Comprehensive time-lag measurement as a diagnostic and analytical tool for non-Fickian transport studies: a salient porous barrier–gaseous permeant test case

Abstract

Concentration-independent permeation of He, Ne and N₂ through a porous barrier, specially constructed by multistep compaction of fine “Carbolac” carbon powder, has been studied. Emphasis was placed on measuring a variety of time lags, supplemented with transient permeation and sorption kinetics. Previous time-lag data, restricted to values of a single time-lag parameter, were instrumental in revealing deviations from Fick’s law in similar solid barrier–penetrant systems; however, they could only provide indirect evidence as to the nature of the underlying causes, namely, time- or spatial dependence of the relevant transport parameters. Thus, an interpretation in terms of time-dependence (induced by the presence of blind pores) was proposed, predicated on calculations indicating that, in theory, spatial dependence (induced by non-uniform compaction) could be reduced to insignificance by adoption of a suitable multistep powder compaction technique. The comprehensive time-lag analysis approach applied here is a general diagnostic and analytical tool, previously successfully tested on graphite barriers, that can discriminate rigorously between the aforementioned non-Fickian functional dependences, as well as provide additional substantial information in either case. This capability is well illustrated by the results obtained in the system under study here, which provide unequivocal evidence of substantial spatial dependence. Furthermore, it is shown that the predicted functional form of the detected spatial dependence (i) can, in conjunction with an adequate physical model and with the results of a previous theoretical parametric study, account fully for all aspects of the observed non-Fickian time-lag behaviour and (ii) correlates satisfactorily with variation of local porosity across the barrier, detected by a suitable X-ray imaging technique. On the other hand, there is no evidence, from time lags or transient kinetics, of any significant time-dependence attributable to slow filling or emptying of blind pores or to other causes.