Laplace transform approach to the rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore

International Journal of Phytoremediation

Volumn 87, Issue 12, 2008, Pages 1373-1395

  Choquet, Catherine ^a   Mikelić, Andro ^b,c  

^a AIX MARSEILLE UNIVERSITY   (France)

^b UNIVERSITÉ DE LYON   (France)

^c UNIVERSITÉ LYON 1   (France)

Author keywords

35B25; 44A10; 76F25; 92E20; Adsorption chemical reaction; Danckwerts boundary conditions; Laplace's transform; Large Peclet number; Singular perturbation; Taylor's dispersion

Indexed keywords

EID: 68149118636     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810802140699     Document Type: Article

References (25)

1. Van Duijn, CJ, Knabner, P, and Schotting, RJ. 1998. An Analysis of Crystal Dissolution Fronts in Flows Through Porous Media, Part 2: Incompatible Boundary Conditions. Adv. Water Resour., 22: 1–16.
2. Van Duijn, CJ, and Knabner, P. 1997. Travelling wave behaviour of crystal dissolution in porous media flow. Eur. J. Appl. Math., 8: 49–72.
3. Van Duijn, CJ, and Pop, IS. 2004. Crystal dissolution and precipitation in porous media: Pore scale analysis. J. Reine Angew. Math., 577: 171–211.
4. Hornung, U, and Jäger, W. 1991. Diffusion, convection, adsorption, and reaction of chemicals in porous media. J. Diff. Equations, 92: 199–225.
5. Knabner, P, Van Duijn, CJ, and Hengst, S. 1995. An analysis of crystal dissolution fronts in flows through porous media, Part 1: Compatible boundary conditions. Adv. Water Resour., 18: 171–185.
6. Mikelić, A, and Primicerio, M. 2006. Modelling and homogenizing a problem of sorption/desorption in porous media. Math. Models Methods Appl. Sci., 16 (11): 1751–1782.
7. Taylor, GI. 1953. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. Royal Soc. A, 219: 186–203.
8. Aris, R. 1956. On the dispersion of a solute in a fluid flowing through a tube. Proc. Roy. Soc. Lond. A., 235: 67–77.
9. Bourgeat, A, Jurak, M, and Piatnitski, AL. 2003. Averaging a transport equation with small diffusion and oscillating velocity. Math. Meth. Appl. Sci., 26: 95–117.
10. Mercer, GN, and Roberts, AJ. 1990. A centre manifold description of contaminant dispersion in channels with varying flow profiles. SIAM J. Appl. Math., 50: 1547–1565.
11. Rosencrans, S. 1997. Taylor dispersion in curved channels. SIAM J. Appl. Math., 57: 1216–1241.
12. Rubinstein, J, and Mauri, R. 1986. Dispersion and convection in porous media. SIAM J. Appl. Math., 46: 1018–1023.
13. Paine, MA, Carbonell, RG, and Whitaker, S. 1983. Dispersion in pulsed systems - I, Heterogeneous reaction and reversible adsorption in capillary tubes. Chem. Eng. Sci., 38: 1781–1793.
14. Balakotaiah, V, and Chang, HC. 1995. Dispersion of chemical solutes in chromatographs and reactors. Phil. Trans. R. Soc. Lond. A, 351: 39–75.
15. Mauri, R. 1991. Dispersion, convection and reaction in porous media. Phys. Fluids A, 3 (5): 743–755.
16. Allaire, G, and Raphael, AL. 2007. Homogenization of a convection–diffusion model with reaction in a porous medium. C. R. Math. Acad. Sci. Paris., 344: 523–528.
17. Balakotaiah, V. 2004. Hyperbolic averaged models for describing dispersion effects in chromatographs and reactors. Korean J. Chem. Eng., 21: 318–328.
18. Chakraborty, S, and Balakotaiah, V. 2005. Spatially averaged multi-scale models for chemical reactions. Adv. Chem. Eng., 30: 205–297.
19. Mikelić, A, Devigne, V, and Van Duijn, CJ. 2006. Rigorous upscaling of the reactive flow through a pore, under dominant Peclet and Damkohler numbers. SIAM J. Math. Anal., 38 (4): 1262–1287.
20. Van Duijn, CJ. 2008. “ Effective dispersion equations for reactive flows with dominant peclet and damkohler numbers ”. In CASA Report 07-20, The Netherlands: TU Eindhoven. (accepted for publication in Advances in Chemical Engineering)
21. Mikelić, A, and Rosier, C. 2007. Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore. Ann. Univ. Ferrara. Sez. VII Sci. Mat., 53: 333–359.
22. Van Genuchten, MTh, and Cleary, RW. 1979. “ Movement of solutes in soil: Computer-simulated and laboratory results chapter 10 ”. In ‘Soil Chemistry B. Physico-Chemical Models’, Edited by: Bolt, GH. 349–386. Amsterdam: Developements in soil sciences 5B, Elsevier Scientific Publishing Company.
23. Vladimirov, VS. 1996. Equations of Mathematical Physics, Mascow, Moscow: URSS.
24. Dautray, R, and Lions, JL. 1984. Analyse mathématique et calcul numérique pour les sciences et techniques, Evolution: Fourier Laplace, Vol. 7, Cea, Paris: Masson.
25. Arendt, W. 2001. Vector-valued Laplace Transforms and Cauchy Problems, Basel: Birkhäuser.