A Computational Multiscale Model for Contact Line Dynamics

TL;DR

This paper introduces a new boundary condition methodology for simulating the dynamics of contact lines between two immiscible fluids, addressing the stress singularity problem and improving numerical accuracy.

Contribution

It combines a contact angle-velocity relation with a phase field model to develop a novel boundary condition for contact line simulations.

Findings

The new boundary condition effectively handles contact line motion.

Numerical results demonstrate improved simulation accuracy.

The approach integrates theoretical and simulation-based relations.

Abstract

The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations challenging, especially when capillary effects are essential for the dynamics of the flow. This paper presents a new boundary methodology, suitable for numerical simulation of flow of two immiscible and incompressible fluids in the presence of moving contact points. The methodology is based on combining a relation between the apparent contact angle and the contact point velocity with the similarity solution for Stokes flow at a planar interface. The relation between angle and velocity can be determined by theoretical arguments, or from simulations using a more detailed model. The approach here uses the phase field model in a micro domain, with physically relevant parameters for molecular diffusion and interface thickness. The methodology is used to formulate a new boundary condition for the velocity. Numerical results illustrate the usefulness.