Hydrodynamic density-functional theory for the moving contact-line problem reveals fluid structure and emergence of a spatially distinct pattern

TL;DR

This paper introduces a hydrodynamic density-functional theory model to study nanoscale effects at the moving contact line, revealing fluid layering, distinct regions, and their impact on contact line dynamics.

Contribution

It develops a novel hydrodynamic DDFT approach combining statistical mechanics with fluid dynamics to analyze contact line behavior at the nanoscale.

Findings

Fluid stratification with oscillatory density near the wall.

Emergence of compression and slip regions with temperature.

Compression significantly influences contact line speed at low temperatures.

Abstract

Understanding the nanoscale effects controlling the dynamics of a contact line -- defined as the line formed at the junction of two fluid phases and a solid -- has been a longstanding problem in fluid mechanics pushing experimental and numerical methods to their limits. A major challenge is the multiscale nature of the problem, whereby nanoscale phenomena manifest themselves at the macroscale. To probe the nanoscale, not easily accessible to other methods, we propose a reductionist model that employs elements from statistical mechanics, namely dynamic-density-functional theory (DDFT), in a Navier-Stokes-like equation -- an approach we name hydrodynamic DDFT. The model is applied to an isothermal Lennard-Jones-fluid with no slip on a flat solid substrate. Our computations reveal fluid stratification with an oscillatory density structure close to the wall and the emergence of two distinct regions as the temperature increases: a region of compression on the vapor side of the liquid-vapour interface and an effective slip region of large shear on the liquid side. The compressive region spreads along the fluid interface at a lengthscale that increases faster than the width of the fluid interface with temperature, while the width of the slip region is bound by the oscillatory fluid density structure and is constrained to a few particle diameters from the wall. Both compressive and shear effects may offset contact line friction, while compression in particular has a disproportionately high effect on the speed of advancing contact lines at low temperatures.