fraction of multiple charges, in good agreement with previous work on agglomerates. The use of a soft X-ray bipolar charger (TSI 3088) yielded systematically higher multiple fractions of positive charges compared to a 85 Kr neutralizer (TSI 3077A), confirming the importance of direct photoionization charging on the former.

“…Recently, Tian et al (2016) investigated the diffusion of fibers in a quiescent air and developed a diffusion-equivalent sphere diameter for characterizing fiber mobility driven by Brownian motion. A comparison of the predicted diffusion-equivalent spheres to the measured mobility equivalent diameters for a series of nanorods (Gopalakrishnan et al 2015b) showed excellent agreement (Tian et al 2016). Melas et al (2014Melas et al ( , 2015 investigated the friction coefficient and mobility radius of the fractal-like aggregates in the transition regime, and the application to straight chain agglomerates.…”

Section: Introductionmentioning

confidence: 91%

“…Accordingly, the equivalent electrical mobility sphere for a non-spherical particle is defined as the sphere achieving the same drift velocity as that of the particle with the same charge in a constant electric field. From a combination of kinetic theory of ion transport in gases (Mason and McDaniel 1988), the collision limited reaction rate theory (Gopalakrishnan et al 2011), bipolar diffusion charging analysis (Gopalakrishnan et al 2015b), and measurements in a combined tandem ion mobility spectrometry-mass spectrometry (IMS-MS) (Hogan and Fern andez de la Mora 2011), the mobility diameter for a non-spherical particle can be expressed as (Gopalakrishnan et al 2015b)…”

Section: Aerodynamic Equivalent Spherementioning

confidence: 99%

Mobility of nanofiber, nanorod, and straight-chain nanoparticles in gases

Tian

Ahmadi

2017

With the fast development of nanotechnology, accurate measurement and classification of nanoparticles are in great need. Nanoparticles frequently appear in non-spherical forms such as long aspect ratio nanofibers, nanotubes, and irregular nano-agglomerates. While the welldeveloped classical studies were mainly in continuum regime with spherical particles, dynamics of the non-spherical nanoparticles is not fully understood. In this study, orientation-averaged mobility of nanofiber and nanorod (with no preferred alignment) is examined by the methods of Brownian diffusion theory, a combination of collision limited reaction rate theory and the bipolar diffusion charging analysis. Comparisons to empirical predictions from the experimental measurements are also made. The study leads to the discovery of a surface-dominated mobility for high aspect ratio nanoparticles with characteristic Knudsen number greater than 5. In view of the extreme relative length scales between particle size and the gas mean free path, particles of all morphologies can be viewed as point collisions; therefore, the equivalent surface mobility diameter is reasonably justified. This finding has been verified in the current study with high aspect ratio particles. For non-spherical particles of more general forms, further investigation is needed. As expected, accuracy of this approximation reduces as the characteristic Knudsen number decreases. When Kn(d L ) < 0.1, the study shows that particle morphology starts to play an important role. A review of particle mobility for all Knudsen number flows is also provided.