The Role of Disjoining Pressure and Thermal Activation in the Invasion of Droplets into Nanopores

Multiphase transport at a nanoscale level plays a key role in applications including drying of nanoporous materials and gas/oil recovery from low permeability rocks. A frequently encountered scenario in multiphase transport is the presence of droplets near nanopores. Whether droplets invade the nanopores or become trapped at their entrance greatly affects the operation of engineered systems. Here we analyze the free energy profile of nanometer-sized droplets entering the nanopore and how the profile is affected by the pressure difference and the size of the droplet and the nanopore. We show that, for nanopores whose surface is fully wetted by water but not the droplet, a droplet larger than the pore diameter must overcome a higher free energy barrier than that predicted by classical theories due to the large disjoining pressure. For smaller nanodroplets, the threshold pressure for their invasion into a given nanopore can be lowered by thermal activation. When a droplet is slightly narrower than a pore, and thus is often assumed to enter the pore freely, a large energy barrier for droplet entry can actually exist. The droplet cannot easily enter the pore even with hydrodynamic drag by moving fluids. Entering the pore through Brownian motion is possible, and the mean entry time depends sensitively on the pore size and can reach seconds or even longer. These findings provide molecular insights on the invasion of droplets into nanopores and lay foundations for large-scale modeling of multiphase nanofluidic transport.