Numerical simulation of Case II transport

Abstract

AbstractA nonlinear conservation equation for the fluid concentration field during onedimensional viscoelastic diffusion is derived by retaining the 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 same as that by Thomas and Windle (1982) for Case II transport (TW model). Orthogonal collocation on Hermite cubic trial functions together with a stiff ordinary differential equations integrator were used to solve the TW model for integral sorption in a dry film. The solutions show good agreement with previous analyses and confirm that strong nonlinearities in both the fluid diffusivity and the mixture viscosity are essential for prediction from the model of wave‐like concentration profiles associated with the Case II process. Also, the numerical results partially confirm the analytical asymptotic analysis of Hui et al. (1987b) for the Case II wave‐front velocity, v. They show that Hui et al.'s formula for the dependence of v on characteristic physical properties does not depend on the details of how the diffusivity and viscosity change with fluid content, as long as both are strongly nonlinear.