超疏水表面上冷凝液滴发生弹跳的机制与条件分析

Mechanism and Condition Analysis of Condensed Drop Jumping on Super-Hydrophobic Surfaces

使用液滴合并前后的体积和表面自由能守恒作为两个限制条件,确定了合并液滴的初始形状,即为偏离平衡态的亚稳态液滴,具有缩小其底半径而向平衡态液滴转变的推动力.进而分析了液滴变形过程中的推动力和三相线(TPCL)上的滞后阻力,建立了液滴变形的动态方程并进行了差分求解.如果液滴能够变形至底半径为0mm的状态,则根据该状态下液滴重心上移的速度确定液滴的弹跳高度.不同表面上冷凝液滴合并后的变形行为的计算结果表明,光滑表面上的液滴合并后,液滴只能发生有限的变形,一般都在达到平衡态之前就停止了变形,因此冷凝液滴不会发生弹跳;粗糙表面上的Wenzel态液滴的三相线上的滞后阻力更大,因而液滴更难以变形和弹跳;具有微纳二级结构表面上只润湿微米结构,但不润湿纳米结构的部分Wenzel态液滴能够变形至Cassie态,但没有明显的弹跳;只有在纳米或微纳二级结构表面上的较小Cassie态液滴合并后,液滴易于变形至底半径为0mm的状态并发生弹跳.因此,Cassie态合并液滴处于亚稳态,并且其三相线上的移动阻力很小,是导致冷凝液滴弹跳的关键因素.

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.