Particle motion nearby and entering rough surfaces

Particle dynamics on rough surfaces is a challenging task in fluid mechanics with applications including microfluidics, reactive substrates, and geophysics. We investigate how substrate geometry and fluid forces jointly determine the onset of particle motion using a fully determined torque balance, and we extend this framework to predict the average velocity of particles traveling over rough surfaces. Three-dimensional lattice Boltzmann simulations coupled with the discrete element method through momentum exchange provide the basis for our analytical description, which is validated against experimental data. Our results show that lift forces arising from fluid inertia govern the evolution of the critical conditions for incipient motion as the system transitions from low to finite Reynolds numbers. Furthermore, the relative importance of fluid drag force and gravity critically influences the particle’s average traveling velocity. The framework provides a physically grounded, fully determined description of incipient particle motion, applicable to engineered systems, biological cells, and fluidized beds, offering predictive insight for microfluidic design, sediment transport, and particulate flow control.