DIFFUSION IN A MULTICOMPONENT INHOMOGENEOUS SYSTEM WITH MOVING BOUNDARIES .1. SWELLING AT CONSTANT VOLUME

A medium B contains a substance C which can diffuse. This mixture B and C is brought into contact with a medium a which itself can diffuse into B. Now C diffuses through a swollen layer of A and B into A. The present study examines mathematically this process which, among other things, could serve as a model for migration in a system consisting of plastic packaging (polymer plus an additive) and the contents of the package. It is assumed that medium A (contents) with a constant diffusion coefficient diffuses into medium B (plastics) and that the diffusion of substance C (additive in the pure B and into A can also be described by constant diffusion coefficients. The diffusion coefficient of substance C in the zone of mixed A and B is taken to be dependent on the concentration of A in B. Partition coefficients are assumed to exist at all interfaces between the media. The general equations of this coupled diffusion process are solved explicitly. The solutions are discussed and illustrated by several special cases.