Phase behaviour of fluids in undulated nanopores

The geometry of walls forming a narrow pore may qualitatively affect the phase behaviour of the confined fluid. Specifically, the nature of condensation in nanopores formed of sinusoidally-shaped walls (with amplitude $A$ and period $P$) is governed by the wall mean separation $L$ as follows. For $L>L_t$, where $L_t$ increases with $A$, the pores exhibit standard capillary condensation similar to planar slits. In contrast, for $L<L_t$, the condensation occurs in two steps, such that the fluid first condenses locally via bridging transition connecting adjacent crests of the walls, before it condenses globally. For the marginal value of $L=L_t$, all the three phases (gas-like, bridge and liquid-like) may coexist. We show that the locations of the phase transitions can be described using geometric arguments leading to modified Kelvin equations. However, for completely wet walls, to which we focus on, the phase boundaries are shifted significantly due to the presence of wetting layers. In order to take this into account, mesoscopic corrections to the macroscopic theory are proposed. The resulting predictions are shown to be in a very good agreement with a density functional theory even for molecularly narrow pores. The limits of stability of the bridge phase, controlled by the pore geometry, is also discussed in some detail.