The physics of confined flow and its application to water leaks, water permeation and water nanoflows: a review

Abstract

This review assesses the current state of understanding of the calculation of the rate of flow of gases, vapours and liquids confined in channels, in porous media and in permeable materials with an emphasis on the flow of water and its vapour. One motivation is to investigate the relation between the permeation rate of moisture and that of a noncondensable test gas such as helium, another is to assist in unifying theory and experiment across disparate fields. Available theories of single component ideal gas flows in channels of defined geometry (cylindrical, rectangular and elliptical) are described and their predictions compared with measurement over a wide range of conditions defined by the Knudsen number. Theory for two phase flows is assembled in order to understand the behaviour of four standard water leak configurations: vapour, slug, Washburn and liquid flow, distinguished by the number and location of phase boundaries (menisci). Air may or may not be present as a background gas. Slip length is an important parameter that greatly affects leak rates. Measurements of water vapour flows confirm that water vapour shows ideal gas behaviour. Results on carbon nanotubes show that smooth walls may lead to anomalously high slip lengths arising from the properties of ‘confined’ water. In porous media, behaviour can be matched to the four standard leaks. Traditional membrane permeation models consider that the permeant dissolves, diffuses and evaporates at the outlet side, ideas we align with those from channel flow. Recent results on graphite oxide membranes show examples where helium which does not permeate while at the same time moisture is almost unimpeded, again a result of confined water. We conclude that while there is no a priori relation between a noncondensable gas flow and a moisture flow, measurements using helium will give results within two orders of magnitude of the moisture flow rate, except in the case where there is anomalous slip or confined water, when moisture specific measurements are essential.