Evaluating the curvature dependence of surface tension in nanoscale capillary filling via molecular dynamics

Theoretical models of capillary flow typically rely on macroscopic governing parameters, such as the dynamic contact angle and effective viscosity. However, as pore dimensions approach the nanoscale, the curvature dependence of surface tension may become relevant, affecting theoretical predictions of capillary flow. The length scales and magnitude of this effect remain unresolved. In this work, we employ all-atom molecular dynamics simulations to investigate spontaneous water imbibition in parallel-plate silica nanochannels with heights ranging from 4.5 to 10.5 nm. The simulation data are used to extract dynamic contact angles, velocity profiles, inertial regimes, and the mean curvature of the menisci, enabling a direct evaluation of the Lucas–Washburn–Bosanquet (LWB) equation. For the 10.5 nm channel, incorporating the dynamic contact angle model into the LWB equation yields excellent agreement with the capillary filling simulation. However, as the channel height decreases, a systematic departure between the theoretical model and the simulation results is observed. To address this, the curvature dependence of surface tension is incorporated using an upper-bound value for the Tolman length. This correction introduces an increase in the effective surface tension, partially compensating for the discrepancies observed in narrower channels. The resulting surface tension enhancement ranges from 11% at 4.5 nm to 4% at 10.5 nm, suggesting that curvature effects become negligible at larger nanoscale confinements. These results indicate that the curvature dependence of surface tension contributes to deviations from classical capillary models at the nanoscale, but does not fully account for them.