Two Phase Diffusion Additional Considerations

As already noted in Chap. 3 a two-phase diffusicm can be modeled after the assumption that the fluid penetrant consists of bound and free (mobile) phases (Carter and Kibler 1978). 

The presence of a bound phase is attributed to the hydrogen bonding between the fluid and the polymeric molecules mentioned in Sect. 3.1 and perhaps also to the clustering of fluid molecules (Rogers 1965). 

In an early formulation of two liquid phases (Vieth and Sladek 1965) it was considered that the fluid consisted of a diffusing phase Cd related by means of Henry s law and of a hole filling portion Ch, expressed by a Langmuir-type sorption process, namely 

Eliminating p between the above expressions it is possible to relate Ch to Cd and, upon assuming that flux is governed by Cd alone, arrive at a diffusion equation that is non-linear in Cd. 

Three numerical finite difference solutions were generated for one-dimensional diffusion in an extended plate that, upon a suitable selection of material parameters, agreed reasonably well with experimental data. 

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