Method to determine the critical concentration Rayleigh number in isothermal passive membrane transport processes

Abstract A method to determine the critical concentration Rayleigh number in isothermal membrane transport processes was worked out. This method is based on equations which include the diffusive permeability coefficient, D ks ; solution parameters (density, ϱ; kinematic viscosity, ν; diffusion coefficient, D ks ) and solute permeability of the complex: boundary layer/membrane/boundary layer (Ω ks i ). Coefficients ω ks and Ω ks i were determined in a single-membrane cell system which consisted of a flat polymeric dialysis membrane and glucose in 0.2 mol.l −1 aqueous solutions. Water was placed on one side of the membrane. The opposite side of the membrane was exposed to the solution. Two configurations (A and B) of a single-membrane-cell system in a gravitational field were studied. In configuration A water was placed in a compartment above the membrane and the solution below. In configuration B the arrangement of water and solution was reversed. The calculation results show that the critical value of the Rayleigh number concentration (R s i ) in configuration A is (R 1 A ) crit = 277.1 and in configuration B, (R 1 B )crit = 225.2.