Mathematical model of the bleaching process with chemical kinetics of first and general order

Beltrán-Prieto, Juan Carlos; Kolomazník, Karel

dc.title	Mathematical model of the bleaching process with chemical kinetics of first and general order	en
dc.contributor.author	Beltrán-Prieto, Juan Carlos
dc.contributor.author	Kolomazník, Karel
dc.relation.ispartof	Reaction Kinetics, Mechanisms and Catalysis
dc.identifier.issn	1878-5190 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued	2018
utb.relation.volume	123
utb.relation.issue	2
dc.citation.spage	485
dc.citation.epage	503
dc.type	article
dc.language.iso	en
dc.publisher	Springer Netherlands
dc.identifier.doi	10.1007/s11144-017-1338-0
dc.relation.uri	https://link.springer.com/article/10.1007/s11144-017-1338-0
dc.subject	Diffusion	en
dc.subject	Efficiency factor	en
dc.subject	Difference finite method	en
dc.subject	Boundary conditions	en
dc.subject	Perturbation method	en
dc.description.abstract	Mathematical modeling of the bleaching process with a chemical reaction and diffusion of bleaching agent into a thin polymeric matrix film by movement through the micropores is studied in the present paper. The model was developed after considering theoretical methods of chemical engineering, the physical operation mechanism of the bleaching process and the main parameters that influence the diffusion mechanism. The efficiency factor for chemical kinetics of first and nth order processes were described using analytical solutions and perturbation methods. For the solution of the dynamic model, two cases of boundary conditions were explored. The first case describes diffusion in a well-stirred medium and the second case describes the situation when the bulk fluid moves slowly and interfacial resistance is present. In the latter case, the difference finite method was used as numerical tool for solving the problem and finding the concentration profile in the direction of the x-axis. Accordingly, experimental measurements were performed to determine the effective diffusion coefficient of bleaching agent in a polymeric matrix. © 2017, Akadémiai Kiadó, Budapest, Hungary.	en
utb.faculty	Faculty of Applied Informatics
dc.identifier.uri	http://hdl.handle.net/10563/1007790
utb.identifier.obdid	43878644
utb.identifier.scopus	2-s2.0-85039862616
utb.identifier.wok	000426807200014
utb.source	j-scopus
dc.date.accessioned	2018-04-23T15:01:44Z
dc.date.available	2018-04-23T15:01:44Z
dc.description.sponsorship	MEYS, Ministry of Education, Youth and Science; MSMT-7778/2014, National Landcare Programme; LO1303, National Landcare Programme
dc.description.sponsorship	Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme Project [LO1303 (MSMT-7778/2014)]
utb.ou	CEBIA-Tech
utb.contributor.internalauthor	Beltrán-Prieto, Juan Carlos
utb.contributor.internalauthor	Kolomazník, Karel
utb.fulltext.affiliation	Juan Carlos Beltrán-Prieto1 • Karel Kolomazník1 ✉ Juan Carlos Beltrán-Prieto [email protected] 1 Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01 Zlín, Czech Republic
utb.fulltext.dates	Received: 19 October 2017 / Accepted: 17 December 2017 / Published online: 27 December 2017
utb.fulltext.references	1. Marsh CA, O’Mahony AP (2009) Three-dimensional modelling of industrial flashing flows. Prog Comput Fluid Dyn an Int J 9:393–398 2. Kurz D, Schnell U, Scheffknecht G (2013) Euler-Euler simulation of wood chip combustion on a grate—effect of fuel moisture content and full scale application. Prog Comput Fluid Dyn an Int J 13:322–332 3. Burström PEC, Antos D, Lundstro¨m TS, Marjavaara BD (2015) A CFD-based evaluation of selective non-catalytic reduction of nitric oxide in iron ore grate-kiln plants. Prog Comput Fluid Dyn An Int J 15:32–46. https://doi.org/10.1504/PCFD.2015.067327 4. Goerner K, Klasen T (2006) Modelling, simulation and validation of the solid biomass combustion in different