Radiation Properties for Polydispersions: Application to Coal

The extinction and absorption coefficients and the asymmetry factor for polydispersions of absorbing spherical particles are analyzed. The results are based upon Mie’s theory for single spherical particles and particle size distributions found in practical systems. Dimensinnless spectral radiation properties are shown to be independent of the explicit size distribution and functions only of the average radii and the index of refraction. The Planck and Rosseland mean coefficients are also presented and the dependence on temperature is explicitly denoted for a large practical temperature range. The results for coal with optical properties which are wavelength dependent indicate the usefulness of the dimensionless and mean properties.

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Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 2. Interparticle forces and the quasi-stationary equilibrium hypothesis

Journal of Fluid Mechanics ◽

10.1017/s0022112084001403 ◽

1984 ◽

Vol 143 ◽

pp. 387-411 ◽

Cited By ~ 11

Author(s):

I. A. Valioulis ◽

E. J. List ◽

H. J. Pearson

Keyword(s):

Monte Carlo Simulation ◽

Particle Size ◽

Monte Carlo ◽

Particle Size Distribution ◽

Size Distribution ◽

Dimensional Analysis ◽

Spherical Particles ◽

Size Distributions ◽

Particle Size Distributions ◽

Coagulation Rate

Hunt (1982) and Friedlander (1960a, b) used dimensional analysis to derive expressions for the steady-state particle-size distribution in aerosols and hydrosols. Their results were supported by the Monte Carlo simulation of a non-interacting coagulating population of suspended spherical particles developed by Pearson, Valioulis & List (1984). Here the realism of the Monte Carlo simulation is improved by accounting for the modification to the coagulation rate caused by van der Waals', electrostatic and hydrodynamic forces acting between particles. The results indicate that the major hypothesis underlying the dimensional reasoning, that is, collisions between particles of similar size are most important in determining the shape of the particle size distribution, is valid only for shear-induced coagulation. It is shown that dimensional analysis cannot, in general, be used to predict equilibrium particle-size distributions, mainly because of the strong dependence of the interparticle force on the absolute and relative size of the interacting particles.

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Effect of lognormal particle size distributions of non-spherical particles on hopper discharge characteristics

Chemical Engineering Research and Design ◽

10.1016/j.cherd.2020.09.001 ◽

2020 ◽

Vol 163 ◽

pp. 230-240

Author(s):

Ya Zhao ◽

Jia Wei Chew

Keyword(s):

Particle Size ◽

Spherical Particles ◽

Size Distributions ◽

Particle Size Distributions ◽

Discharge Characteristics ◽

Hopper Discharge

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RADIATIVE PROPERTIES OF (SPHERICAL) PARTICLES AND OF PARTICLE-SIZE DISTRIBUTIONS**Chapter 4 is by S. S. Penner.

Radiation and Reentry ◽

10.1016/b978-0-12-395687-3.50007-7 ◽

1968 ◽

pp. 208-230

Author(s):

S.S. Penner ◽

Daniel B. Olfe

Keyword(s):

Particle Size ◽

Radiative Properties ◽

Spherical Particles ◽

Size Distributions ◽

Particle Size Distributions

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Method of Calculating True Particle Size Distributions from Observed Sizes in a Thin Section

Microscopy and Microanalysis ◽

10.1017/s1431927698980102 ◽

1998 ◽

Vol 4 (2) ◽

pp. 122-127 ◽

Cited By ~ 3

Author(s):

E. Bruce Nauman ◽

Timothy J. Cavanaugh

Keyword(s):

Particle Size ◽

Thin Section ◽

Previous Method ◽

Spherical Particles ◽

Average Particle ◽

Particle Sizes ◽

Size Distributions ◽

Particle Size Distributions ◽

Negative Particle ◽

Transmission Microscopy

Particle size distributions obtained from a thin section are usually a skewed version of the true distribution. A previous method for determining the parent distribution was questionable because negative particle frequencies could be obtained. Here, we describe a method of determining parent distributions of spherical particles using a model with adjustable parameters. Our calculated distributions are somewhat broader than the distributions obtained with previous methods, but the average particle sizes are nearly identical. The newly developed model is applicable to any type of transmission microscopy.

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Particle size distributions from small-angle scattering using global scattering functions

Journal of Applied Crystallography ◽

10.1107/s0021889804008969 ◽

2004 ◽

Vol 37 (4) ◽

pp. 523-535 ◽

Cited By ~ 228

Author(s):

G. Beaucage ◽

H. K. Kammler ◽

S. E. Pratsinis

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Small Angle ◽

Particle Surface ◽

Spherical Particles ◽

Radius Of Gyration ◽

Size Distributions ◽

Particle Size Distributions ◽

Bet Analysis

Control and quantification of particle size distribution is of importance in the application of nanoscale particles. For this reason, polydispersity in particle size has been the focus of many simulations of particle growth, especially for nanoparticles synthesized from aerosols such as fumed silica, titania and alumina. Single-source aerosols typically result in close to a log-normal distribution in size and micrograph evidence generally supports close to spherical particles, making such particles ideal candidates for considerations of polydispersity. Small-angle X-ray scattering (SAXS) is often used to measure particle size in terms of the radius of gyration,Rg, using Guinier's law, as well as particle surface area,S/V, from the Porod constantBand the scattering invariantQ. In this paper, the unified function is used to obtain these parameters and various moments of the particle size distribution are calculated. The particle size obtained from BET analysis of gas adsorption data directly agrees with the moment calculated fromS/V. Scattering results are also compared with TEM particle-counting results. The potential of scattering to distinguish between polydisperse single particles and polydisperse particles in aggregates is presented. A generalized index of polydispersity for symmetric particles, PDI =BRg4/(1.62G), whereGis the Guinier prefactor, is introduced and compared with other approaches to describe particle size distributions in SAXS, specifically the maximum-entropy method.

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