Particle motion nearby rough surfaces

Interactions between particles and boundaries are ubiquitous in nature and play a pivotal role in microfluidic applications. Here, we study the hydrodynamic couplings between particles and solid, rough boundaries that are characterized by periodic and random surface shapes. Using the Lorentz reciprocal theorem, we derive analytical expressions for the mobility tensor of a spherical particle and investigate its gravity driven sedimentation near a random rough wall. Our theory and experiments show that the particle exhibits translation perpendicular to the gravitation force, in striking contrast to its motion near a planar wall, and follows the surface shape in close proximity to the boundary. Overall, our results should lay the foundation to study microswimmer motion close to random, heterogeneous boundaries.