Ostwald Ripening of Precipitates I. Numerical Solution for the Particle Size Distribution Function in Closed Systems

1983 ◽  
Vol 87 (4) ◽  
pp. 318-324 ◽  
Author(s):  
Gerd Venzl
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Numerical Solution ◽  
Size Distribution ◽  
Ostwald Ripening ◽  
Size Distribution Function ◽  
Particle Size Distribution Function ◽  
Closed Systems

Informational Measures of the Shape of the Amoroso Distributions for the Research of Dispersed Materials

2021 ◽  
Vol 1031 ◽  
pp. 58-66
Author(s):  
Vitaly Polosin
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Applied Research ◽  
Particle Distribution ◽  
Size Distribution Function ◽  
Distribution Model ◽  
Information Uncertainty ◽  
Particle Size Distribution Function

For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. The article proposes a uniform model for setting the interval of information uncertainty of non-symmetric particle size distributions. Based on the analysis of statistical and information uncertainty intervals, new shape coefficients of distribution models are constructed, these are the entropy coefficients for shifted and non shifted distributions of the Amoroso family. Graphics of dependence of entropy coefficients of non-symmetrical distributions show that distributions well-known are distinguish at small of the shapes parameters. Also it is illustrated for parameters of the form more than 2 that it is preferable to use the entropy coefficients for the unshifted distributions.The material contains also information measures for the well-known logarithmic normal distribution which is a limiting case of distribution Amorozo.

scholarly journals From nucleation and coarsening to coalescence in metastable liquids

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190247 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Irina V. Alexandrova
Keyword(s):  
Mass Transfer ◽  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Ostwald Ripening ◽  
Intermediate Stage ◽  
Size Distribution Function ◽  
The Right ◽  
Transfer Mechanisms

The transition of a metastable liquid (supersaturated solution or supercooled melt) occurring from the intermediate stage (where the crystals nucleate and grow) to the concluding stage (where the larger particles evolve at the expense of the dissolution of smaller particles) is theoretically described, with allowance for various mass transfer mechanisms (reaction on the interface surface, volume diffusion, grain-boundary diffusion, diffusion along the dislocations) arising at the stage of Ostwald ripening (coalescence). The initial distribution function (its ‘tail’) for the concluding stage (forming as a result of the evolution of a particulate assemblage during the intermediate stage) is taken into account to determine the particle-size distribution function at the stage of Ostwald ripening. This modified distribution function essentially differs from the universal Lifshitz–Slyozov (LS) solutions for several mass transfer mechanisms. Namely, its maximum lies below and is shifted to the left in comparison with the LS asymptotic distribution function. In addition, the right branch of the particle-size distribution lies above and is shifted to the right of the LS blocking point. It is shown that the initial ‘tail’ of the particle-size distribution function completely determines its behaviour at the concluding stage of Ostwald ripening. The present theory agrees well with experimental data. This article is part of the theme issue ‘Patterns in soft and biological matters’.

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