A THEORY OF THE SIZE DISTRIBUTION OF PARTICLES IN A COMMINUTED SYSTEM

1943 ◽  
Vol 21a (6) ◽  
pp. 57-64 ◽  
Author(s):  
Laurence Griffith
Keyword(s):  
Statistical Mechanics ◽  
Size Distribution ◽  
Size Distributions ◽  
Colloidal Systems ◽  
Mathematical Procedure ◽  
Classical Statistical Mechanics ◽  
Distribution Laws ◽  
Size Distribution Of Particles

It is shown that the problem of the size distribution of particles in a system that has been ground can be treated by the general methods of the theory of probability. The mathematical procedure employed is almost identical m form with that used in the classical statistical mechanics of gases, although the fundamental ideas are different, as the molecules of a solid are not free to move. The distribution laws developed agree with the known empirical laws for particles of sizes down to about one micron, but proof of the theory will depend upon study of size distributions in colloidal systems.

Transport Methods of Determining Particle Size Distributions in Colloidal Systems

1981 ◽  
Vol 54 (4) ◽  
pp. 882-891 ◽  
Author(s):  
C. D. Shuster ◽  
J. R. Schroeder ◽  
D. McIntyre
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Size Range ◽  
Size Distributions ◽  
Rotor Speed ◽  
Colloidal Systems ◽  
Particle Size Distributions ◽  
Density Distributions ◽  
Yield Information

Abstract The two techniques examined in this work yield information about the particle size distribution of the latexes studied. The ease of measurement is improved over previous methods used on broadly distributed latexes. The TPC curves for both the natural and synthetic latexes correlate with the centrifuge curves. Both techniques show the Hevea to have larger particles than the guayule. The techniques also show SBR latex samples 1 and 2 to have larger particles than samples 3 and 4. The TPC is useful only for particles between 0.3 µm and 20 µm in size. The centrifuge can be used for any size range of particles by altering the rotor speed or eluant density. By employing the proper mathematics, these data could be easily converted from optical density distributions to particle size distributions.

scholarly journals A model for the size distribution of marine microplastics: A statistical mechanics approach

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259781
Author(s):  
Kunihiro Aoki ◽  
Ryo Furue
Keyword(s):  
Statistical Mechanics ◽  
Size Distribution ◽  
Gradual Increase ◽  
Rapid Decrease ◽  
The Other ◽  
Sea Surface ◽  
Size Distributions ◽  
Occurrence Probability ◽  
Biological Uptake ◽  
Data Source

The size distribution of marine microplastics provides a fundamental data source for understanding the dispersal, break down, and biotic impacts of the microplastics in the ocean. The observed size distribution at the sea surface generally shows, from large to small sizes, a gradual increase followed by a rapid decrease. This decrease has led to the hypothesis that the smallest fragments are selectively removed by sinking or biological uptake. Here we propose a new model of size distribution, focusing on the fragmentation of marine plastics. The model is inspired by ideas from statistical mechanics. In this model, the original large plastic piece is broken into smaller pieces once by the application of “energy” or work by waves or other processes, under two assumptions, one that fragmentation into smaller pieces requires larger energy and the other that the occurrence probability of the “energy” exponentially decreases toward larger energy values. Our formula well reproduces observed size distributions over wide size ranges from micro- to mesoplastics. According to this model, the smallest fragments are fewer because large “energy” required to produce such small fragments occurs more rarely.

scholarly journals Effect of Strain-Induced Precipitation on the Recrystallization Kinetics in a Model Alloy

2021 ◽  
Author(s):  
Mo Ji ◽  
Martin Strangwood ◽  
Claire Davis
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Avrami Exponent ◽  
Model Alloy ◽  
Size Distributions ◽  
Recrystallization Kinetics ◽  
Grain Size Distributions ◽  
Recrystallized Grain Size ◽  
Nb Addition

AbstractThe effects of Nb addition on the recrystallization kinetics and the recrystallized grain size distribution after cold deformation were investigated by using Fe-30Ni and Fe-30Ni-0.044 wt pct Nb steel with comparable starting grain size distributions. The samples were deformed to 0.3 strain at room temperature followed by annealing at 950 °C to 850 °C for various times; the microstructural evolution and the grain size distribution of non- and fully recrystallized samples were characterized, along with the strain-induced precipitates (SIPs) and their size and volume fraction evolution. It was found that Nb addition has little effect on recrystallized grain size distribution, whereas Nb precipitation kinetics (SIP size and number density) affects the recrystallization Avrami exponent depending on the annealing temperature. Faster precipitation coarsening rates at high temperature (950 °C to 900 °C) led to slower recrystallization kinetics but no change on Avrami exponent, despite precipitation occurring before recrystallization. Whereas a slower precipitation coarsening rate at 850 °C gave fine-sized strain-induced precipitates that were effective in reducing the recrystallization Avrami exponent after 50 pct of recrystallization. Both solute drag and precipitation pinning effects have been added onto the JMAK model to account the effect of Nb content on recrystallization Avrami exponent for samples with large grain size distributions.

