Impalement of fakir drops
By Sung Hoon Kang
Title: Impalement of fakir drops
Reference: M. Reyssat, J. M. Yeomans, and D. Quere, Europhys. Lett. 81, 26006 (2008).
Soft matter keywords
hydrophobicity, fakir state, impalement, surface energy, contact angle
Abstract from the original paper
Water drops deposited on hydrophobic materials decorated with dilute micro-posts generally form pearls. Owing to the hydrophobicity of the material, the drop sits on the top of the posts. However, this “fakir state” is often metastable: if the drop impales inside the texture, its surface energy is lowered. Here we discuss the transition between these two states, considering the drop size as a parameter for inducing this transition: remarkably, it is found that a drop impales when it becomes small, which is interpreted by considering its curvature. This interpretation allows us to propose different recipes for avoiding this detrimental effect.
Soft matter example
In this paper, the authors used hydrophobic surface with regular arrays of micropillars for studying the transition between "fakir state" and "impaled state" as a function of the drop size. They fabricated samples with controlled geometry and coated with a fluropolymer. The contact angle for water on a flat surface was between 100-110° while it was ~160° for a surface with texture.
Figure 1 shows the images of a water drop evaporating on a sample with the micropillars of diameter = 3um, height = 4.8 um and mutual distance of 17 um. During a first stage (first five snapshots), the contact angle remained constant as the drop evaporated at a receding angle of 138±3° and the advancing one of 165±2°. However, when the drop becomes smaller than a critical radius R* of 75 um, the angle became much smaller by about 80° with time scale of 1 ms and it continued decreasing: the liquid was very efficiently pinned and the receding angle gradually vanished to zero even though the material was hydrophobic. The authors argued that this phenomenon could be resulted from an impalement of the drop in the texture and they confirmed their interpretation by examining the trace left on the material after evaporation as shown in Fig 2. As shown in Fig. 2., a circular stain was observed at the bottom state of the solid, where it followed the pillars where pinning happened, indicating the drop sank insdie the texture .
Then, the authors studied the mechanism and the conditions for such a transition. They did geometrical analysis by considering the curvature of the liquid/vapor pockets below the drop. For small pillars (h<<l), the critical radius R*~l2/h becomes large, which indicates that we can build a super-hydrophobic material resisting a pinning transition by reducing the size of the microstructures. Having microstructures on the order of 100 nm, we can have a critical radii of the same order. This might be related to the existence of sub-structures at this scale in nature such as plant surfaces or some mosquito's eyes, which remains dry .
Another way of avoiding impalement of the drop is to make the structure higher while keeping the distance l between posts large enough to maintain a strong hydrophobicity. If the impaled state has lower energy than the fakir state, once the drop touches the bottom surface, it should propagate and this contact can be started by the bending of the interfaces as the drop became smaller. Thus, by having long enough pillars, we can avoid this transition. Figure 3 shows the succesive states of an evaporating drop deposited on a sbustrate of the same pillar density as the Figs. 1 and 2, but with much higher pillars (36.5 um instead of 4.8 um. It was observed that the drop remained at the top of the pillars.
 R. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel and T. A. Witten, Nature 389, 827-829 (1997).
 X. F. Gao, X. Yan, X. Yao, L. Xu, K. Zhang, J. H. Zhang, B. Yang and L. Jiang, Adv. Mater. 19, 2213-2217 (2007).