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

Abstract

AbstractMass 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.