title: Wetting theory for small droplets on textured solid surfaces.
abstract: Conventional wetting theories on rough surfaces with Wenzel, Cassie-Baxter, and Penetrate modes suggest the possibility of tuning the contact angle by adjusting the surface texture. Despite decades of intensive study, there are still many experimental results that are not well understood because conventional wetting theory, which assumes an infinite droplet size, has been used to explain measurements of finite-sized droplets. Here, we suggest a wetting theory applicable to a wide range of droplet size for the three wetting modes by analyzing the free energy landscape with many local minima originated from the finite size. We find that the conventional theory predicts the contact angle at the global minimum if the droplet size is about 40 times or larger than the characteristic scale of the surface roughness, regardless of wetting modes. Furthermore, we obtain the energy barrier of pinning which can induce the contact angle hysteresis as a function of geometric factors. We validate our theory against experimental results on an anisotropic rough surface. In addition, we discuss the wetting on non-uniformly rough surfaces. Our findings clarify the extent to which the conventional wetting theory is valid and expand the physical understanding of wetting phenomena of small liquid drops on rough surfaces.
authors.affiliation: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea.
authors.forename: Donggyu
authors.initials: D
authors.lastname: Kim
authors.affiliation: Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental, and Mechanical Engineering, University of Trento, Trento, Italy.|Center for Materials and Microsystems, Fondazione Bruno Kessler, Trento, Italy.|School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London, United Kingdom.
authors.forename: Nicola M
authors.initials: NM
authors.lastname: Pugno
authors.affiliation: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea.
authors.forename: Seunghwa
authors.initials: S
authors.lastname: Ryu