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.

We have considered in this work the Wilhelmy plate tensiometer to characterize the wetting properties of two model surface textures: (i) a series of three superhydrophobic micropillared surfaces and (ii) a series of two highly water-repellent surfaces microtextured with a femtosecond laser. The wetting forces obtained on these surfaces with the Wilhelmy plate technique were compared to the contact angles of water droplets measured with the sessile drop technique and to the bouncing behavior of water droplets recorded at a high frame rate. We showed that it is possible with this technique to directly measure triple-line anchoring forces that are not accessible with the commonly used sessile drop technique. In addition, we have demonstrated on the basis of the bouncing drop experiments wetting transitions induced by the specific test conditions associated with the Wilhelmy plate tensiometer for the two series of textured surfaces. Finally, the tensiometer technique is proposed as an alternative test for characterizing the wetting properties of highly liquid-repellent surface, especially under immersion conditions.

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