Green's Function and Eigenvalue Representation of Time Lag for Absorptive Permeation Across a Heterogeneous Membrane

Abstract

The time‐lag problem is treated for absorptive penetration across a heterogeneous membrane, where both the diffusivity D(x) and the partition coefficient K(x) depend on the coordinate x (0 ≦ x ≦ h), with 0 and h being the coordinates of the upstream and downstream faces, respectively. A new concept of time‐lag distribution is introduced, and the first (time) moment and the second (time) moment over this distribution are also difined and treated in the Lapalce domain in conjuction with the Green's function G(x,y), and eigenvalues associated with the time‐independent diffusion equation subject to the absorbing boundary condition at both ends of the membrane. Our central results include and , where λi is the ith eigenvalue of the aforementioned diffusion equation. The merits of these new resprentations and comparison with the treatments of Frisch or Eyring are also discussed.