Abstract
The problem of mass transfer for diffusion and adsorption in non-regular disperse and porous multilayer media with no stationary regimes of mass exchange processes on the mass exchanged surfaces, which is described by systems of differential equations with boundary conditions and contact conditions, is introduced. The exact analytical solution of the problem by the application of Laplace, Fourier and Bessel integral transforms and the fundamental function method of Cauchy is established. Models were selected in accordance with component distribution in the multilayer media Me-MeO area. The solution of equation systems for different models as well as the investigation of the functions made it possible to find the effective meaning of the diffusion coefficient. The investigations will allow to correct multilayer chemical composition, to understand better the high-temperature oxidation mechanism and adsorption mechanism in nanoporous n-component structures.
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References
Lykov A.V., Mykhaylov Y.A. (1963) The theory of mass transport, (State Energy Publishing, Moscow) 535.
Ufliand Y. (1967) Integral transformations in problems of theory of elasticity, (Nauka, Saint Petersburg).
Sergienko I., Skopetsky, Deineka B. (1991) The mathematical modelling and research of process in no regular medias, Kyiv, Naukova Dumka (Academic Publishers) 432.
Lenyuk M.P., Petryk M. (2000) Fourier, Bessel integral transformations with spectral parameter in mathematical modelling problems of mass transfer in non regular media, Kyiv, Naukova Dumka (Academic Publishers) 372.
Stepanov V.V. (1959) Course of differential equations, (Physical and Mathematical Publ., Moscow), 468.
N'Gokoli-Kekele P., Springuel-Huet M.-A., Fraissard J. (2002) An Analytical Study of Molecular Transport in Zeolite Bed. Adsorption, (Kluwer Academic Publishers, Dordrecht) 8, 35–44.
Bonardet J.-L., Fraissard J., Gédéon A., Springuel-Huet M.-A. (1999) Catal. Rev.-Sci. Eng., 41, 115–225.
Chen, N.Y., T.F. Degnan, M.C. Smith (1994) Molecular Transport and Reaction in Zeolites: Design and Application of Shape Selective Catalysis, (V.C.H. Weinheim, New York).
Kärger, J., Ruthven D. (1992) Diffusion in Zeolites and Other Microporous Solids (John Wiley & Sons, New York).
Magalhães, F.D., Laurence R.L., Conner W.C., Springuel-Huet M.-A., Nosov A., Fraissard J. (1997) Study of molecular transport in beds of zeolite crystallites: semi-quantitative modelling of 129Xe NMR experiments, J. Phys. Chem. B, 101, 2277–2284.
Springuel-Huet, M.-A., Nosov A., Kärger J., Fraissard J., 129Xe NMR study of bed resitance to molecular transport in assemblages of zeolite crystallites (1996) J. Phys. Chem., 100, 7200–7203.
Mathiu-Blaster Sicard J. (1999) Thermodynamics of irreversible processes applied to solute transport in nonsaturated porous media, J. Non Equilibrium Thermodyn., 24, 107–122.
Zapolsky H., Pareige C., Marteau L., Blavette D., Chen L.Q. (2001) Atom probe analyses and numerical calculation of ternary phase diagram in Ni- Al-V, Calphad, 25, 125–134.
de Boor R. (2000) Contemporary progress in porous theory, Appl. Mech. Rev., 53 (12), 323–369.
Mongiovi M.S. (2002) Thermo mechanical Effects in the Flow of Fluid in Porous Media. Math. And Comp. Modelling, 35, 111–117.
Petryk M., Babiyk M. (2000) Mathematical Modelling, Saint Petersburg, 1, 133–137.
Krimitsas N., Vorobiev E., Petryk M., (2000) Continuous solid/liquid expression in screw press: process analysis and modelling, Proceedings of 8th World Filtration Congress FC-8, Brighton (UK), Vol. 2, 763–766.
Petryk M. (2002) Modelling and investigation of mass exchange of biological materials processes, Thermoynamics, Microstructures and Plasticity. NATO Advanced Study Institute, Frejus (France), 74.
Petryk M., Petryk N., Matiega V. (2002) The Intensification of Process of Vibrofiltration in non Regular Cylinder Media, Proceedings ICEST-2002, Compiegne (France) 1, 143–149.
Petryk M., (1998) Mathematical model of the filtration process half- limited mediums in conical canals. Ternopil State Technical University Bulletin, 3, 20–29.
Shabliy O., Petryk M., Vasylyuk P., Katerynyuk 1., (1999) Diffusion processes in oxide layer of Fe-Cr alloys, Ternopil State Technical University Bulletin, 1, 5–13.
Vasylyuk P.M., Butenko L.I., (1989) Increase of the Fe-Cr alloys resistance, Metals. AS USSR, 1, 154–156.
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PETRYK, M., SHABLIY, O., LENIUK, M., VASYLUK, P. (2006). MATHEMATICAL MODELLING AND RESEARCH FOR DIFFUSION PROCESSES IN MULTILAYER AND NANOPOROUS MEDIA. In: Conner, W.C., Fraissard, J. (eds) Fluid Transport in Nanoporous Materials. NATO Science Series II: Mathematics Physics and Chemistry, vol 219. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4382-1_34
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DOI: https://doi.org/10.1007/1-4020-4382-1_34
Publisher Name: Springer, Dordrecht
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