Model experimental study of scale invariant wetting behaviors in Cassie-Baxter and Wenzel regimes

In this work, we discuss quantitatively two basic relations describing the wetting behavior of microtopographically patterned substrates. Each of them contains scale invariant topographical parameters that can be easily expressed onto substrates decorated with specifically designed micropillars. The first relation discussed in this paper describes the contact angle hysteresis of water droplets in the Cassie-Baxter regime. It is shown that the energy at the origin of the hysteresis, that has to be overcome for moving the triple line, can be invariantly expressed for hexagonal pillars by varying the pillars width and interpillar distance. Identical contact angle hystereses are thus measured on substrates expressing this scale invariance for pillar widths and interpillar distances ranging from 4 to 128 μm. The second relation we discuss concerns the faceting of droplets spreading on microtopographically patterned substrates. It is shown in this case that the condition for pinning of the triple line can be fulfilled by simultaneously varying the height of the pillars and the interpillar distance, leading to faceted droplets of similar morphologies. The invariance of these two wetting phenomena resulting from the simultaneous and homothetic variation of topographical parameters is demonstrated for a wide range of pattern dimensions. Our results show that either of those two wetting behaviors can be simply achieved by the proper choice of a dimensionless ratio of topographical length scales.