New Kinetic Computerized Model for Multicomponent Mass Transfer in Bi-Functional Matrix of NanoComposites

Anatoliy Kalinitchev

Institute for Physical Chemistry and Electro Chemistry, Russian Academy of Science, Moscow, Russia.

DOI: 10.4236/anp.2013.22028                

Abstract

The aim of this theoretical investigation is the description of the multicomponent mass transfer process in the Nano- Composites (NC)—novel materials with the bi-functional matrix. The new theoretical NC Model is assigned for the modern theoretical investigations of the multicomponent mass transfer kinetics in the bi-functional NC materials. This NC Model for the multicomponent mass transfer in the bi-functional NC matrix includes into the consideration the proposed key conception—two co-existing routes: I—chemical reactions onto the active NC centers-sites, and II—diffusion mass transfer inside the bi-functional NC matrix. All the results are presented in the terms of the additional key concept: propagating multicomponent concentration waves (W⁺) in the NC matrix. The used W⁺ concept for the description of the multicomponent NC mass transfer kinetics give the clear interpretation of the computerized results. The mass transfer process in the NC matrix has been described theoretically by computerized simulation. The results of the calculations are new and illustrated by author’s animations showing visually the propagation of the multicomponent concentration waves (W) inside the various NC matrixes: r-beads, cylindrical ro-fibers, or planar L-membranes. Two variants of modeling for mass transfer diffusion kinetics in the bi-functional NC matrixes with one (Variant 1), or two (Variant 2) dissociation-association reactions at the active nano-sites (R⁰) are considered theoretically.

Keywords

NanoComposites; Mass Transfer; Concentration Waves; Diffusion; Multicomponent Kinetics; Bi-Functional Matrix; Active Nano-Sites

