A mathematical model and mesh-free numerical method for contact-line motion in lubrication theory

TL;DR

This paper presents a new mathematical model and mesh-free numerical method for simulating contact-line motion in lubrication theory, effectively resolving singularities and capturing droplet spreading physics including Tanner's Law.

Contribution

The paper introduces a novel mesh-free numerical approach that accurately models contact-line dynamics and handles both complete and partial wetting scenarios.

Findings

Successfully resolves contact-line singularity

Accurately models droplet spreading including Tanner's Law

Provides analytical solutions for partial wetting cases

Abstract

We introduce a mathematical model with a mesh-free numerical method to describe contact-line motion in lubrication theory. We show how the model resolves the singularity at the contact line, and generates smooth profiles for an evolving, spreading droplet. The model describes well the physics of droplet spreading -- including Tanner's Law for the evolution of the contact line. The model can be configured to describe complete wetting or partial wetting, and we explore both cases numerically. In the case of partial wetting, the model also admits analytical solutions for the droplet profile, which we present here.