Metastable Wetting on Superhydrophobic Surfaces: Continuum and Atomistic Views of the Cassie-Baxter–Wenzel Transition

In this Letter, we develop a continuum theory for the Cassie-Baxter–Wenzel (CB–W) transition. The proposed model accounts for the metastabilities in the wetting of rough hydrophobic surfaces, allows us to reconstruct the transition mechanism, and identifies the free energy barriers separating the CB and W states as a function of the liquid pressure. This information is crucial in the context of superhydrophobic surfaces, where there is interest in extending the duration of the metastable superhydrophobic CB state. The model is validated against free energy atomistic simulations.

Figure 1

Left: definition of the contact angle $\theta$, of the free surface ${\Sigma }_{lv}$, and of the free surface displacement. Right: minimal solutions of equations (i)–(iii) in a 2D groove having depth $h$ and width $l$: pinned (solid line), symmetric (dashed) asymmetric (dotted-dashed) solutions. The extremal values for the pinned configuration are indicated by a dotted line.

Figure 2

The dimensionless grand potential $\omega$ as a function of the normalized volume of liquid inside the groove $z=Z/V$, at different values of the (over)pressure: $\Delta \tilde{p}=(p_l-p_v)/\Delta p_{\max }=0.05$, 0.5, and 1.0. The contact angle is taken to be ${\theta }_Y\simeq 110°$ and the aspect ratio of the groove $\alpha =l/h=1$. The grand potential is shifted so that the W state always corresponds to $\omega =0$.

Figure 3

(a) Grand potential barriers $\Delta {\omega }^{†}$ as a function of the dimensionless pressure (same $\alpha$ and ${\theta }_Y$ as in Fig. 2). $\Delta {\omega }^{†}$ is computed as the grand potential difference between a local minimum and the transition state (maximum): in continuous line, the barrier from the W to the transition state; in dotted-dashed, from CB. The dashed line represents the estimated coexistence pressure $\Delta {\tilde{p}}_c$ for the CB and W states, which is attained for $\Delta \tilde{p}\simeq 0.14$. (b) Coexistence pressure as a function of the aspect ratio $\alpha$, for different contact angles (log-scale on abscissas). The triangle identifies $\Delta {\tilde{p}}_c$ of panel A.

Figure 4

Grand potential and free energy profiles as a function of the filling level (d)–(f), both from the present continuum theory and constant pressure atomistic simulations. Pressure increases from panel (d) to (f); the pressure differences used to fit the continuum theory are $\Delta \tilde{p}=0.01$, 0.17, and 3.0, for panels (d)–(f), respectively. In panels (a)–(c) sample atomistic configurations extracted from simulation in (e) are reported, corresponding to CB, transition, and W states, respectively.