scholarly journals Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study

2004 ◽  
Vol 4 (5) ◽  
pp. 1255-1263 ◽  
Author(s):  
B. Mayer ◽  
M. Schröder ◽  
R. Preusker ◽  
L. Schüller
Keyword(s):  
Remote Sensing ◽  
Size Distribution ◽  
Droplet Size ◽  
Cloud Droplet ◽  
Droplet Size Distribution ◽  
Single Scattering ◽  
Effective Radius ◽  
Radiative Properties ◽  
High Angular Resolution ◽  
Size Distributions

Abstract. Cloud single scattering properties are mainly determined by the effective radius of the droplet size distribution. There are only few exceptions where the shape of the size distribution affects the optical properties, in particular the rainbow and the glory directions of the scattering phase function. Using observations by the Compact Airborne Spectrographic Imager (CASI) in 180° backscatter geometry, we found that high angular resolution aircraft observations of the glory provide unique new information which is not available from traditional remote sensing techniques: Using only one single wavelength, 753nm, we were able to determine not only optical thickness and effective radius, but also the width of the size distribution at cloud top. Applying this novel technique to the ACE-2 CLOUDYCOLUMN experiment, we found that the size distributions were much narrower than usually assumed in radiation calculations which is in agreement with in-situ observations during this campaign. While the shape of the size distribution has only little relevance for the radiative properties of clouds, it is extremely important for understanding their formation and evolution.

Factors Influencing the Particle Size Distribution in an Abrasive Waterjet

1991 ◽  
Vol 113 (4) ◽  
pp. 402-411 ◽  
Author(s):  
T. J. Labus ◽  
K. F. Neusen ◽  
D. G. Alberts ◽  
T. J. Gores
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Cutting Speed ◽  
Target Material ◽  
Abrasive Waterjet ◽  
Sieve Analysis ◽  
Size Distributions ◽  
Mixing Process ◽  
Jet Mixing

A basic investigation of the factors which influence the abrasive jet mixing process was conducted. Particle size analysis was performed on abrasive samples for the “as-received” condition, at the exit of the mixing tube, and after cutting a target material. Grit size distributions were obtained through sieve analysis for both water and air collectors. Two different mixing chamber geometries were evaluated, as well as the effects of pressure, abrasive feed rate, cutting speed, and target material properties on particle size distributions. An analysis of the particle size distribution shows that the main particle breakdown is from 180 microns directly to 63 microns or less, for a nominal 80 grit garnet. This selective breakdown occurs during the cutting process, but not during the mixing process.

scholarly journals On the Shape–Slope Relation of Drop Size Distributions in Convective Rain

2005 ◽  
Vol 44 (7) ◽  
pp. 1146-1151 ◽  
Author(s):  
Axel Seifert
Keyword(s):  
Size Distribution ◽  
Gamma Distribution ◽  
Drop Size ◽  
Empirical Relation ◽  
Size Distributions ◽  
Shape Parameters ◽  
Raindrop Size Distribution ◽  
Raindrop Size ◽  
Drop Size Distributions ◽  
Good Agreement

Abstract The relation between the slope and shape parameters of the raindrop size distribution parameterized by a gamma distribution is examined. The comparison of results of a simple rain shaft model with an empirical relation based on disdrometer measurements at the surface shows very good agreement, but a more detailed discussion reveals some difficulties—for example, deviations from the gamma shape and the overestimation of collisional breakup.

scholarly journals Methodology for determining rom size distribution

2014 ◽  
Vol 67 (4) ◽  
pp. 405-412
Author(s):  
Christiane Ribeiro da Silva ◽  
Vládia C. G. de Souza ◽  
Jair C. Koppe
Keyword(s):  
Size Distribution ◽  
Distribution Curve ◽  
Size Distributions ◽  
Sampling Protocol ◽  
Product Size ◽  
Operational Conditions ◽  
Specific Protocol ◽  
Open Side ◽  
Ore Dressing

A methodology to determine the size distribution curve of the ROM was developed in a Brazilian iron ore mine. The size of the larger fragments was determined taking photographs and setting the scale of the images to analyze their dimensions (length of their edges and areas). This was implemented according to a specific protocol of sampling that involves split and homogenization stages in situ of a considerable quantity of ore (about 259 metric tonnes). During the sampling process, larger fragments were separated and smaller size material was screened. The methodology was developed initially in order to preview the performance of a primary gyratory crusher that is fed directly from trucks. Operational conditions of the equipment such as closed and open-side settings could be adjusted previously, obtaining different product size distributions. Variability of size of the fragments affects subsequent stages of crushing and can increase circulating load in the circuit. This leads to a decrease of productivity or recovery of the ore dressing. The results showed insignificant errors of accuracy and reproducibility of the sampling protocol when applied to friable itabirite rocks.

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