Variational approach to contact line dynamics for thin films

TL;DR

This paper develops a variational framework for modeling contact line dynamics in thin viscous films, reducing the problem to a thin-film equation and demonstrating its feasibility through numerical simulations of gravity-driven droplets.

Contribution

It introduces a novel variational approach to contact line dynamics in thin films, including model reduction and numerical implementation.

Findings

Successful numerical scheme for 1D contact line problems

Demonstration of gravity-driven droplet simulations

Insights into contact line behavior in thin films

Abstract

This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed and discussed. Feasibility of this modeling approach is shown by constructing a numerical scheme in 1D and by computing numerical solutions for the problem of gravity driven droplets. Some implications of the contact line model are highlighted in this setting.