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Kalinitchev, “Kinetic and Dynamic Chromatographic Systems, and Models of Mass Transport: Behavior of Multicomponent Concentration Waves,” Protection of Metals and Physical Chemistry of Surfaces Journal, Vol. 47, No. 6, 2011, pp. 570-579.
[2]	A. Kalinitchev, “Mass Transfer Kinetics Modeling in Bi functional Ion Exchangers with Chemical Reactions on Active Centers,” In: M. Cox, Ed., IEX 2012 Intern. IEx Conference, Version of full Papers. S. “Fundamentals” (Book-El.). SCI & Ext. Abstracts, 2012, pp. 1-18 & pp. 123-125.
[3]	T. Kravchenko, L. Polyansky, A. Kalinitchev and D. Konev, “Nano Composites Metal-Ion Exchangers,” 2009.
[4]	E. Kiprianova, T. Kravchenko, D. Konev, A. Kalinitchev and W. Hoell, “Reducing Sorption of the Molecular Oxygen from Water by Silver-Sulpho-Cation Exchanger NanoComposite with Various Ionic Forms,” Russian Journal of Physical Chemistry, Vol. 84, No. 6, 2010, pp. 1104-1110.
[5]	F. Helfferich and Y-I. Hwang, “Kinetics of Acid Uptake by Weak Base Anion Exchangers. Mechanism of Proton Transfer,” Am. I. Ch. E. Symp. Ser., Vol. 81, 1985, pp. 17-27.
[6]	A. I. Kalinitchev, E. V. Kolotinskaya and T. D. Semeno vskaya, “Computerized Analyses of the Diffusion Pro cesses in Complexing Ionites,” Journal of Chromatography, Vol. 243, No. 1, 1982, pp. 17-24. doi:10.1016/S0021-9673(00)88159-5
[7]	Y.-I. Hwang and F. Helfferich, “Generalized Model for Multispecies IEx Kinetics including Fast Chemical Reactions,” Reactive Polymers, Vol. 5, 1987, pp. 237-252.
[8]	D. Petruzelli, F. Helfferich, L. Liberti, J. Millar, and R. Passino, “Kinetics of IEx with Intraparticle Rate Control: Models Accounting for Interaction in the Solid Phase,” Reactive Polymers, Vol. 7, 1987, pp. 1-13.
[9]	A. Kalinitchev, “Investigation of Intraparticle IEx Kinetics in Selective Systems,” In: J. Marinsky and Y. Marcus, Eds., IEx & Solv. Extr., Vol. 12, Marcel Dekker, New York, 1995, pp. 149-196.
[10]	F. Helfferich, “Ion Exchange Kinetics,” In: J. I. Marinsky, Ed., Ion Exchange (A Series of Adv.), Vol. 1, St. University of New York at Buffalo, New York, 1966.
[11]	R. Haase, “Thermodynamics of Irreversible Processes,” 1967.
[12]	F. Helfferich, “Ion Exchange,” Chapter 6, Mc.Graw-Hill., New York, 1962.
[13]	F. Helfferich, “Ion Exchange Kinetics-Evolution of a Theory,” In: L. Liberti and F. Helfferich, Eds. Mass Transfer & Kinetics of IEx, Sijthoff and Nordhoff, The Hague, 1983, pp. 157-179. doi:10.1007/978-94-009-6899-8_6
[14]	F. Helfferich and G. Klein, “Multicomponent Chromatography. Theory of Interference,” M. Dekker Inc., New York, 1970.
[15]	F. H. Festschrift, “Industrial & Engineering Chemistry Research,” Journal of the American Chemical Society, Vol. 34, No. 8, 1995, pp. 2551-2922.
[16]	D. Tondeur and M. Bailly, “Unifying Concept in Non Linear Unsteady Processes. PII. Multicomponent Waves, Competition and Diffusion,” Chemical Engineering and Process, Vol. 22, No. 2, 1987, pp. 91-105. doi:10.1016/0255-2701(87)80035-1
[17]	D. Tondeur, “Paradigms and Paradoxes in Modeling Adsorption and Chromatographic Separations,” Industrial & Engineering Chemistry Research, Vol. 34, No. 8, 1995, pp. 2782-2788. doi:10.1021/ie00047a029
[18]	Y. L. Hwang, “Wave Propagation in Mass Transfer Processes: From Chromatography to Distillation,” Industrial & Engineering Chemistry Research, Vol. 34, No. 8, 1995, pp. 2849-2864. doi:10.1021/ie00047a039
[19]	A. E. Rodrigues and D. Tondeur, “Percolation Process: Theory and Applications,” Sijthoff & Nordhoff, The Hague, 1981. doi:10.1007/978-94-009-8579-7
[20]	A. Kalinitchev, “Nonlinear Theory of Multicomponent Sorption Dynamics and Chromatography,” Russian Che mical Reviews, Vol. 65, No. 2, 1996, pp. 95-115. doi:10.1070/RC1996v065n02ABEH000201
[21]	W. Hoell and A. Kalinitchev, “The Theory of Formation of Surface Complexes and Its Application to the Description of Multicomponent Dynamic Sorption Systems,” Russian Chemical Reviews, Vol. 73, No. 4, 2004, pp. 351-370. doi:10.1070/RC2004v073n04ABEH000768
[22]	R. Courant and K. Friedrichs, “Supersonic flow and Shock Waves,” Springer-Verlag, Berlin, 1999.
[23]	I. Prigogine and R. Herman, “Kinetic Theory of Vehicular Traffic,” Elsevier, New York, 1971.
[24]	G. Whitham, “Linear and Nonlinear waves,” Wiley, New York, 1974.
[25]	A. Kalinitchev and W. Hoell, “Multicomponent Ion Exchange Dynamics with the Equilibria Described by Surface Complexation Theory,” In: M. Cox, Ed. IEX 2004, Ion Exchange Technology for Today and Tomorrow, Soc. Chem. Ind., London, 2004, pp. 53-58.
[26]	A. Kalinitchev and W. Hoell, “Theoretical Principles of Multicomponent Frontal and Displacement Elution Chromatography on the Basis of Surface Complexation Theory,” In: M. Cox, Ed., IEX 2008, Recent Advances in IEx Theory & Practice, Soc. Chem. Ind., London, 2008, pp. 85-93.
[27]	G. Korn and T. Korn, “Mathematical Handbook,” Mc Graw-Hill, New York, 1968.