Hydrodynamic Lubrication of Rough Particles Leads to Friction-like Behavior

Hydrodynamic interactions between particles in near-contact configurations dominate the rheological behavior of concentrated suspensions. We study these interactions between cylindrical and spherical particles in near contact using lubrication theory, focusing on the effects of surface roughness. Numerical solutions find that unexpectedly large pressures are generated when two rough particles slide past each other, leading to hydrodynamic forces and torques that are much greater than for smooth particles. Notably, we find that roughness leads to a purely hydrodynamic coupling between rotation and translation reminiscent of dry solid friction, a feature that is absent for smooth particles. We gain insight into these features by developing an analytic theory that resolves the flow around roughness asperities. The theory finds that the near-contact approach of asperities leads to singular and highly localized pressure distributions that generate not only forces, but also torques on the particle. The theoretically predicted hydrodynamic forces and torques are in excellent quantitative agreement with numerical solutions. For rough spheres, we show that the hydrodynamic resistance to tangential sliding scales with the inverse of the separation distance, as opposed to scaling logarithmically with distance for smooth spheres.