A novel technique for measuring solute diffusivities in entrapment matrices used in immobilization

Abstract

A novel technique has been developed for measuring effective solute diffusivities in entrapment matrices used for cell immobilization. In this technique radiotracers were used to measure effective diffusivities and equilibrium partition coefficients of the solute between the liquid and solid matrix. Ca‐alginate was used in this study, because it is one of the most commonly employed matrices for the immobilization of microbial, plant and mammalian cells. The experimental apparatus consisted of a single spherical Ca‐alginate bead which was attached to a rotating rod and immersed in water containing C¹⁴‐glucose. The rotational speed of the spherical bead was controlled and resulted in excellent mixing, and negligible external film mass transfer resistance, which allowed the measurement of true effective solute diffusivity within the solid matrix. The rates of C¹⁴‐glucose diffusion within the Ca‐alginate sphere were measured using a scintillation spectrometer. A mathematical model of unsteady‐state diffusion in a sphere was used with appropriate boundary conditions, and the effective diffusivity of glucose was found from the best fit of the experimental data using a computer regression analysis method. Using 2% (w/v) Ca‐alginate beads in this new radiotracer technique the effective diffusivity and partition coefficient of glucose were found to be 6.62 × 10⁻¹⁰ m²/s and 0.98, respectively. The accuracy, advantages, and simplicity of this new method for diffusivity measurements are also compared to other existing methods.