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

Abstract 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 ( h 1 , h 2 ) 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 ( h 1  =  h 2  ≡  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 (≡ R 2 / R 1 ) has been investigated. Attention has also been directed towards the utilisation of time-lags for estimating an ‘effective’ (steady-state) diffusion coefficient.