Scaling in diffusive transport through membranes

Chemical Engineering Science

Volumn 51, Issue 17, 1996, Pages 4115-4125

  Grzywna, Z J ^a  

^a SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

diffusion; fractals; generalized dimension; membrane; scaling; sorption

Indexed keywords

DIFFUSION; FRACTALS; MASS TRANSFER; MATHEMATICAL MODELS; MEMBRANES; PARTIAL DIFFERENTIAL EQUATIONS; SORPTION; SYSTEMS ANALYSIS;

DIMENSIONAL ANALYSIS; GENERALIZED DIMENSION; MACROSCOPIC PROPERTIES; MICROSCOPIC PROPERTIES; SCALING;

TRANSPORT PROPERTIES;

EID: 0030239487     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/0009-2509(96)00014-0     Document Type: Article

References (20)

1. Avnir, D., editor 1989, The Fractal Approach to Heterogeneous Chemistry. Surfaces, Colloids, Polymers. Wiley, Chichester.
2. Coppens, M.-O., Froment, G. F., 1975, Diffusion and reaction in a fractal catalyst pore-II. Diffusion and first-order reaction. Chem. Engng Sci. 50, 1027-1039.
3. Coppens, M.-O., Froment, G. F., 1995, Diffusion and reaction in a fractal catalyst pore-I. Geometrical aspects. Chem. Engng Sci. 50, 1013-1026.
4. Crank, J., 1975, The Mathematics of Diffusion. Clarendon Press, Oxford.
5. Gadomski, A., Grzywna, Z. J. and Łuczka J., 1993, The growing processes in diffusive and convective fields. Chem. Engng Sci. 48, 3713-3721.
6. Giona, M., Adrover, A. and Giona, A. R., 1995, Convection-diffusion transport in disordered structures: numerical analysis based on the exit-time equation. Chem. Engng Sci. 50, 1001 -1011.
7. Grzywna, Z. J., 1992, Local and global description of transport through membranes, in (edited by Kuczera, J. and Przestalski, S.), Proceedings of the XI School on Biophysics of Membrane Transport, pp. 175-191. AUW, Wrocław.
8. Grzywna, Z. J., 1993, Membrane transport from the fractal perspective. ICB Seminars Series, (4).
9. Grzywna, Z. J., Gadomski, A. and Jçdrycha, M., 1993, Casting membranes through DLA. Proceedings of the Polymer Conference, Cambridge, UK.
10. Grzywna, Z. J., Izydorczyk, J., Podkówka, J. and Salwiński, J., 1975, Sorption characterization of Poltherm and Estrofol membranes. Polimery, Warsaw, 20, 338.
11. Gustafson, K. E., 1987, Introduction to Partial Differential Equations and Hilbert, Space Methods. 2nd Edn. Wiley, New York.
12. Guyer, R. A., 1984, Diffusion on the Sierpiński gaskets: a random walker on a fractally structured object. Phys. Rev. A 29, 2751.
13. Havlin, S. and Ben-Avraham, P., 1987, Diffusion in disordered media. Adv. Phys. 36, 695.
14. Helmboltz, H., 1873, Monatsber. der Preuss. Akademie der Wiss. zu Berlin.
15. Jarzçbski, A. B. and Lorenc, J., 1995, Pore network connectivity and effective diffusivity of silica aerogels. Chem. Engng Sci. 50(2), 357-360.
16. Mandelbrot Benoit, B., 1983. The Fractal Geometry of Nature. W. H. Freeman, New York.
17. McCabe, W. L., and Smith, J. C., 1976, Unit Operations of Chemical Engineering. McGraw-Hill, New York.
18. Naylor, A. W. and Sell, G. R., 1982, Linear Operator Theory in Engineering and Science. Springer, New York.
19. O'Shaughnessy, B. and Procaccia, I., 1985, Diffusion on fractals. Phys. Rev. A 32(5), 3073-3083.
20. Takayasu, H., 1990, Fractals in the Physical Sciences. Manchester University Press, New York.