Figure 1

Normalized pressure drop between the bulk phases, as a function of the normalized separation distance. The bottom inset schematically represents the problem geometry. In the top inset a few equilibrium interface profiles are shown. At high pressures, the liquid virtually occupies all spaces. Transition from this normal state tends to first occur at $d/l\approx 0.8$. The bottommost curve in the top inset marks that transition. The dashed line located above this curve is a subsequent snapshot of the interface at $d/l\approx 0.9$. The two curves at the top (corresponding to $d/l\approx 1$ and $d/l\approx 1.1$, respectively) represent partially dewetted states at lower pressures, leading to the formation of completely detached interfaces from the base of the substrate. Such transitions from normal to superhydrophobic states are also confirmed from the corresponding MD simulations [18]. The equilibrium interfacial locations depicted in the inset also compare well with the MD simulation predictions (shown by markers in the inset), even to a quantitative extent. The small-scale solvent fluctuations become significantly more important as the distance of separation “$d$” is progressively reduced, especially in the limit as $d/\sigma \to 1^{-}$. In the figure, LBE represents simulation results obtained by solving the lattice Boltzmann equations.Reuse & Permissions

Figure 2

Normalized slip length as a function of $\Delta p/p_{\mathrm{cap}}$. In the inset, the same is also depicted as a function of the normalized separation distance. The triangular markers represent slip length values for smooth walls (i.e., $H_1\to 0$). The simulation results correspond to a shear-induced flow by moving the upper wall with a velocity $U$ and the lower wall with a velocity $-U$. The slip length, $\beta$ (independent of $U$ with typically linear velocity profiles) is determined as the distance between the wall position (bottom layer of the substrate) and the depth at which the extrapolated velocity profile reaches the nominal wall velocity, $U$. The inset shows that in the normal state ($d/\sigma <1$, approximately), the slip length is found to be rather small (roughness reduces slip), whereas in the superhydrophobic state the slip length is substantially enhanced.Reuse & Permissions