Pervaporation-induced drying in networks of channels of variable width

We study the influence of variations of cross-section on the drying dynamics by pervaporation in microfluidic channels surrounded by water-permeable polydimethylsiloxane (PDMS) walls. Single channels of linearly increasing and decreasing width display similar drying time, but different dynamics towards final drying. Single channels with stepwise increasing or decreasing width show jumps of the drying velocity when the meniscus separating the water-filled and the dry part of the channel crosses the steps. In branched networks, narrower branches tend to dry faster than wider ones. All these observations are rationalised in the framework of a model based on the solution of the diffusion equation of water through PDMS, accounting precisely for the local channel geometry, provided the section variation is slow. This model shows that drying velocity depends strongly on the local channel width at the meniscus location. It captures quantitatively our measurements, except the magnitude of the velocity jumps in channels with steps. Implications and perspectives of this study are discussed in the context of leaf drying by the so-called air seeding mechanism in trees.