Diffusion of methylene blue in glass fibers – Application of the shrinking core model

Diffusion of mass in a solid cylinder with concentration dependent diffusivity (or temperature-dependent thermal conductivity in case of heat diffusion) does not admit of an analytical solution except in special cases. The ‘shrinking core model’ has been used to develop an approximate analytical solution in certain circumstances. The model, generally useful to describe heterogeneous solid–fluid reactions, is applied to theoretically analyze the adsorption–diffusion phenomena of methylene blue dye in a glass fiber in the present work. Theoretical equations have been derived for the case of diffusivity as an exponential function of concentration. The diffusivity parameters are evaluated by global minimization of the error between the experimental and the theoretical concentration history. Other forms of diffusivity, namely constant diffusivity and diffusivity varying linearly with concentration are found to involve larger errors. A parametric sensitivity analysis of the error has been done. The shrinking core model could satisfactorily interpret the experimental dye concentration profile in the substrate.