Drop-on-fiber is commonly observed in daily life and is closely related to digital microfluidics. The wetting behavior of droplet-on-fiber is different from that of droplet-on-plane due to the global cylindrical shape. It is generally believed that the equilibrium geometric shape of a droplet on a fiber takes either asymmetric clam-shell or axisymmetric barrel conformation in the absence of gravity. The barrel-to-clam-shell transition is determined by the stability condition. Nonetheless, experimental observations showed that both barrel and clam-shell conformations can coexist in some situations and thus indicated the existence of the multiple stable states. In this Article, the phase diagrams of droplet-on-fiber, that is, the plots of droplet volume against contact angle, are established on the basis of the finite-element simulation (Surface Evolver). When the gravity effect is absent, there are three regimes including barrel, clam-shell, and coexistence of barrel and clam-shell. As the gravity effect is considered, there exist three regimes, including (I) downward clam-shell, (II) coexistence of barrel and clam-shell, and (III) falling-off.

The wetting behavior of a liquid drop sitting on an inclined plane is investigated experimentally and theoretically. Using Surface Evolver, the numerical simulations are performed based on the liquid-induced defect model, in which only two thermodynamic parameters (solid-liquid interfacial tensions before and after wetting) are required. A drop with contact angle (CA) equal to θ is first placed on a horizontal plate, and then the plate is tilted. Two cases are studied: (i) θ is adjusted to the advancing CA (θ(a)) before tilting, and (ii) θ is adjusted to the receding CA (θ(r)) before tilting. In the first case, the uphill CA declines and the downhill CA remains unchanged upon inclination. When the tilted drop stays at rest, the pinning of the receding part of the contact line (receding pinning) and the depinning of the advancing part of the contact line (advancing depinning) are observed. The free energy analysis reveals that upon inclination, the reduction of the solid-liquid free energy dominates over the increment of the liquid-gas free energy associated with shape deformation. In the second case, the downhill CA grows and the uphill CA remains the same upon inclination. Advancing pinning and receding depinning are noted for the tilted drop at rest. The free energy analysis indicates that upon inclination, the decrease of the liquid-gas free energy compensates the increment of the solid-liquid free energy. The experimental results are in good agreement with those of simulations.

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.

A desert beetle tilts its body forward into the fog-laden wind to collect water by the hydrophilic patches on its superhydrophobic back. In this study, the pinning and dewetting mechanism of a tilted drop pinned by a designed patch on a superhydrophobic surface with negligible contact angle hysteresis (CAH) is explored both experimentally and theoretically. The patch is designed in different shapes including square, rectangle, and triangle. For a square or rectangular patch, the uphill contact angle (CA) of the tilted drop vary with the inclined angle (α) of the plate. The drop remains pinned until the critical inclined angle (αc) is achieved. As α = αc, the uphill CA of the drop reduces to the receding angle of the patch. The magnitude of αc grows approximately linearly with the pinning length (ωp), which is related to the patch size. It is found that ωp equals the side length (w) of square or rectangular patch perpendicular to the sliding direction. While ωp on square patches remains essentially unchanged before sliding, ωp on the triangular patch grows with increasing α. However, the relation between sin(α) and ωp for the triangular patch is consistent with that between sin(αc) and w for square and rectangular patches. Surface evolver simulations based on free energy minimization are performed to reproduce the wetting and dewetting behavior. The simulation outcomes agree quite well with the experimental results.

Superhydrophobic surfaces generally involve completely nonwetting or partially wetting roughness. Because the contact angle is closely related to the liquid-gas interfacial tension, the shape of the liquid-gas interfaces within the grooves plays a key role in determining the droplet wetting behavior. We consider a droplet with volume, V, atop holes with radius, r, and obtain the analytical expression of the bottom liquid-air shape based on surface free energy minimization. It is found that the bottom shape in terms of the interfacial angle, theta(1), depends on the hole size through V/r(3) in addition to the intrinsic contact angle, theta(*). For a given droplet volume, the smaller the hole size (r(3)/V --> 0), the more flat the interface (theta(1) --> 0). In addition, the flatness of the interface grows with reducing the intrinsic contact angle. Numerical simulations of Surface Evolver are performed to confirm our theory. Moreover, wetting experiments in which the gravity effect cannot be neglected are conducted, and the results are consistent with those by numerical simulations. Our result points out that such wall-free capillarity may be useful in extracting liquid from microfluidic device spontaneously.