  We propose a moving-boundary scenario to model the penetration of diffusants
into dense and foamed rubbers. The presented modelling approach recovers
experimental findings related to the diffusion of cyclohexane and the resulting
swelling in a piece of material made of ethylene propylene diene monomer rubber
(EPDM). The main challenge is to find out relatively simple model components
which can mimic the mechanical behavior of the rubber. Such special structure
is identified here so that the computed penetration depths of the diffusant
concentration are within the range of experimental measurements. We investigate
two cases: a dense rubber and a rubber foam, both made of the same matrix
material.
  After a brief discussion of scaling arguments, we present a finite element
approximation of the moving boundary problem. To overcome numerical
difficulties due to the \textit{a priori} unknown motion of the diffusants
penetration front, we transform the governing model equations from the physical
domain with moving unknown boundary to a fixed fictitious domain. We then solve
the transformed equations by the finite element method and explore the
robustness of our approximations with respect to relevant model parameters.
Finally, we discuss numerical estimations of the expected large-time behavior
of the material.
