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Experimental identification of entropy model of comminution process

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Abstract

The entropy model based on population balance enables theoretical prediction of particle size distribution of comminution product. Selection and breakage functions occur in this model. The form of the selection function was determined experimentally. Informational entropy was used for the breakage function determination. Parameters of both functions can be estimated from experiments. The parameter identification of the entropy model was carried out on the basis of research on limestone comminution. Grinding tests were carried out in a laboratory fluidised bed jet mill. The results of the experimental identification confirm the accuracy of the entropy model.

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Abbreviations

a :

parameter of selection function

b ij :

breakage function

c K :

constant factor of Kick’s hypothesis (J/kg)

c R :

constant factor of Rittinger’s hypothesis (J m/kg)

e ij :

density of used energy (J/kg)

f p i :

particle size distribution of product

f s j :

particle size distribution of feed

Fp (x ):

cumulative particle size distribution of product

Fs (x ):

cumulative particle size distribution of feed

i :

size class number of product

j :

size class number of feed

m :

number of size classes

p ij :

transition function

S j :

selection function

x :

particle size (μm)

x i :

arithmetic mean of size limits of i th class of product (μm)

y j :

arithmetic mean of size limits of j thclass of feed (μm)

α:

parameter of power form of selection function

λ:

Lagrange multiplier (kg/J)

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Authors and Affiliations

  1. Department of Boilers and Thermodynamics, Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Armii Krajowej 19C, 42218, Czestochowa, Poland

    Henryk Otwinowski, Daniel Zbroński & Dariusz Urbaniak

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  1. Henryk Otwinowski
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Correspondence to Henryk Otwinowski.

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Otwinowski, H., Zbroński, D. & Urbaniak, D. Experimental identification of entropy model of comminution process. Granular Matter 9, 377–386 (2007). https://doi.org/10.1007/s10035-007-0049-z

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