plants. Prog Comput Fluid Dyn an Int. J. 6:225–234 5. Al Halbouni A, Giese A, Flamme M, Goerner K (2006) Applied modelling for bio and lean gas fired micro gas turbines. Prog Comput Fluid Dyn An Int J 6:235. https://doi.org/10.1504/PCFD.2006.010032 6. Finlayson BA (2006) Introduction to Chemical Engineering Computing. Wiley, New Jersey 7. Foust AS, Wenzel LA, Clump CW et al (1980) Principles of unit operations. Wiley, New Delhi 8. Welty J, Wicks C, Wilson R (2008) Fundamentals of Momentum, heat, and Mass Transfer. John Wiley and Sons, Mexico 9. Holman J (1992) Heat Transfer. McGraw-Hill, New York 10. Constantinides A (1987) Applied numerical methods with personal computers. McGraw-Hill, New York 11. Griffiths DV, Smith IM (1991) Numerical Methods for Engineers. Blackwell Scientific Publications, Oxford 12. Peiró J, Sherwin S (2005) Finite difference, finite element and finite volume methods for partial differential equations. In: Yip S (ed) Handb. Springer, New York, pp 2415–2446 13. Thomée V (2001) From finite differences to finite elements: A short history of numerical analysis of partial differential equations. J Comput Appl Math 128:1–54. https://doi.org/10.1016/S0377-0427(00)00507-0 14. Bathe K-J (1994) Keynote paper: remarks on the development of finite element methods and software. Int J Comput Appl Technol 7:101–107 15. Beltrán-Prieto JC, Kolomazník K (2016) Application of finite difference method in the study of diffusion with chemical kinetics of first order. MATEC Web Conf 76:4032. https://doi.org/10.1051/matecconf/20167604032 16. Tosun I (2007) Modeling in Transport Phenomena. Elsevier, Amsterdam 17. Godongwana B (2016) Effectiveness factors and conversion in a biocatalytic membrane reactor. PLoS ONE 11:e0153000. https://doi.org/10.1371/journal.pone.0153000 18. Adagiri GA, Babagana G, Susu AA (2012) Effectiveness factor for porous catalysts with specific exothermic and endothermic reactions under Langmuir-Hinshelwood kinetics. Int J Res Rev Appl Sci 13:716–739 19. Yang J, Shaofen L (1988) Approximate analytical solution of effectiveness factor for porous catalyst (I) approximate expression. J Chem Ind Eng 3:11–22 20. Do DD, Bailey JE (1982) Approximate analytical solutions for porous catalysts with nonuniform activity. Chem Eng Sci 37:545–551. https://doi.org/10.1016/0009-2509(82)80117-6 21. Rice RG, Do DD (2012) Applied mathematics and modeling for chemical engineers. Wiley, New York 22. Bejan A, Kraus AD (2003) Heat transfer handbook. Wiley, New Jersey 23. Coulson JM, Richardson JF (2017) Chemical Engineering. Butterworth-Heinemann, Madras 24. American Public Health Association (APHA), the American Water Works Association (AWWA) and the WEF (WEF) (1999) Standard methods for the examination of water and wastewater, APHA method 4500-CIO2. APHA, Baltimore 25. Yasuda H, Lamaze CE, Ikenberry LD (1968) Permeability of solutes through hydrated polymer membranes. part I. diffusion of sodium chloride. Die Makromol Chemie 118:19–35. https://doi.org/10.1002/macp.1968.021180102 26. Shenoy V, Rosenblatt J (1995) Diffusion of macromolecules in collagen and hyaluronic acid, rigidrod-flexible polymer, composite matrixes. Macromolecules 28:8751–8758. https://doi.org/10.1021/ma00130a007 27. Sun Y-M, Liang M-T, Chang T-P (2012) Time/depth dependent diffusion and chemical reaction model of chloride transportation in concrete. Appl Math Model 36:1114–1122. https://doi.org/10.1016/J.APM.2011.07.053 28. Masaro L, Zhu XX (1999) Physical models of diffusion for polymer solutions, gels and solids. Prog Polym Sci 24:731–775. https://doi.org/10.1016/S0079-6700(99)00016-7
utb.fulltext.sponsorship	This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme Project No. LO1303 (MSMT-7778/2014).
utb.scopus.affiliation	Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, Zlín, Czech Republic
utb.fulltext.projects	LO1303 (MSMT-7778/2014)