Theoretical consideration of wetting on a cylindrical pillar defect: pinning energy and penetrating phenomena.

Wetting on a cylindrical pillar defect is discussed in terms of the free-energy difference ΔG. Wetting is divided into wetting on a flat surface, a pinning effect at the apex of the defect, and wetting on a pillar wall. First, we confirmed that ΔG between before and after ideal wetting on a flat surface can be derived as a function of the contact angle θ in which the free-energy minimum is obtained as the equilibrium contact angle θ(eq) described by Young's and Wenzel's laws. Second, the pinning effect at the apex in the cross section of the pillar defect is discussed in ΔG, where the pinning effect is shown to originate from the energy barrier by an increase in the air-liquid interfacial area of a pinned droplet induced by deformation. Next, the ΔG profiles of wetting on the pillar wall are drawn based on the theory of Carroll (Carroll, B. J. J. Colloid Interface Sci.1976, 57, 488-495) to better understand the ΔG profile during penetration. Differences in the manner of wetting between the wetting state on a flat surface and the pillar wall are reflected in ΔG. Finally, penetration of a droplet into a pillar defect is comprehensively discussed on the basis of wetting on a flat surface and a pillar wall. If we consider a simple manner of penetration, another type of energy barrier resulting from an anomalous deformation of the air-liquid interface of the penetrating droplet can be theoretically suggested. Consequently, two types of energy barrier are found. These energy barriers should play a significant role in the hysteresis of wetting, the liquid-repellent Cassie-Baxter state (CB), and the CB-Wenzel wetting transition on a microtextured surface.