Stokes resistance of a cylinder near a slippery wall

Motivated by observations of large effective slip over nanostructured surfaces, we analyze here the hydrodynamic resistance to the rigid-body motion of a cylinder near a slippery wall - perhaps the simplest anisotropic configuration which nonetheless exhibits a nontrivial translation-rotation coupling. Focusing upon the lubrication limit, the properly scaled resistance-matrix coefficients depend only upon the ratio of the slip length to the cylinder-wall clearance. A distinct feature of a lubrication analysis with slippage is that the pressure field cannot be determined in closed form; nonetheless, the dependence upon the slip length of the resistance coefficients is explicitly obtained. The limit of large slip length, where the wall behaves as a free surface, is elucidated. Considering the companion problem of a slippery cylinder, we observe a symmetry relating the two problems.