Science of Water Leaks: Validated Theory for Moisture Flow in Microchannels and Nanochannels

Water is ubiquitous; the science of its transport in micro- and nanochannels has applications in electronics, medicine, filtration, packaging, and earth and planetary science. Validated theory for water vapor and two-phase water flows is a “missing link”; completing it enables us to define and quantify flow in a set of four standard leak configurations with dimensions from the nanoscale to the microscale. Here we report the first measurements of water vapor flow rates through four silica microchannels as a function of humidity, including under conditions when air is present as a background gas. An important finding is that the tangential momentum accommodation coefficient (TMAC) is strongly modified by surface layers of adsorbed water molecules, in agreement with previous work on the TMAC for nitrogen molecules impacting a silica surface in the presence of moisture. We measure enhanced flow rates for two-phase flows in silica microchannels driven by capillary filling. For the measurement of flows in nanochannels we use heavy water mass spectrometry. We construct the theory for the flow rates of the dominant modes of water transport through each of the four standard configurations and benchmark it against our new measurements in silica and against previously reported measurements for nanochannels in carbon nanotubes, carbon nanopipes, and porous alumina. The findings show that all behavior can be described by the four standard leak configurations and that measurements of leak behavior made using other molecules, such as helium, are not reliable. Single-phase water vapor flow is overestimated by a helium measurement, while two-phase flows are greatly underestimated for channels larger than 100 nm or for all channels when boundary slip applies, to an extent that depends on the slip length for the liquid-phase flows.