Fickean diffusion model

Lefebvre et developed a generalized Fickean diffusion model using the free-volume concept. A finite-element model that accounts for Schapery s nonlinear viscoelastic constitutive relation(25) and the nonlinear diffusion model of Lefebvre et was discussed by Roy and Reddy. ( 4,45)... 

The two-dimensional nonlinear Fickean diffusion model used in the present study is the one developed by Lefebvre et Fick s law for the two-dimensional diffusion of a penetrant within an isotropic material is given by... 

A review of the theoretical basis, finite-element model, and sample applications of the program NOVA are presented. The updated incremental Lagrangian formulation is used to account for geometric nonlinearity (i.e., small strains and moderately large rotations), the nonlinear viscoelastic model of Schapery is used to account for the nonlinear constitutive behavior of the adhesive, and the nonlinear Fickean diffusion model in which the diffusion coefficient is assumed to depend on the temperature, penetrant concentration, and dilational strain is used. Several geometrically nonlinear, linear and nonlinear viscoelastic and moisture... 

Scharfer et al. set up a multi-component transport model to describe the diffusion driven mass transport of water and methanol in PEM [170]. For a PEM in contact with liquid methanol and water on one side and conditioned air on the other, the corresponding differential equations and boundary conditions were derived taking into account the polymers three-dimensional swelling. Phase equilibrium parameters and unknown diffusion coefficients for Nafion 117 were obtained by comparing the simulation results to water and methanol concentration profiles measured with confocal Raman spectroscopy. The influence of methanol concentration, temperature and air flow rate was predicted by the model. Although there are indications for an influence of convective fluxes, the measured profiles are ascribed to a Fickean diffusion. Furthermore, the assumption to describe the thermodynamic phase equilibrium as liquid-type equilibrium also at the lower surface of the membrane, which is in contact with a gas phase, can be confirmed by their results. 

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