Abstract
We study the properties of a Laplacian potential around an irregular object of finite surface resistance. This describes the concentration in a problem of diffusion towards an irregular membrane of finite permeability. We show that using a simple fractal generator one can approximately predict the localization of the active zones of a fractal membrane of infinite permeability. When the the permeability of the membrane is finite there exists a crossover length L c : In pores of size smaller than L c the flux is homogeneously distributed. In pores of size larger than L c the same behavior as in the case of infinite permeability is observed, namely the flux concentrates at the entrance of the pore. From this consideration one can predict the active surface localization in the case of finite permeability. We then show that a coarse-graining procedure, which maps the problem of finite permeability into that of infinite permeability, permits to obtain the dependence of the resistance and of the active surface on the surface and bulk properties. Finally, we show that the fractal geometry can be the most efficient for a membrane that has to work under very variable conditions.
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Gutfraind, R., Sapoval, B. (1994). Scaling and Active Surface of Fractal Membranes. In: Nonnenmacher, T.F., Losa, G.A., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8501-0_22
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DOI: https://doi.org/10.1007/978-3-0348-8501-0_22
Publisher Name: Birkhäuser, Basel
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