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Two parameter kinetic equation of size dependent crystal growth
Author(s) -
Rojkowski Z.
Publication year - 1978
Publication title -
kristall und technik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0023-4753
DOI - 10.1002/crat.19780131103
Subject(s) - mathematics , crystal (programming language) , exponential function , standard deviation , kinetic energy , distribution (mathematics) , least squares function approximation , residual , function (biology) , statistics , thermodynamics , mathematical analysis , statistical physics , chemistry , physics , classical mechanics , evolutionary biology , computer science , biology , programming language , algorithm , estimator
The previously proposed hyperbolic, three parameter empirical model of size dependent crystal growth can be reduced to the two parameter one of the form\documentclass{article}\pagestyle{empty}\begin{document}$$ G(L) = \frac{{\left[{G_0 G_l^2 \tau + G_l (G_l - G_0)L} \right]}}{{\left[{G_l^2 \tau + \left({G_l - G_0} \right)L} \right]}}. $$\end{document}This simplification reduces dimension of the least squares correlation of crystal size distribution in MSMPR crystallizer thus saving amount of calculations with a negligible loss of accuracy estimated by means of the mean residual square deviation. The additional advantage is that a differential balance of crystal number in MSMPR crystallizer can be solved analytically for the simplest case of the exponential function of secondary nuclei size distribution. Correlations for single experiment with ammonium alum are presented.