Intrusion of liquids into liquid infused surfaces with nanoscale roughness

We present a theoretical study of the intrusion of an ambient liquid into pores of a nano-corrugated wall w. The pores are prefilled with a liquid lubricant which adheres to the walls of the pores more strongly than the ambient liquid. The two liquids are modeled as a binary mixture of two types of particles, A and B. The mixture can decompose into an A-rich(ambient) liquid, and a B-rich(lubricant) liquid. The wall attracts B particles more strongly than A particles. The ratio of w-A to w-B interaction strengths is changed to tune the contact angle ${\theta}_{AB}$ formed by the A-rich/B-rich liquid interface between the two fluids and the corresponding planar wall. We use classical density functional theory, in order to capture the effects of microscopic details on the intrusion transition as a function of composition and pressure of the ambient liquid, for various values of ${\theta}_{AB}$ and different pit sizes. We also studied the reverse process in which a pore initially filled with the ambient liquid is refilled with the lubricant. For small ${\theta}_{AB}$ ,there is no hysteresis. However, beyond a certain ${\theta}_{AB}$, we find the presence of hysteresis, which increases with increasing ${\theta}_{AB}$. The dependence of location of the intrusion on ${\theta}_{AB}$ and on the pit size, 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. The quantitative discrepancies become larger for narrower cavities. For the considered geometry, macroscopic capillarity theory predicts an open hysteresis loop above a threshold value of ${\theta}_{AB} = 54.7^\circ$. This threshold, however, shifts to much higher values if widths of the pores become smaller than roughly ten times the diameter of the fluid particles.