Abstract
Fick's first law is modified to be applicable for the transport of gases in inhomogeneous polymeric membranes having continuous, concentrationβdependent, gradients of solubility and diffusivity along the flux direction (x axis). The membranes are considered to be in the rubbery state, and all gases in the membranes are assumed to be mobile. The modified Fick's law is derived from the consideration of standard chemical potential difference between the membrane and gas phases, and of fugacity coefficients in the membrane.
\documentclass{article}\pagestyle{empty}\begin{document} $J=-D\left{dC/dx - C(d\ln {S/dx})\right}/L$\end{document}
where J is the flux, D is the diffusion coefficient, C is the concentration in the membrane; x is the dimensionless space coordinate (0 β¦ x β¦ 1); S is the solubility; and L is the membrane thickness. The above equation is applicable for the cases where D and S are dependent on concentration. It is also solved analytically or numerically by a simulation method for some model membranes. Flux difference due to the flow direction and concentration profiles in the model membranes are discussed.