  Surface roughness becomes relevant if typical length scales of the system are
comparable to the scale of the variations as it is the case in microfluidic
setups. Here, an apparent boundary slip is often detected which can have its
origin in the assumption of perfectly smooth boundaries. We investigate the
problem by means of lattice Boltzmann (LB) simulations and introduce an
``effective no-slip plane'' at an intermediate position between peaks and
valleys of the surface. Our simulations show good agreement with analytical
results for sinusoidal boundaries, but can be extended to arbitrary geometries
and experimentally obtained surface data. We find that the detected apparent
slip is independent of the detailed boundary shape, but only given by the
distribution of surface heights. Further, we show that the slip diverges as the
amplitude of the roughness increases.

Soft Condensed Matter;Fluid Dynamics