United Probabilistic Nature and Model of Chemical and Mechanical Reactions of Consecutive Destruction of Substance
American Journal of Physical Chemistry
Volume 4, Issue 6, December 2015, Pages: 42-47
Received: Oct. 8, 2015;
Accepted: Oct. 21, 2015;
Published: Oct. 31, 2015
Views 2928 Downloads 72
Vitaliy Pavlovich Malyshev, Chemical and Metallurgical Institute, Karaganda, Republic of Kazakhstan
Astra Mundukovna Makasheva, Chemical and Metallurgical Institute, Karaganda, Republic of Kazakhstan
Yuliya Sergeevna Zubrina, Chemical and Metallurgical Institute, Karaganda, Republic of Kazakhstan
Into development of mathematical methods of forecasting of grinding process materials based on different aspects of the application of systems theory, the authors propose to be likened to and summarize chemical and mechanical processes of sequential destruction of matter on the basis of a single probability of their nature. Expression for the rate of direct reaction of substances is opened taking into account sense of product of the mole fractions of reacting molecules as probabilities of their simultaneous presence at any point of reactionary space (a concentration factor Pconc), a steric factor of Pst – as probabilities of successful mutual orientation of molecules, an activation factor of Pa – as probabilities of overcoming of a power barrier of activation under the influence of the frequency of impacts of Z: V=Z∙Pconc∙ Pst ∙ Pа. Probabilistic representation of the rate of chemical reactions more directly reflects randomized the state of the reacting system and can be generalized to any of its variants, in particular, mechanical. This allowed us to consider the process of grinding material from new point of view, and moreover - to liken of its kinetics successive irreversible reactions to give the general expression for the output of the intermediates (fractions) at any time for any number of destruction stages. On this basis calculated the entropy of mixing of fractions and the dynamics of change corresponding to the log-normal distribution of fractions which known by data of practices.
Vitaliy Pavlovich Malyshev,
Astra Mundukovna Makasheva,
Yuliya Sergeevna Zubrina,
United Probabilistic Nature and Model of Chemical and Mechanical Reactions of Consecutive Destruction of Substance, American Journal of Physical Chemistry.
Vol. 4, No. 6,
2015, pp. 42-47.
Copyright © 2015 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Kafarov V.V., Dorohov I.N., Arutyunov S. Yu. System analysis of processes of chemical technology. The grinding process of bulk materials. M.: Nauka, 1985. – 440 p.
Bernotat S., Schönerl K.: Size Reduction. In: Ullmann’s Encyclopaedia of Industrial Chemistry. VCH, Weinheim, 1998.
Andreev S.E., Tovarov V.V., Petrov V.A. Laws of grinding and calculus of characteristics distribution of particle size distribution. – M.: Mettalurgizdat, 1959. – 437 p.
Linch A. Cycles of crushing and grinding. – M. Nedra, 1980. – 343 p.
Hodakov G.S. Physic of grinding. – M.: Nauka, 1972. – 308 p.
The mathematical description and calculation algorithms of mill of cement industry. / Ed. M.A. Verdiyan. M.: NIITSement. – 94 p.
L.G. Austin. Introduction to the mathematical description of grinding as a rate process. Powder Technology, 5 (1971/1972) pp. 1-17.
Filichev P.V. Forecasting of characteristics of grinding processes through the application of the principle of maximum entropy. Dissertation of the candidate of technical sciences. – Ivanovo, 1999. – 103 p.
Emanuel N. M., Knorre D.G. Course of chemical kinetics. The textbook for chemical faculties. Prod. the 3rd, reslave. and additional – M.: The higher school, 1974. – 400 p.
Malyshev V.P., Turdukozhayeva A.M. (Makasheva). What Thunder There and is not Heard When Using Ball Mills? // Journal Materials Science and Engineering A. – 2013. – № 2. – V. 3. – P. 131-144.
Malyshev V.P., Turdukozhayeva A.M., Kaykenov D.A. Development of the theory of crushing ores on the basis of the molecular theory of impacts and formal kinetics of consecutive reactions//Ore concentration. – 2012. – № 4. – P. 29-35.
Malyshev V.P., Turdukozhayeva A.M., Kaykenov D.A. Display of process wet crushing in ball mills probabilistic model//Ore concentration. – 2013. – № 1. – P. 27-30.
Rodigin N.M., Rodigina E.N. Consecutive chemical reactions. Mathematical analysis and calculation. – M.: Reports of Academy of Sciences of the USSR, 1960. – 140 p.
Malyshev V.P., Turdukozhayeva A.M. Kaykenov D. A. Development of mathematical model of consecutive destruction of substance by a method of direct integration// Reports of National Academy of Sciences The Republic of Kazakhstan. – 2012. – № 4. – P. 5-13.
Razumovsky N.K. The character of distribution of contents metals in ore fields// Reports of Academy of Sciences of the USSR. – 1940. – V. 28. – № 9. – P. 815-817.
Kolmogorov A.N. About logarithmic normal law distribution of the sizes at particles when crushing// Reports of Academy of Sciences of the USSR. – 1994. – V. 31. – № 2. – P. 99-101.
Malyshev V.P., Makasheva A.M., Zubrina Y.S. General view of the integrals in the decomposition of a complex function into elementary fractional. // DNANRK. – 2014. No. 6. – P. 11-14.
Malyshev V.P., Zubrina Y.S., Kaikenov D.A., Makasheva A.M. Analysis of convergence and limit of the amount of functional series for fractional composition at the sequential destruction. // DNANRK. – 2015. No. 4. P. 78-83.
Malyshev V.P., Turdukozhayeva A.M. Determination of effective energy of activation, the period of semi-crushing and entropy of crushing on the basis of the probabilistic theory of process// Ore concentration. – 2013. – № 5. – P. 17-20.
Malyshev V.P., Turdukozhayeva A.M., Bekturganov N.S., Kaykenov D A. Logarifmic normal distribution of fractions when crushing materials as an attractor in probabilistic model of process// Reports of National Academy of Sciences The Republic of Kazakhstan. – 2013. – № 6. – P. 46-52.
Dickerson R., Gray G., Haight D. Basic laws of chemistry: in 2 volumes. Trans. from English. – M.: Mir. 1982. – 620 p. – V. 2. – P. 350.