  We report measurements of the hydrodynamic drag force acting on a smooth
sphere falling down under gravity to a plane decorated with microscopic
periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil)
invades the surface texture being in the Wenzel state. A significant decrease
in the hydrodynamic resistance force as compared with that predicted for two
smooth surfaces is observed. To quantify the effect of roughness we use the
effective no-slip boundary condition, which is applied at the imaginary smooth
homogeneous isotropic surface located at an intermediate position between top
and bottom of grooves. Such an effective condition fully characterizes the
force reduction measured with the real surface, and the location of this
effective plane is related to geometric parameters of the texture by a simple
analytical formula.
