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Updated: Aug 6, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Mathematical model describing thickness changes of concentration boundary layers controlled by polymeric membrane
Andrzej Slezak1, Izabella Slezak, Arkadiusz Bryll
1Department of Biology and Biophysics, Czgstochowa University of Technology. ajslezak@zim.pcz.czest.pl
Abstract:
In the paper, by applicating the classic definition of concentration Rayleigh number and the second Kedem-Katchalsky equation, there was deriven the equation of the fourth degree, which makes thicknesses (deltah and deltal) dependent on the concentration difference (Ch-Cl), concentration Rayleigh number (Rc), membrane permeability parameters (omega, xi s) and solutions (Dl, Dh), physico-chemical parameters of solutions (v(l), v(h), rho l, rho h, delta rho/deltaC), temperature (T) and gravitational acceleration (g). On the basis of the obtained formula for isothermal conditions (T = const) and constant gravitational field (g = const), there were calculated non-linear dependencies delta h = f(Ch-Cl)(Rc, zeta s), delta h = f (Rc)((Ch-Cl),zeta s) and delta h = f(delta s)((Ch-Cl),Rc).
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