L.M. Hocking has proposed [“A moving fluid interface on a rough surface,” J. Fluid Mech., 76, 801, (1976)] that contact lines are able to move over solid surfaces because microscopic irregularities in the surface induce flow structures that may be interpreted as “velocity slip” from a macroscopic point of view.
A computational investigation of this hypothesis is easily carried out using FLOW-3D. The test selected consists of a two-dimensional solid surface with a pattern of transverse, regularly spaced, rectangular slots. The slots are 2mm deep and 10mm wide, and spaced to have 10mm wide solid pieces between them. These dimensions are typical of scratches on relatively smooth surfaces. The static contact angle between liquid and solid was chosen to be 60°. Water is the working fluid. The test consisted of placing the rough surface on the bottom of a channel of height 15mm and driving water at an average 30cm/s through the channel. The top of the channel has a free-slip boundary.
Hocking’s assertion that micro-scale disturbances can be interpreted as a kind of velocity slip when looked at from the point of larger scales is supported by the computed velocity field. This is shown graphically in the x-y plot, which gives the computed horizontal velocity distribution in the layer of control volumes immediately above the surface. With further grid refinement, the velocity above the solid portions of the surface would tend to zero, but above the slots the velocity remains non-zero. Averaging this velocity over many roughness slots results in a non-zero horizontal velocity that could be interpreted as an effective slip.