May the Knudsen equation be legitimately, or at least usefully, applied to dilute adsorbable gas flow in mesoporous media?

The question of applicability of Knudsen's equation to dilute adsorbable gas flow in mesoporous media was the subject of a recent debate between Ruthven el al. (2009), Ruthven (2010) and Bhatia and Nicholson (2010, 2011). Here, we present a critique of the said debate and introduce new information of critical importance, which has nevertheless been disregarded by both sides thereof. It is pointed out that von Smolukowski's derivation leaves no doubt that Knudsen's equation is meant to apply to the limiting case of zero gas adsorption. In practice, this limit may be expected to be approached at high temperature/low gas adsorbability but the crux of the matter is (i) choice of the right transport parameter (in this case the reduced permeability) to provide a useful criterion of approach to the Knudsen limit and (ii) thorough study of the course followed by the said parameter in its approach to the said limit. In this light, we begin our review of the aforesaid new information with conventional surface flow theory, which can deal satisfactorily with higher and moderate, but not with the case of weak, adsorption (because the reduced permeability does not converge smoothly to the Knudsen limit). Even so, we show that it can provide a good answer to a significant question raised in the aforesaid debate. We continue with the more advanced (but still analytical) surface flow approach of Nicholson and Petropoulos (1973), which has provided a plausible physical mechanism for the experimentally observed passage of the reduced permeability through a minimum with rising temperature, in the weak adsorption region. It is shown here that the said experimental data constitute the first observations (including the fine structure) of what we have called apparent or quasiKnudsen (to avoid confusion with proper Knudsen) flow behavior, which is the central theme of the debate in question. We then pass onto a discussion on the confirmation of the above interpretation of quasiKnudsen-flow fine structure, as well as the identification of conditions favorable to the appearance of such flow in practice, afforded by the results of ab initio evaluation of dilute adsorbable gas flow, under suitable adsorption potentials, in model pores (and model pore networks) by and Petropoulos (1981, 1985) and Petropoulos and Petrou (1991). (C) 2011 Elsevier Ltd. All rights reserved.