Intrusion of liquids into liquid-infused surfaces with nanoscale roughness

We present a theoretical study of the intrusion of an ambient liquid into the pores of a nanocorrugated wall w. The pores are prefilled with a liquid lubricant that adheres to the walls of the pores more strongly than the ambient liquid does. The two liquids are modeled as a binary liquid mixture of two species of particles, A and B. The mixture can decompose into a liquid rich in A particles, representing the ambient liquid, and another one rich in B particles, representing the liquid lubricant. The wall is taken to attract the B particles more strongly than the A particles. The ratio w-A/w-B of these interaction strengths is changed in order to tune the contact angle θ_{AB} formed by the A-rich/B-rich liquid interface between the two fluids and a planar wall, composed of the same material as the one forming the pores. We use classical density functional theory in order to capture the effects of microscopic details on the intrusion transition, which occurs as the concentration of the minority component or the pressure in the bulk of the ambient liquid is varied, moving away from bulk liquid-liquid coexistence within the single-phase domain of the A-rich bulk ambient liquid. These liquid structures have been studied as a function of the contact angle θ_{AB} and for various widths and depths of the pores. We also studied the reverse process in which a pore initially filled with the ambient liquid is refilled with the liquid lubricant. The location of the intrusion transition, with respect to its dependence on the contact angle θ_{AB} and the width of the pore, qualitatively follows the corresponding shift of the capillary-coexistence line away from the bulk liquid-liquid coexistence line, as predicted by a macroscopic capillarity model. Quantitatively, the transition found in the microscopic approach occurs somewhat closer to the bulk liquid-liquid coexistence line than predicted by the macroscopic capillarity model. The quantitative discrepancies become larger for narrower cavities. In cases in which the wall is completely wetted by the lubricant (θ_{AB}=0) and for small contact angles, the reverse transition follows the same path as for intrusion; there is no hysteresis. For larger contact angles, hysteresis is observed. The width of the hysteresis increases with increasing contact angle. A reverse transition is not found inside the domain within which the ambient liquid forms a single phase in the bulk once θ_{AB} exceeds a geometry-dependent threshold value. According to the macroscopic capillarity theory, for the considered geometry, this is the case for θ_{AB}>54.7^{∘}. Our computations show, however, that nanoscale effects shift this threshold value to much higher values. This shift increases strongly if the widths of the pores become smaller (below about ten times the diameter of the A and B particles).