Liquid Drops on a Rough Surface

TL;DR

This paper studies how micro-structured rough surfaces influence the equilibrium shape and contact angle of liquid drops, using homogenization theory to quantitatively describe the effects of surface roughness.

Contribution

It introduces a homogenization-based framework to analyze the shape of liquid drops on rough surfaces, extending prior qualitative theories with quantitative results.

Findings

Quantitative description of drop shape on rough surfaces

Analysis of contact angle modifications due to roughness

Application of periodic homogenization theory to wetting phenomena

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 micro-structure 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.