A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading

TL;DR

This paper compares various models for contact line motion in thin droplet spreading, analyzing their pressure, stress, and boundary conditions through asymptotic analysis, revealing regimes where models agree.

Contribution

It provides a comprehensive asymptotic comparison of multiple contact line models, highlighting conditions under which they predict similar spreading behaviour.

Findings

All models predict the same quasistatic spreading in certain regimes.

Different microscopic boundary conditions influence contact line dynamics.

Disjoining pressure and slip models show comparable results under specific parameters.

Abstract

The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin two-dimensional droplet on a planar substrate. The models analysed include three disjoining pressure models based on van der Waals interactions, a model introduced for polar fluids, and a liquid-gas diffuse-interface model; Navier-slip and two non-linear slip models are investigated, with three microscopic contact angle boundary conditions imposed (two of these contact angle conditions having a contact line velocity dependence); and the interface formation model is also considered. In certain parameter regimes it is shown that all of the models predict the same quasistatic droplet spreading behaviour.