The effect of the embedded interface dynamics on mass transport in immiscible polymer blends

Mass transport of solvents into immiscible blends may exhibit a non-Fickian behavior due to the deformation of the embedded interface that couples with diffusion. We introduce an interface area covariant tensor N as a structural state variable and derive a set of thermodynamically-consistent PDEs and ODEs transport equations for the bulk and time-dependent boundaries. The proposed model, which is a reformulation of that derived by El Afif (2008) and El Afif et al. (2003), improves both mathematically and numerically the investigation of the diffusion-interface coupling and provides reasonable predictions of the sorption-permeation one dimensional treatment affording good agreement with experimental data. The tensor N englobes, into a single morphological quantity, all information regarding diffusion-induced changes in the size and shape anisotropy of the interface area. Predicted results include concentration, components of N , residual stresses, mass-uptake, and swelling. Scaling leads to three relevant dimensionless parameters: a mixing-interface coupling constant and bulk and boundary diffusion Deborah numbers.