Critical assessment of quasi-steady-state method to determine effective diffusivities in alginate gel membranes

The application of the quasi-steady-state (QSS) method for measuring effect ive diffusivities (D-e) using the diffusion-cell technique was evaluated cr itically. Diffusion experiments with glucose and lactic acid across a gel m embrane containing immobilized Lactobacillus rhamnosus were used as illustr ation cases. The correct estimation of D-e is based on the assumption that a QSS is satisfied. A theoretical error analysis was performed to quantitat e the impact of estimating D-e when some conditions result in the QSS not b eing fulfilled. These conditions may be caused by: (1) not measuring/calcul ating the solute mass in the gel (M-m,M-t); (2) errors in measurements of s olute concentration; and (3) when the volume of sample withdrawal is not fa ctored in. It was found that the errors in estimating D-e when M-m,M-t and the concentration measurement errors were not taken into account would be o ver 200%, depending on the prevailing conditions. In addition, the errors a ssociated with the sample withdrawal increased linearly with the relative s ampling fraction. In order to apply the QSS method, a procedure based on an accurate mass balance has been proposed to qualitatively, and quantitative ly, validate the QSS assumption. This procedure uses a statistical t-test t o check whether the solute flux-in equals the flux-out. To estimate D-e acc urately, it is essential that the attainment of the QSS is validated, the a ccuracy of concentration measurement is established, and the effect of samp le withdrawal taken into account. (C) 1999 Elsevier Science S.A. All rights reserved.