# A Hydrodynamic Model of Movement of a Contact Line Over a Curved Wall

## TL;DR

This paper develops a two-dimensional hydrodynamic model for the movement of a contact line over curved surfaces, addressing stress singularities and improving boundary condition prescriptions in two-phase flow simulations.

## Contribution

It extends the classical hydrodynamic solution to curved walls and proposes a method for applying non-singular boundary conditions near moving contact points.

## Key findings

- The model accurately predicts contact line movement over curved surfaces.
- Simulations show improved advection of contact points with the new boundary conditions.
- The approach mitigates stress singularities in numerical simulations.

## Abstract

The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional hydrodynamic model for the velocity field at a contact point moving with constant velocity over a curved wall. The model is a perturbation of the classical Huh and Scriven hydrodynamic solution [11], which is only valid for flow over a flat wall. The purpose of the hydrodynamic model is to investigate the macroscopic behavior of the fluids close to a contact point. We also present an idea for how the hydrodynamic solution could be used to prescribe macroscopic Dirichlet boundary conditions for the velocity in the vicinity of a moving contact point. Simulations demonstrate that the velocity field based on the non-singular boundary conditions is capable of accurately advecting the contact point.