Motion of a single particle partially exposed in a simple shear flow

The motion of particles over rough surfaces in shear flows is a fundamental problem in fluid mechanics, with applications spanning geophysics, material science, and microfluidics. This study extends Goldman et al.'s theoretical framework for a sphere near a flat surface to rough surfaces, incorporating a correction factor dependent on the effective penetration depth of the fluid flow into the rough substrate. The validity of this approach is assessed through three-dimensional lattice Boltzmann simulations coupled with the discrete element method through momentum exchange. Our results confirm that the theoretical predictions closely match the simulations for particle Reynolds numbers up to two, with deviations increasing at higher particle Reynolds numbers due to inertial effects. We further explore the impact of roughness and friction, demonstrating that surface roughness, defined by the gap distance between substrate spheres, significantly alters hydrodynamic interactions. While friction has a minor influence on the translational velocity, it plays a dominant role in the angular velocity, particularly during particle ascent over roughness-induced hills. A broad range of friction coefficients is covered by the simulations, revealing that deviations from the theory increase as frictional effects become more pronounced. Our findings establish a generalized framework for particle motion over rough surfaces, applicable across various surface geometries and flow conditions.