  We explore hydrodynamic interactions between microswimmers and corrugated, or
rough, surfaces, as found often in biological systems and microfluidic devices.
Using the Lorentz reciprocal theorem for viscous flows we derive exact
expressions for the roughness-induced velocities up to first order in the
surface-height fluctuations and provide solutions for the translational and
angular velocities valid for arbitrary surface shapes. We apply our theoretical
predictions to elucidate the impact of a periodic, wavy surface on the
velocities of microswimmers modeled in terms of a superposition of Stokes
singularities. Our findings, valid in the framework of a far-field analysis,
show that the roughness-induced velocities vary non-monotonically with the
wavelength of the surface. For wavelengths comparable to the swimmer-surface
distance a pusher can experience a repulsive contribution due to the reflection
of flow fields at the edge of a surface cavity, which decreases the overall
attraction to the wall.

Soft Condensed Matter;Fluid Dynamics