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Soft Matter and Biological Physics

Eur. Phys. J. E 3, 389-394

Time evolution of near membrane layers

K. Dworecki1 - T. Koszto\lowicz1 - St. Mrówczynski1,2 - S. Wasik1

1 Institute of Physics, Pedagogical University, ul. Konopnickiej 15, PL 25-406 Kielce, Poland
2 So\ltan Institute for Nuclear Studies, ul. Hoza 69, PL 00-681 Warsaw, Poland

dworecki@pu.kielce.pl
tkoszt@pu.kielce.pl
mrow@fuw.edu.pl

Received 12 November 1999 and Received in final form 3 July 2000

Abstract
The near membrane layer is a region where the concentration of the substance transported across the membrane is significantly decreased. Its thickness is defined as a length over which the concentration drops k times with k being an arbitrary large number. The time evolution of such a layer is studied experimentally by means of the laser interferometric method. It is shown that within the experimental errors the thickness of the near membrane layer grows in time for any k as $a \sqrt t$ with the coefficient a being independent of the initial concentration and the membrane permeability. Time evolution of the near membrane layers is also analyzed theoretically. The regularities found experimentally are naturally described within the model which has been earlier developed by one of us. In particular, a scales as ${\rm erfc}^{-1}(1/k)$.

PACS
66.10.Cb Diffusion and thermal diffusion - 82.65.Fr Film and membrane processes: ion exchange, dialysis, osmosis, electroosmosis

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