title: Mathematical model describing thickness changes of concentration boundary layers controlled by polymeric membrane parameters and concentration Rayleigh number.
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).
authors.affiliation: Department of Biology and Biophysics, Czgstochowa University of Technology. ajslezak@zim.pcz.czest.pl
authors.forename: Andrzej
authors.initials: A
authors.lastname: Slezak
authors.forename: Izabella
authors.initials: I
authors.lastname: Slezak
authors.forename: Arkadiusz
authors.initials: A
authors.lastname: Bryll
authors.forename: Jolanta
authors.initials: J
authors.lastname: Jasik-Slezak
authors.forename: Jacek
authors.initials: J
authors.lastname: Młynarski
mesh_terms: D004058:Diffusion; D000431:Ethanol; D006112:Gravitation; D008567:Membranes, Artificial; D008956:Models, Chemical; D009997:Osmotic Pressure; D010539:Permeability; D011108:Polymers; D012996:Solutions / Q000737:chemistry*; D014783:Viscosity
chemical_list: D008567:Membranes, Artificial; D011108:Polymers; D012996:Solutions; D000431:Ethanol