title: Estimation of thickness of concentration boundary layers by osmotic volume flux determination.
abstract: The estimation method of the concentration boundary layers thicknesses (δ) in a single-membrane system containing non-electrolytic binary or ternary solutions was devised using the Kedem-Katchalsky formalism. A square equation used in this method contains membrane transport (L(p), σ, ω) and solution (D, C) parameters as well as a volume osmotic flux (J(v)). These values can be determined in a series of independent experiments. Calculated values δ are nonlinearly dependent on the concentrations of investigated solutions and the membrane system configuration. These nonlinearities are the effect of a competition between spontaneously occurring diffusion and natural convection. The mathematical model based on Kedem-Katchalsky equations and a concentration Rayleigh number (R(C)) was presented. On the basis of this model we introduce the dimensionless parameter, called by us a Katchalsky number (Ka), modifies R(C) of membrane transport. The critical value of this number well describes a moment of transition from the state of diffusion into convective diffusion membrane transport.
authors: Department of Public Health, Częstochowa University of Technology, Armia Krajowa al. 36b, 42 200 Częstochowa, Poland. ajslezak@zim.pcz.pl
authors: Jolanta S
authors: JS
authors: Jasik-Ślęzak
authors: Kornelia M
authors: KM
authors: Olszówka
authors: Andrzej
authors: A
authors: Slęzak