Permeability and the time lag for downstream absorptive permeation with concomitant reaction across a series–parallel path studied by the matrix method

Abstract

Based on Siegel's theory, the permeability (P) and the downstream time lag (t_L) for absorptive unidirectional permeation, accompanying a first-order reaction, across a membrane composed of two parallel laminae in series with another lamina, have been calculated from the transmission matrix of the whole membrane. This matrix can be constructed from the transmission matrix of each component lamina. The transmission matrix of the whole membrane is first calculated from the matrices of the component laminae in the Laplace domain. P and t_L are then derived from the first row and second column of the transmission matrix of the whole membrane according to Siegel's theory. Thus, P and t_L can be represented in terms of the elements of the transmission matrix, and hence the diffusion parameters, of each component lamina. The directional symmetry of t_L is also proven, based on the unity value of the determinant of the transmission matrix. The advantage of the matrix method is also discussed.