An equilibrium phase diagram of drops at the bottom of a fiber standing on superhydrophobic flat surfaces

Abstract

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 paper, the phase diagrams of drop-on-fiber/plane, that is, the plots of the droplet volume against the liquid–fiber contact angle, are established on the basis of the finite-element simulation for liquid–plane contact angles of 70° and 165°. The general features of the 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.