Particle motion nearby rough surfaces

TL;DR

This paper develops an analytical model to understand how rough surfaces influence particle motion in fluids, revealing nonmonotonic velocity behavior and increased displacement variability due to surface roughness effects.

Contribution

The study introduces a novel analytical framework for particle dynamics near rough surfaces, extending beyond traditional flat-wall models.

Findings

Roughness causes nonmonotonic velocity dependence on surface wavelength.

Particles exhibit continuous translation transverse to applied forces.

Displacement variance grows quadratically over time due to roughness-induced sedimentation variability.

Abstract

We study the hydrodynamic coupling between particles and solid, rough boundaries characterized by random surface textures. Using the Lorentz reciprocal theorem, we derive analytical expressions for the grand mobility tensor of a spherical particle and find that roughness-induced velocities vary nonmonotonically with the characteristic wavelength of the surface. In contrast to sedimentation near a planar wall, our theory predicts continuous particle translation transverse and perpendicular to the applied force. Most prominently, this motion manifests itself in a variance of particle displacements that grows quadratically in time along the direction of the force. This increase is rationalized by surface roughness generating particle sedimentation closer to or farther from the surface, which entails a significant variability of settling velocities.