Hydrodynamic Interactions of Spherical Particles in A Fluid Confined by A Rough And No-Slip Wall

TL;DR

This paper develops a theoretical framework to analyze how surface roughness and no-slip boundary conditions affect the hydrodynamic interactions and mobility of spherical particles near a deformed boundary wall.

Contribution

It introduces a model to quantify the effects of sinusoidal boundary deformations on particle mobility and interactions in a viscous fluid.

Findings

Surface roughness can increase a particle's self mobility.

Mobility varies depending on the particle’s position relative to surface features.

Surface deformations influence two-body hydrodynamic interactions.

Abstract

In this article we develop a theoretical framework to study the hydrodynamic interactions in the presence of a non-flat and no-slip boundary. We calculate the influence of a small amplitude and sinusoidal deformations of a boundary wall in the self mobility and the two body hydrodynamic interactions for spherical particles. We show that the surface roughness enhances the self mobility of a sphere in a way that, for motion in front of a local hump of the surface, the mobility strength decreases while it increases for the motion above a local deep of the rough surface. The influence of the surface roughness in the two body hydrodynamic interactions is also analyzed numerically.