NUMERICAL-SIMULATION OF CASE-II TRANSPORT

A nonlinear conservation equation for the fluid concentration field du ring one-dimensional viscoelastic diffusion is derived by retaining th e concentration dependencies of physical properties in the fluid flux expression from the nonequilibrium thermodynamic treatment of Durning and Tabor (1986). The result is specialized to the limit of small, but finite, diffusion Deborah numbers to give a model essentially the sam e as that by Thomas and Windle (1982) for Case II transport (TW model) . Orthogonal collocation on Hermite cubic trial functions together wit h a stiff ordinary differential equations integrator were used to solv e the TW model for integral sorption in a dry film. The solutions show good agreement with previous analyses and confirm that strong nonline arities in both the fluid diffusivity and the mixture viscosity are es sential for prediction from the model of wave-like concentration profi les associated with the Case II process. Also, the numerical results p artially confirm the analytical asymptotic analysis of Hui et al. (198 7b) for the Case II wave-front velocity, v. They show that Hui et al.' s formula for the dependence of v on characteristic physical propertie s does not depend on the details of how the diffusivity and viscosity change with fluid content, as long as both are strongly nonlinear.