Towards Accurate Modeling of Moving Contact Lines

TL;DR

This paper develops a multiscale model for moving contact lines that overcomes the stress singularity issue by introducing an intermediate region and boundary conditions, achieving quadratic convergence in simulations.

Contribution

It introduces a novel multiscale approach with an analytical velocity expression to accurately model moving contact lines at the macroscopic level.

Findings

Errors in contact line velocity converge at rate p≈2

The model effectively handles the stress singularity problem

Boundary conditions improve simulation accuracy

Abstract

A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in developing the macroscopic part of an accurate multiscale model for a moving contact line problem in two space dimensions. We assume that a micro model has been used to determine a relation between the contact angle and the contact line velocity. An intermediate region is introduced where an analytical expression for the velocity exists. This expression is used to implement boundary conditions for the moving contact line at a macroscopic scale, along a fictitious boundary located a small distance away from the physical boundary. Model problems where the shape of the interface is constant thought the simulation are introduced. For these problems, experiments show that the errors in the resulting contact line velocities converge with the grid size $h$ at a rate of convergence $p\approx 2$.