Hydrodynamics of moving contact lines: macroscopic versus microscopic

TL;DR

This paper compares macroscopic and microscopic models of moving contact lines, demonstrating that slight modifications in boundary conditions can reconcile the two approaches and eliminate nonphysical solutions.

Contribution

It shows that a small change in boundary conditions allows macroscopic models to accurately reflect microscopic dynamics in moving contact-line problems.

Findings

Macroscopic models can be regularized with boundary condition adjustments.

Molecular dynamics simulations validate the limits of macroscopic approaches.

Elimination of nonphysical solutions near contact lines.

Abstract

The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as the ones used for macro-droplets? To the greatest degree, this question should be addressed to the moving contact-line problem. The problem is naturally multiscale, where even using a slip boundary condition results in spurious numerical solutions and transcendental stagnation regions in modelling in the vicinity of the contact line. In this publication, it has been demonstrated via the mutual comparison between macroscopic modelling and molecular dynamics simulations that a small, albeit natural, change in the boundary conditions is all that is necessary to completely regularize the problem and eliminate these nonphysical effects. The limits of macroscopic approach applied to the moving contact-line problem have been tested and validated from the first microscopic principles of molecular dynamic simulations.