Friction-like Behavior in the Hydrodynamic Lubrication of Rough Particles

Hydrodynamic interactions between particles in near-contact configurations dominate the mechanics of concentrated suspensions. We study these interactions numerically and theoretically by modeling rough spheres in near-contact using Reynolds lubrication theory. Using numerical solutions, we find that the horizontal force acting on the spheres due to translational motion is much larger than for smooth spheres. We develop an analytic framework for the near-contact regime by modeling the local interaction between individual asperities on each particle. This local problem identifies forces associated with normal motion between asperities that arise from horizontal translation of the particles. The force scales with the inverse of separation distance, much more strongly than the logarithmic dependance expected for smooth spheres, and suggests the problem is strongly singular when the particles come close to contact. Additionally, we find that local stresses act similarly to a point force at the minimum separation point, which yields a corresponding torque on the particles. The theoretical force and torque are in excellent agreement with the numerical results, and the analytic formulation shows that they are strongly coupled. This coupling is not seen with smooth spheres separated by fluid, but is very similar to the results of dry frictional contacts.