Fickian-Based Empirical Approach for Diffusivity Determination in Hollow Alginate-Based Microfibers Using 2D Fluorescence Microscopy and Comparison with Theoretical Predictions

Hollow alginate microfibers (od = 1.3 mm, id = 0.9 mm, th = 400 µm, L = 3.5 cm) comprised of 2% (w/v) medium molecular weight alginate cross-linked with 0.9 M CaCl₂ were fabricated to model outward diffusion capture by 2D fluorescent microscopy. A two-fold comparison of diffusivity determination based on real-time diffusion of Fluorescein isothiocyanate molecular weight (FITC MW) markers was conducted using a proposed Fickian-based approach in conjunction with a previously established numerical model developed based on spectrophotometric data. Computed empirical/numerical (Dempiricial/Dnumerical) diffusivities characterized by small standard deviations for the 4-, 70- and 500-kDa markers expressed in m²/s are (1.06 × 10-9 ± 1.96 × 10-10)/(2.03 × 10-11), (5.89 × 10-11 ± 2.83 × 10-12)/(4.6 × 10-12) and (4.89 × 10-12 ± 3.94 × 10-13)/(1.27 × 10-12), respectively, with the discrimination between the computation techniques narrowing down as a function of MW. The use of the numerical approach is recommended for fluorescence-based measurements as the standard computational method for effective diffusivity determination until capture rates (minimum 12 fps for the 4-kDa marker) and the use of linear instead of polynomial interpolating functions to model temporal intensity gradients have been proven to minimize the extent of systematic errors associated with the proposed empirical method.