Random-roughness hydrodynamic boundary conditions

TL;DR

This study uses lattice Boltzmann simulations to investigate how random surface roughness affects hydrodynamic forces during high-speed liquid film drainage, revealing a force reduction not due to slip but due to an effective shift in boundary position.

Contribution

It demonstrates that roughness-induced force reduction aligns with no-slip conditions at an intermediate boundary position, challenging previous slip-based interpretations.

Findings

Hydrodynamic resistance decreases with roughness but not due to slip.

Force matches no-slip boundary conditions at an intermediate boundary.

Boundary shift depends on roughness height and density.

Abstract

We report results of lattice Boltzmann simulations of a high-speed drainage of liquid films squeezed between a smooth sphere and a randomly rough plane. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. However, this force reduction does not represent slippage. The computed force is exactly the same as that between equivalent smooth surfaces obeying no-slip boundary conditions, but located at an intermediate position between peaks and valleys of asperities. The shift in hydrodynamic thickness is shown to depend on the height and density of roughness elements. Our results do not support some previous experimental conclusions on very large and shear-dependent boundary slip for similar systems.