Hydrodynamic origin of friction between suspended rough particles

Tangential interactions between particles play a central role in suspension rheology. We show that surface roughness significantly enhances the strength of hydrodynamic interactions between closely separated particles in relative sliding motion. Using numerical solutions of the lubrication equation, we show that tangential forces due to sliding motion between rough spheres scale inversely with the separation distance, as opposed to the weaker logarithmic scaling for smooth spheres. A fully analytic theory identifies these features as the consequence of asperity-scale squeeze flows, quantitatively recovering the numerical results. These singular hydrodynamic forces are associated with similarly singular torques. The need to resolve the hydrodynamic singularity couples the particles’ rotation to their translation, and forces them to roll without slip, recovering a kinematic constraint that is central to understanding dense suspension rheology. Despite their purely hydrodynamic origin and occurring without contact, these features resemble several aspects of rolling and sliding contact friction.