Modeling Diffusivity Through Alginate-Based Microfibers: A Comparison of Numerical And Analytical Models Based On Empirical Spectrophotometric Data
The study of mass transport across hollow and solid 3D microfibers to study metabolic profiles is a key aspect of tissue engineering approach. A new modified numerical mathematical model based on Fickian equations in cylindrical coordinates has been proposed for determining the membrane diffusivity of 2% (w/v) alginate-based stents cross-linked with 10% CaCl2. Based on the economical and direct spectrophotometric measurements, using this model, inward diffusivities ranging from 5.2x10-14 m2/s 2.93x10-12m2/s were computed for solutes with Stokes radii ranging between 0.36 to 3.5 nm, diffusing through bare alginate and alginate-chitosan-alginate microfibers. In parallel an analytical solution to the cylindrical Fickian equation was derived to validate the numerical solution using experimental diffusion data from a solid stent. Excellent agreement was found between the numerical and analytical models with a maximum calculated residual value of 4%. Using these models, a flexible computational platform is proposed to conduct custom diffusion and MW cut-off characterization across micro-porous microfibers not limited to alginate in composition.
Djomehri, S., Mobed-Miremadi, M., & Keralapura, M. (2013). Modeling Diffusivity Through Alginate-Based Microfibers: A Comparison of Numerical and Analytical Models Based on Empirical Spectrophotometric Data. Journal of Membrane and Separation Technology, 2(1), 74-87–87.