Time-lags for radial transport with boundary-layer resistance in a ν-dimensional membrane

By means of an extension of the procedure due originally to Frisch [J. Phys. Chem. 61 (1957) 93], expressions have been derived for the ingoing and outgoing time-lags pertaining to radial transport with boundary-layer resistance in slab, hollow cylinder and spherical shell membranes. The derivation relates to a constant diffusion coefficient, D and complements an earlier treatment (for slab membranes only) [J. Membrane Sci. 186 (2001) 63] which employed the Jaeger procedure [J. Membrane Sci. 117 (1996) 79]. For the geometrically asymmetric hollow cylinder and spherical shell membranes both ‘forward’ and ‘reverse’ flow have been considered. Assuming the transfer coefficients (h1, h2) to be unaffected by flow reversal, expressions for the resultant ‘adsorption’ and ‘desorption’ time-lags have been deduced and identities between them evaluated. For the three membrane systems considered there are, in each case, only three distinguishable (boundary) time-lags. Final considerations have been limited to membranes of fixed thickness, l, with equal transfer coefficients (h1 = h2 ≡ h) at the boundaries. The dependence of the ratio of each time-lag to the corresponding limiting (k → ∞) value upon k (≡hl/D) and q (≡R2/R1) has been investigated. Attention has also been directed towards the utilisation of time-lags for estimating an ‘effective’ (steady-state) diffusion coefficient.