Abstract: The initial shape of a coalesced drop is determined by the conservation of drop volume and the surface free energy before and after two or more condensed drops merge. The coalesced drop is in a metastable state with a driving force to reduce its base radius toward equilibrium state. This driving force and resistance on the three-phase contact line (TPCL) are analyzed during drop transformation. A dynamic equation describing the shape conversion of the drop is proposed and solved. The jumping height of a merged drop is determined by the speed at which the center of gravity moves up when the base radius of the drop reduces to 0 mm on a super-hydrophobic surface. Calculations show that a coalesced drop on a flat surface can transform its shape only in a limited fashion. It will not jump since its transformation stops before it reaches equilibrium. A wetted drop on a rough surface is even more difficult to transform and jump because of the greater TPCL resistance. However, on a two-tier surface, a partially wetted drop impaling only the micro-scale roughness exhibits a shape transition to a Cassie state upon coalescence, but without obvious jumping. Only after the coalescence of two or more small Cassie-state drops on a textured surface, can the merged composite drop easily transform to a 0 mm base radius and jump. It can be concluded that key factors governing condensed-drop jumping are the merged composite drop in a metastable state and a small TPCL resistance on nano or micro-nano two-tier surfaces.

Key words: Super-hydrophobic surface, Nano, Micro-nano two-tier texture, Condensation, Drop transformation, Jumping, Mechanism, Model