Effective diffusivity and tortuosity in a porous glass immobilization matrix

Abstract

The effective diffusivity of glucose in porous glass beads was determined using a transient method. Predictions for the intraparticle and surface concentrations were made by an analytical solution of the mass balance. The value of the diffusivity was expected to be lower than the value of the corresponding diffusion coefficient in water, but the opposite was observed. This effect results from intraparticle fluid flow, leading to high values of the “apparent” effective glucose diffusivity. To measure diffusion only and to prevent any internal convection during the diffusion experiment, the pores of the porous glass beads were filled with Ca-alginate gel. For these glass beads (internal porosity, ɛ, equal to 0.56), we found an effective glucose diffusivity of 2.2×10−10 m2/s at 30°C. Using the relationship to effective intraparticle diffusivity (Deff)=effective diffusivity in 1% Ca-alginate beads (Dgel) ɛ/τ (with τ the tortuosity factor) this gives τ=1.7. For known ɛ and measuring τ by the method described, the Deff can be calculated for other porous materials or diffusing substances. Knowledge of the exact value of the effective diffusivity is a necessity in bioreactor modelling and was demonstrated by prediction of the residence time distribution profiles in a packed-bed bioreactor containing immobilized yeast cells.