Hydrodynamic interactions between rough surfaces

In the study of particle suspensions, away from the jamming threshold, it is common to interpret the effective viscosity in terms of the volume fraction, neglecting roughness effects. Here we show that particle roughness can significantly modify viscous dissipation in configurations that represent fixed volume-fraction conditions. We derive a hydrodynamic model for the forced interaction of a two-dimensional particle, where roughness is represented by a periodic corrugation, with an adjacent wall. In particular, we address the limit of small nominal particle-wall separation, with the corrugation amplitude comparable with said separation. A lubrication analysis provides the rectilinear and angular velocities of the particle as functions of the instantaneous angular configuration. The particle may either translate while rotating or become "locked" in a specific phase and translate without rotation. The time-averaged rectilinear velocity, which is the object of interest, is a purely geometric quantity, obtained without the need to address any time dynamics.