Curvature Effects on Drop Wetting

Wetting phenomenon is easily seen in our daily life. The research about wetting can provide useful information for industry, science, and microfluidics applications. In this dissertation, there are four major parts to investigate the effects of solid-liquid surfaces’ curvature on drop wetting. For the first part, droplet-on-fiber is commonly seen and the drop at the bottom of a rigid fiber standing vertically on a flat surface is closely related to dip-pen nanolithography. A combined approach of numerical simulation and experimental observation is conducted to investigate the equilibrium shape of a drop-on-fiber/plane system. For superhydrophobic surfaces, the equilibrium geometrical shape of the drop adopts either axisymmetric barrel or asymmetric clam-shell conformation. In contrast, for hydrophilic surfaces, the equilibrium drop shape adopts either axisymmetric bell-like or asymmetric half-bell-like conformation. At the transition between the two conformations, both conformations can coexist and the multiple steady states are indicated. In this study, the phase diagrams of drop-on-fiber/plane, that is, the plots of droplet volume against liquid-fiber contact angle, are established on the basis of the finite-element simulation for liquid-plane contact angle 70° and 165°. The general features of phase diagrams for drop-on-fiber/plane systems in the presence of gravity are similar to those of drop-on-fiber in the absence of gravity. Three regimes, barrel only (bell-like only), clam-shell only (half-bell-like only), and coexistence, can be identified. However, on superhydrophobic surfaces, the regime of clam-shell only is deflated, since the gravitational energy benefits barrel more than clam-shell. On the other hand, on hydrophilic surfaces, the regime of bell-like only prevails owing to the spreading tendency of the drop and the coexistent regime diminishes significantly. For the second part, the equilibrium morphology of a drop in a horizontal tube can provide useful information for two-phase flow in microfluidics devices in which the capillary force dominates. A drop-in-tube system is analogous to a drop-on-fiber one and two conformations are obtained, adhered drop and liquid slug, by the approaches of experiments and Surface Evolver simulations. The adhered drop conformation tends to exist at small volume, whereas the liquid slug conformation is favored at larger volume. Around the transition volume between the two conformations, both morphologies can coexist. The experimental results are consistent with those of simulation outcomes. The morphological phase diagram of the drop-in-tube system is constructed via SE simulations by varying the drop volume and contact angle. Three regimes can be identified through the upper and lower boundary curves: adhered drop only, liquid slug only, and coexistence. Compared to the case with negligible gravity, the adhered drop is more favored than the liquid slug in the presence of gravity. As a result, the coexistence regime expands substantially. For the third part, controlling the droplet equilibrium location and shape on a conical fiber is essential to industrial applications such as dip-pen nanolithography. In this study, the equilibrium conformations of a drop on a vertical, conical fiber has been investigated by the finite element method, Surface Evolver simulations. Similar to the morphology of a drop on a cylinder, two different types (barrel shape and clam-shell shape) can be obtained. In the absence of gravity, the droplet moves upwards (lower curvature) and the total surface energy decays as the drop ascends. Whatever the initial conformation of the drop on a conical fiber is, the rising drop exhibits the clam-shell shape eventually and there is no equilibrium location. However, in the presence of gravity, the drop can stop at the equilibrium location stably. For a given contact angle, the clam-shell shape is generally favored for smaller drops but the barrel shape is dominant for larger drops. In a certain range of drop volume, the coexistence of both barrel and clam-shell shapes is observed. For large enough drops, the falling-off state is seen. For the fourth part, the formation of a liquid bridge between a cone and a plane is related to dip-pen nanolithography. The meniscus shape and rupture process of a liquid meniscus between a cone and a plane are investigated by Surface Evolver, many-body dissipative particle dynamics, and macroscopic experiments. Dependent on the cone geometry, cone-plane separation, and wetting properties of cone and plane, three types of menisci can be observed before rupture and two types of wetting competition outcomes are seen after breakup. It is interesting to find that after rupture, the bulk of the liquid bridge volume is not necessarily retained by the cone which is more wettable. In fact, a sharp hydrophilic cone often loses wetting competition to a hydrophobic plane. To explain our findings, the “apparent” contact angle of the cone is introduced and the behavior of drop-on-cone/plane system is analogous to that of a liquid bridge between two parallel planes based on this concept.