Pinning of a solid--liquid--vapour interface by stripes of obstacles

TL;DR

This paper investigates how striped obstacles can pin a solid-liquid-vapor interface, using a Hamiltonian model, simulations, and mean field theory to estimate pinning conditions and contact line behavior.

Contribution

It introduces a macroscopic Hamiltonian approach, estimates pinning stripe density, and develops a 2D mean field theory for contact line behavior.

Findings

Pinning stripe density estimate matches simulations.

Mean field theory accurately predicts contact line height.

Collective pinning occurs at specific stripe densities.

Abstract

We use a macroscopic Hamiltonian approach to study the pinning of a solid--liquid--vapour contact line on an array of equidistant stripes of obstacles perpendicular to the liquid. We propose an estimate of the density of pinning stripes for which collective pinning of the contact line happens. This estimate is shown to be in good agreement with Langevin equation simulation of the macroscopic Hamiltonian. Finally we introduce a 2--dimensional mean field theory which for small strength of the pinning stripes and for small capillary length gives an excellent description of the averaged height of the contact line.