Membrane transport of the non-homogeneous ternary solutions: mathematical model of thicknesses of the concentration boundary layers.

We have presented the mathematical model, which can be the basis of determination of a numerical algorithm for the thickness of concentration boundary layers calculation for ternary nonelectrolyte solutions. This model is based on Rayleigh equation and second Kedem-Katchalsky equation for ternary solutions. In proposed model, the thickness of concentration boundary layers is controlled by concentration Rayleigh number.

[Osmo-diffusive transport through microbial cellulose membrane: the computer model simulation in 3D graphic of the dissipation energy for various values of membrane permeability parameters]. / Transport osmotyczno-dyfuzyjny przez membrane z celulozy bakteryjnej: modelowanie komputerowe w grafice 3D dyssypacji energii dla róznych wartosci parametrów przenikania membrany.

Linear non-equilibrium thermodynamics (LNET) has been used to express the dissipation function in single-membrane system with mechanical and osmotic pressures difference and volume and solute fluxes in a homogeneous binary non-electrolyte solution. On the basis of Kedem-Katchalsky model equations, the dissipation function in single-membrane system was derived in practical forms. Using that function, the numerical calculations for microbial cellulose polymeric membrane were performed. The results of computer simulations were illustrated by 3D graphic.