Determination of diffusion coefficient from transitory uptake or release kinetics: Incidence of a recirculation loop

The determination of the diffusion coefficient of a solute in a solid matrix (polymers, gels, adsorbents) is often determined based on batch kinetics experiments performed when a given amount of matrix is put into a stirred cell containing a defined volume of diluting fluid (gas or liquid). There is, however, a strong trend to develop smaller and smaller volume set-ups (due to, for instance, the cost of either the solute or the matrix in biological or pharmaceutical fields). Furthermore, a continuous monitoring of the solute concentration in the release (or exhaustion) medium is obviously attractive and frequently applied, in place of a sequential manual sampling protocol. This option demands, however, most often a continuous recirculation loop to be implemented on the cell volume, so that a continuous detector (such as spectrophotometric, conductimetric or refractive index) can be used. The objective of this work is to analyze the influence of such a recirculation loop, which may affect significantly the hydrodynamics (fluid residence time distribution) as well as the dynamics (delayed signal) of the experimental kinetics, in order to evaluate the impact on the diffusion coefficient determination. Numerical simulations covering a broad range of situations have been performed, and an experimental validation on a system consisting of alginate hydrogel beads as a model matrix and pullulan molecules (molecular weight ranging between 730 and 880 000) as model solute is reported. Practical guidelines are finally proposed in order to estimate, through ab initio shortcut methods, the error induced by the recirculation loop, based on explicit experimental parameters (cell/loop volume, recirculation loop residence time, solute diffusion time constant).