Liquid Drops on a Rough Surface. Issue 12 (10th October 2018)

• Record Type: Journal Article
• Authors: Feldman, William M.; Kim, Inwon C.
• Is Part Of: Communications on pure and applied mathematics. Volume 71:Issue 12(2018:Dec.)
• Page Start: 2429
• Page End: 2499
• Publication Date: 2018-10-10
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21793
• Languages: English
• ISSNs: 0010-3640

Abstract

Abstract: We consider a liquid drop sitting on a rough solid surface at equilibrium, a volume‐constrained minimizer of the total interfacial energy. The large‐scale shape of such a drop strongly depends on the microstructure of the solid surface. Surface roughness enhances hydrophilicity and hydrophobicity properties of the surface, altering the equilibrium contact angle between the drop and the surface. Our goal is to understand the shape of the drop with fixed small‐scale roughness. To achieve this, we develop a quantitative description of the drop and its contact line in the context of periodic homogenization theory, building on the qualitative theory of Alberti and DeSimone. © 2018 Wiley Periodicals, Inc.