Coupled imbibition and evaporation of droplets deposited on a nanoporous layer

TL;DR

This study combines theoretical modeling and experiments to analyze how droplets imbibe and evaporate on nanoporous layers, revealing critical humidity effects and complex vapor transport mechanisms affecting infiltration dynamics.

Contribution

It introduces a unified analytical framework for droplet and halo dynamics considering Kelvin effects and experimentally demonstrates humidity-dependent behavior in nanoporous silicon.

Findings

Halo formation times diverge at a critical humidity due to Kelvin effects.

Imbibition coefficient appears to diverge, indicating complex vapor transport.

Humidity can be used to control droplet infiltration and evaporation patterns.

Abstract

Liquids in nanoscale hydrophilic pores generate capillary pressures so large that they could theoretically climb kilometers against gravity. However, droplets on thin nanoporous layers form imbibition fronts stopping at millimeters or less due to evaporation competing with capillary flow. Such droplet infiltration dynamics is of growing interest for studying confined fluids and for applications such as water harvesting, printing, chemical delivery, actuation, and sensing. Here, we investigate theoretically and experimentally the spontaneous imbibition and evaporation of sessile droplets into thin mesoporous layers, focusing on their dependence on imposed relative humidity (RH). Theoretically, we provide a unified analytical approach for the dynamics of the wetted annulus ("halo") around the droplet, accounting for arbitrary halo dimensions and confinement-induced thermodynamic shifts (Kelvin effect). Experimentally, we study water droplets on oxidized porous silicon layers (pore diameter 3-4 nm, thickness 5 $\mu$m), systematically investigating how halo and droplet dynamics depend on RH. We show that halo formation timescales diverge at a critical RH due to the Kelvin effect, as illustrated by comparing RH-dependent evaporation rates in the halo (confined liquid) and in the droplet (bulk liquid). Our analysis also reveals an apparent divergence of the imbibition coefficient, unexplained by standard capillary models, suggesting a key role for Kelvin-driven vapor transport along the porous surface. The complex couplings revealed by our study call for caution in interpreting halo dynamics data. Our results also highlight RH as a powerful control parameter for tuning droplet imbibition behavior and infiltration patterns.