Coupled Imbibition and Evaporation of Droplets Deposited on a Nanoporous Layer

Liquids in nanoscale hydrophilic pores generate capillary pressures so large that they could theoretically climb several kilometers against gravity. But droplets deposited on thin nanoporous layers form imbibition fronts that stop at only millimeters or less, due to evaporation competing with the capillary flow. Recently, there has been growing interest in such droplet infiltration dynamics, either as a way to study the behavior of confined fluids or in connection with applications, e.g., in water harvesting, printing, chemical delivery, actuation, sensing, etc. Here, we investigate both theoretically and experimentally the spontaneous imbibition and evaporation of sessile droplets into a thin mesoporous layer, focusing on their dependence on imposed relative humidity (RH). Theoretically, we provide a unified analytical approach for the dynamics of the wetted annulus ("halo") that forms around the droplet. This approach accounts for halos of arbitrary dimensions and incorporates confinement-induced thermodynamic shifts (Kelvin effect). Experimentally, we study the case of water droplets deposited on oxidized porous silicon layers (pore diameter ∼3-4 nm, thickness ≃5 μm) and systematically investigate how the halo and droplet dynamics depend on RH. In particular, we show that the time scales of halo formation diverge at a critical RH. This phenomenon is due to the Kelvin effect, which is clearly illustrated when comparing the dependence on RH of evaporation rates in the halo (confined liquid) and in the droplet (bulk liquid). Our analysis also shows an apparent divergence of the imbibition coefficient, which cannot be explained by standard capillary models. This observation suggests an important role of Kelvin-driven vapor transport along the porous surface. The complex couplings revealed by our study call for caution when interpreting halo dynamics data. Our results also demonstrate RH as a powerful control parameter for tuning droplet imbibition behavior and infiltration patterns.